diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/comparison.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/comparison.mat new file mode 100644 index 0000000..5007b27 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/comparison.mat differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/data.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/data.mat new file mode 100644 index 0000000..a86eb34 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Data/data.mat differ diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/PearsonIcelandModels.mlx b/Pearson_and_Loveless_Tectonics_2021_Inputs/PearsonIcelandModels.mlx new file mode 100644 index 0000000..abf1b32 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/PearsonIcelandModels.mlx differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/GPSCoordinates.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/GPSCoordinates.m new file mode 100644 index 0000000..6db7ced --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/GPSCoordinates.m @@ -0,0 +1,89 @@ +function [anglesbetween, misfit, results, rakes] = GPSCoordinates(faults, faultsHotspot, d, bc, azimuth, hotspotContribution, GPSData) +%GPScomparison evaluates model results in comparison with strain axes +%derived from GPS velocity data +%Inputs: +% faults: meshed fault map faultsHotspot: meshed fault map and spherical mesh hotspot +% d: nelx3 array of boundary conditions & bc: NEL-by-3 array specifying type +% of boundary conditions, see tribemx for specifications +% azimuth: angle of uniaxial remote stress, defined clockwise from due east +% hotspot Contribution: amount of element-normal dislocation on the hotspot +% in mm/yr +% GPSData: comparison data, including: stationsTotal (UTM coordinates of GPS stations, column 1: +% Eastings, column 2: Northings), GPS (trends of axes of maximum and minimum extensional strain calculated +% directly from GPS velocities, 1:max, 2:min), and stationsList(UTM coordinates, broken down by region in order: +% NW, CW, SW, NC, CC, SC, NE, CE, SE) + + +%Outputs: +%anglesbetween: angular misfits between axis of maximum extension for each +%comparison data point +%misfit: overall average misfit for model +%results: axes of maximum extension for each observation coordinate defined for +%the model +%rakes: overall rake calculated for each fault from the model + +%set up grid of observation points at each GPS station location +stationsTotal=GPSData{1}; +GPS=GPSData{2}; +stationsList=GPSData{3}; +xyutm=GPSData{4}; +obs.x=stationsTotal(:, 1); obs.y=stationsTotal(:, 2); obs.z=0*obs.x; +obs.v="d"; +obs.rc=[xyutm(1,1), xyutm(1,2), 0]; %reference coordinates, close to the plate boundary + +%run tribemx to calculate displacements at each station +d(sum(faults.nEl)+1:end, 3)=hotspotContribution; +[REMSrotate, ~]=calculateREMS(azimuth); +[slip, trac, out] = tribemx(faultsHotspot, d, bc, REMSrotate, obs); +disp2=[out.u(:,1), out.u(:,2)]; +faultsHotspot=rake(faultsHotspot, slip); +rakes=faultsHotspot.sliprake; + + +start=0; type=1; plotpar=0; +array=zeros(9, 1); arrayAlt=zeros(9, 1); misfitAlt=zeros(9, 1); +misfit=zeros(9, 1); anglesbetween=zeros(9,1); results=zeros(9,1); +for k=1:9 %run for each of the 9 regions + %calculate strains based on displacement + stationsNew=stationsList{1, k}; + nStations=length(stationsNew); + par = [500e3, nStations, 250e3]; + [~,~,~,pstrains,~] = GridStrain(stationsNew,disp2(start+1:start+length(stationsNew), :),type,par,plotpar); + start=start+length(stationsNew); + %rename + e1mag = pstrains(1, 1, :); e1mag = e1mag(:); + e1tre = pstrains(1, 2, :); e1tre = e1tre(:); + e1plu = pstrains(1, 3, :); e1plu = e1plu(:); + e2mag = pstrains(2, 1, :); e2mag = e2mag(:); + e2tre = pstrains(2, 2, :); e2tre = e2tre(:); + e2plu = pstrains(2, 3, :); e2plu = e2plu(:); + e3mag = pstrains(3, 1, :); e3mag = e3mag(:); + e3tre = pstrains(3, 2, :); e3tre = e3tre(:); + e3plu = pstrains(3, 3, :); e3plu = e3plu(:); + + %permutations + e1horizmag = e1mag; % Default assumption is that e1 horizontal is e1 + e1horiztre = e1tre; + e1horizplu = e1plu; + vert_e1 = e1plu == pi/2; % Logical index of any e1 plunges that are vertical + e1horizmag(vert_e1) = e2mag(vert_e1); % Reassign those values to be e2 values + e1horiztre(vert_e1) = e2tre(vert_e1); + e1horizplu(vert_e1) = e2plu(vert_e1); + e3horizmag = e3mag; % Default assumption is that e3 horizontal is e3 + e3horiztre = e3tre; + e3horizplu = e3plu; + vert_e3 = e3plu == pi/2; % Logical index of any e3 plunges that are vertical + e3horizmag(vert_e3) = e2mag(vert_e3); % Reassign those values to be e2 values + e3horiztre(vert_e3) = e2tre(vert_e3); + e3horizplu(vert_e3) = e2plu(vert_e3); + array(k, 1)=rad2deg(e1horiztre); + arrayAlt(k, 1)=mod(rad2deg(e1horiztre)+180, 360); + misfit(k, 1)=mod(abs(array(k, 1)-GPS(k, 1)), 180); + misfitAlt(k, 1)=mod(abs(arrayAlt(k, 1)-GPS(k, 1)), 180); + anglesbetween(k, 1)=min(misfit(k,1), misfitAlt(k,1)); + results(k,1)=array(k,1); +end +results(:,2)=zeros(9,1); +misfit=mean(anglesbetween); +end + diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/calculateREMS.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/calculateREMS.m new file mode 100644 index 0000000..1616077 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/calculateREMS.m @@ -0,0 +1,11 @@ +function[REMS, remsinitial]=calculateREMS(alpha) +%calculate uniaxial remote stress tensor at a given azimuth, given as an +%angle counterclockwise from due East +rotation=zeros(2,2); +rotation(1,1)=cosd(alpha); rotation(2,2)=cosd(alpha); +rotation(2,1)=sind(alpha); rotation(1,2)=-sind(alpha); +a=[6e6 0; 0 0]; +remsinitial=rotation'*a*rotation; +REMS=zeros(1,6); +REMS(1)=remsinitial(1,1); REMS(2)=remsinitial(2,2); REMS(4)=remsinitial(1,2); +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/gmshfaults_Windows.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/gmshfaults_Windows.m new file mode 100644 index 0000000..2f52c9e --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/gmshfaults_Windows.m @@ -0,0 +1,53 @@ +function allstring = gmshfaults_Windows(topdir, botdir, sz, path) +% gmshfaults Meshes faults in 3D using Gmsh. +% gmshfaults(BOTDIR, ELSIZE) meshes all faults whose bottom coordinates +% are contained in text files within the folder BOTDIR, using the +% element size specified using ELSIZE. Geometry (.geo) and mesh (.msh) +% files are saved to the bottom coordinate directory. +% +% ALL = gmshfaults(...) returns a string to the command line that can be +% used to read all faults in using ReadPatches.m, i.e. +% >> p = ReadPatches(ALL); +% +% + +% Hard code full path to top coordinates directory here +%topdir = ['~' filesep, 'Desktop', filesep,'chile', filesep,'Manual_Faultloc_All', filesep,'Manual_Faultloc_Originals', filesep,'Manual_Faultloc_16km']; + +% List all bottom coordinate files +files = dir([botdir filesep '*.txt']); + +for i = 1:size(files, 1) + % Read bottom coordinates + botcoords = load([botdir filesep files(i).name]); + % Get number of coordinates + nc = size(botcoords, 1); + % Read top coordinates + topcoords = load([topdir filesep files(i).name]); + % Write the Gmsh geometry file + geofile = [botdir filesep files(i).name(1:end-4) '.geo']; + fid = fopen(geofile, 'w'); + fprintf(fid, 'charl = %g;\n', sz); + fprintf(fid, 'Point(%g) = {%g, %g, %g, charl};\n', [1:2*nc; [topcoords(:, 1); flipud(botcoords(:, 1))]'; [topcoords(:, 2); flipud(botcoords(:, 2))]'; [topcoords(:, 3); flipud(botcoords(:, 3))]']); + fprintf(fid, 'CatmullRom(%g) = {%g:%g};\n', [1:2; [1 nc+1; nc 2*nc]]); + fprintf(fid, 'CatmullRom(%g) = {%g,%g};\n', [3:4; [nc 2*nc; nc+1 1]]); + fprintf(fid, 'Line Loop(1) = {1, 3, 2, 4};\nRuled Surface(1) = {1};\n'); + fclose(fid); + fid = fopen('infile.txt','rt') ; + + % Mesh using Gmsh (default) + % system(sprintf('/Applications/Gmsh/Gmsh.app/Contents/MacOS/gmsh -2 %s -o %s.msh -v 0 > junk', geofile, geofile(1:end-4))); + % Mesh using Gmsh (Linux) +% system(sprintf('gmsh -2 %s -o %s.msh -v 0 > junk', geofile, geofile(1:end-4))); + % Mesh using Gmsh (Windows) + system(sprintf(strcat(path,' -2 %s -o %s.msh -v 0 > junk'), geofile, geofile(1:end-4))); + +end + +% Make a space-separated string of all .msh files +alldir = dir([botdir '/*.msh']); +xlsfiles={alldir.name}; +[~,idx]=natsort(xlsfiles); +alldir=alldir(idx); +allstring = sprintf('%s ', alldir.name); +allstring = allstring(1:end-1); % Remove trailing space \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/makeStereonet.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/makeStereonet.m new file mode 100644 index 0000000..e8eb2e9 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/makeStereonet.m @@ -0,0 +1,30 @@ +function [] = makeStereonet(results, type) +%makeStereonet plots an equal area stereonet, plotting axes on top +figure +Stereonet(0,90*pi/180,10*pi/180,1); +hold on +results=deg2rad(results); +for i=1:length(results) + %Plot sigma1/P axis/maximum extension (black, filled circle) + [xp,yp] = StCoordLine(results(i,1),results(i,2),1); + h2=plot(xp,yp,'ko','MarkerFaceColor','k'); + %Plot T axis (red circle) + if size(results, 2)==4 + [xp,yp] = StCoordLine(results(i,3),results(i,4),1); + h3=plot(xp,yp,'ro','MarkerFaceColor','r'); + elseif size(results, 2)==6 + [xp,yp] = StCoordLine(results(i,3),results(i,4),1); + h3=plot(xp,yp,'bo','MarkerFaceColor','b'); + [xp,yp] = StCoordLine(results(i,5),results(i,6),1); + h4=plot(xp,yp,'ro','MarkerFaceColor','r'); + end +end +legend('Location','northwest'); +if type==0 || type==2 + legend([h2 h3],{'P', 'T'}); +elseif type==1 || type==3 + legend([h2 h3 h4],{'σ1','σ2', 'σ3'}); +else + legend(h2,{'Extension'}); +end +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/meshFaults.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/meshFaults.m new file mode 100644 index 0000000..4c8a685 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/meshFaults.m @@ -0,0 +1,15 @@ +function [faults, faultsHotspot] = meshFaults(filename, hotspot, dips, path) +%meshFaults takes in fault mesh and spherical hotspot mesh and outputs +%patch for running in tribemx +faults=load(filename); +coords=utmconv(faults(:,[1 2]), 0); +faults=[coords, faults(:,3)]; +save ('faultsutm.txt', 'faults', '-ascii') +maketopbotcoords('faultsutm.txt', 10e3); +rotatefaultcoords_dir('faultsutm_botcoords', dips); +addpath(strcat(erase(filename, '.txt'), 'utm_botcoords'), strcat(erase(filename, '.txt'), 'utm_botcoords_truedip'), strcat(erase(filename, '.txt'), 'utm_topcoords')); +faults=gmshfaults_Windows('faultsutm_topcoords', 'faultsutm_botcoords_truedip', 7500, path); +faults = ReadPatches(faults); +faults = PatchCoordsx(faults); +faultsHotspot=patchcat(faults, hotspot); +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/momentTensorsCoordinates.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/momentTensorsCoordinates.m new file mode 100644 index 0000000..00b9420 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/momentTensorsCoordinates.m @@ -0,0 +1,208 @@ +function [momAxes, degreeOfMisfit, anglesbetween, rakes]= momentTensorsCoordinates( faults, faultsHotspot, d, bc, alpha, momentTensorGrid) +%momentTensorsCoordinates solves for angular misfit with comparison moment tensor axes +%defined at a series of observation coordinates + +%Inputs: +% faults: meshed fault map faultsHotspot: meshed fault map and spherical mesh hotspot +% d: nelx3 array of boundary conditions & bc: NEL-by-3 array specifying type +% of boundary conditions, see tribemx for specifications +% alpha: angle of uniaxial remote stress, defined clockwise from due east +% momentTensorGrid: comparison data: longitude/latitude (columns 1-2), +% depth (column 3), pressure axes (columns 4:5), tension axes (columns 6:7, +% moment magnitude (column 8) + + +%Outputs: +%momAxes: moment tensor axes for each observation coordinate defined for +%the model +%degreeOfMisfit: average overall angular misfit +%anglesbetween: angular misfits between pressure and tension axes for each +%comparison data point +%rakes: overall rake calculated for each fault from the model + + +%calculate starting inputs +rotation=zeros(2,2); +rotation(1,1)=cosd(alpha); +rotation(2,2)=cosd(alpha); +rotation(2,1)=sind(alpha); +rotation(1,2)=-sind(alpha); +a=[6e6 0; 0 0]; +remsinitial=rotation'*a*rotation; +REMS=zeros(1,6); +REMS(1)=remsinitial(1,1); +REMS(2)=remsinitial(2,2); +REMS(4)=-remsinitial(1,2); +ends=cumsum(faults.nEl); begs=[1; ends(1:end-1)+1]; +momComparison=momentTensorGrid(:,4:7); + +%make grid of observation coodinates +momGrid=[utmconv(momentTensorGrid(:, 1:2), 0, '27W'), momentTensorGrid(:,3)]; +obs.x=momGrid(:,1); obs.y=momGrid(:,2); +obs.z=momGrid(:,3)*-1000; +obs.v = 'e'; +[slip, trac, out] = tribemx(faultsHotspot, d, bc, REMS, obs); +faultsHotspot=rake(faultsHotspot, slip); +rakes=faultsHotspot.sliprake; +%calculate moment tensor axes +maxes=zeros(length(obs.x), 6); paxes2=[]; magnitudes=[]; +for i=1:length(obs.x) + maxes(i, :)=-out.e(i, 1:6); + paxes = PrincipalStress([maxes(i, 1), maxes(i, 4), maxes(i, 5); maxes(i, 4), maxes(i, 2), maxes(i, 6); maxes(i, 5), maxes(i, 6), maxes(i, 3)], pi/2, 0, pi/2); + paxes2=[paxes2; paxes(:, 2:3)]; + magnitudes=[magnitudes; paxes(:, 1)]; +end + +%adjust formatting for plunges (must be positive in order to come out +%correctly), trends must then be switched by 180' to remain consistent +%with which side of plunge is being considered +momAxes=[]; +for j=1:3 + k=paxes2(j:3:end, :); %take either P-axis, B-axis, or T-axis + for i=1:length(k) + if k(i, 2)<0 + k(i, 2)=-k(i, 2); + if k(i, 1)0 + angles=anglesbetween(i, :); + if length(nonzeros(logical(angles<35)))==1 + count=count+1; + end + if length(nonzeros(logical(angles<35)))==2 + count2=count2+1; + end + end +end +fit1=count; +fitBoth=count2; + +%degree of misfit as the average angle between Ps and Ts for the two vectors +anglesbetween2=(anglesbetween(:,1)+anglesbetween(:,2))/2; +for i=1:length(momComparison) + if momComparison(i, 1)~=0 + count(i,1)=anglesbetween2(i,1)*momentTensorGrid(i,8)/sum(momentTensorGrid(:,8)); + end +end +degreeOfMisfit=sum(count); +end + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/momentTensorsFaults.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/momentTensorsFaults.m new file mode 100644 index 0000000..83d1977 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/momentTensorsFaults.m @@ -0,0 +1,225 @@ +function [ fitBoth, fit1, degreeOfMisfit, anglebetweenPnew, anglebetweenTnew, pressure, tension] = momentTensorsFaults( faults, faultsHotspot, d, bc, alpha, toCompareP, toCompareT, G, varargin) +%momentTensorsFaults solves for angular misfit with comparison moment tensor axes +%defined at a series of faults + +%Inputs: +% faults: meshed fault map faultsHotspot: meshed fault map and spherical mesh hotspot +% d: nelx3 array of boundary conditions & bc: NEL-by-3 array specifying type +% of boundary conditions, see tribemx for specifications +% alpha: angle of uniaxial remote stress, defined clockwise from due east +% G: pre-calculated Green's functions, derived from tribemx +% toCompareP/toCompareT: pressure and tension axes, respectively, from +% comparison data +% varargin: + +%Outputs: +%fitBoth/fit1: the number of regions in which both moment tensor axes are fit well/one is fit well +%degreeOfMisfit: average overall angular misfit +%anglebetweenPnew/anglebetweenTnew: angular misfits between pressure and tension axes for each +%comparison data point +%pressure/tension: model output of pressure and tension axes + + +%run slip, rake, and slip magnitude calculations +[REMSrotate, ~]=calculateREMS(alpha); +numvarargs=length(varargin); %slip is pre-calculated when running for a gradient of remote stress +if numvarargs==1 + slip=varargin; +else + [slip, ~] = tribemx(faultsHotspot, d, bc, REMSrotate, G); +end +faultsHotspot=rake(faultsHotspot, slip); +rakes=faultsHotspot.sliprake(1:size(faults.v)); +dips=faultsHotspot.dip(1:size(faults.v)); +strikes=faultsHotspot.strike(1:size(faults.v)); +strikesAndDips=[deg2rad(strikes), deg2rad(dips)]; +slipmag=zeros(sum(faults.nEl), 1); +for i=1:sum(faults.nEl) + slipmag(i)=sqrt(slip(i, 1)^2+slip(i, 2)^2+slip(i, 3)^2); +end + + +%convert rakes on each element to plunges and trends +[trends, plunges]=raketoTrendPlunge(strikes, dips, rakes); + +%run PTAxes to determine trend and plunge of +%pressure and tension for each element, then adjust for multiple faults in +%a single region +ends=cumsum(faults.nEl); +begs=[1; ends(1:length(ends)-1)+1]; +pressures=zeros(length(ends), 2); +tensions=zeros(length(ends), 2); + +for i=1:length(ends) + [pressures(i, :), tensions(i, :)]=MomTens(strikesAndDips(begs(i):ends(i), 1:2), [deg2rad(trends(begs(i):ends(i))), deg2rad(plunges(begs(i):ends(i)))], slipmag(begs(i):ends(i))); +end +%adjust for regions with multiple faults +numbers=[25, 26, 0, 0; 27, 28, 0, 0; 29, 30, 0, 0; 5, 34, 35, 37]; %defined numbers of faults where multiple are in a single region +for i=1:size(numbers, 1) + [pressures, tensions]=multipleFaults(pressures, tensions, begs, ends, strikesAndDips, trends, plunges, slipmag, nonzeros(numbers(i, :)).'); +end + + +%adjust formatting for plunges (must be positive in order to come out +%correctly), trends must then be switched by 180' to remain consistent +%with which side of plunge is being considered +for i=1:length(pressures) + if pressures(i, 2)<0 + if pressures(i, 1)0 + angles=anglesbetween(i, :); + if length(nonzeros(logical(angles<35)))==1 + count=count+1; + end + if length(nonzeros(logical(angles<35)))==2 + count2=count2+1; + end + end +end +fit1=count; +fitBoth=count2; + +%subtract overcount due to multiple faults representing one region +numbers=[25, 26, 0, 0; 27, 28, 0, 0; 29, 30, 0, 0; 5, 34, 35, 37]; %defined numbers of faults where multiple are in a single region +for i=1:size(numbers, 1) + [fitBoth, fit1]=overcount(nonzeros(numbers(i, :)).', anglebetweenPnew, anglebetweenTnew, fitBoth, fit1); +end + + +%degree of misfit as the average angle between Ps and Ts for the two vectors +count=0; +count2=0; +for i=1:length(ends) + if toCompareP(i, 1)~=0 + count=count+(anglebetweenPnew(i, 1)+anglebetweenTnew(i, 1)); + count2=count2+2; + end +end +degreeOfMisfit=count/(count2); +end + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/multipleFaults.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/multipleFaults.m new file mode 100644 index 0000000..1fbd159 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/multipleFaults.m @@ -0,0 +1,13 @@ +function [pressures, tensions]=multipleFaults(pressures, tensions, begs, ends, strikesAndDips, trends, plunges, slipmag, faultNumbers) +%calculate pressure and tension axes for region containing multiple faults + +total=[]; +for i=faultNumbers + total=[total, begs(i):ends(i)]; +end +[pressures(faultNumbers(1), :), tensions(faultNumbers(1), :)]=MomTens(strikesAndDips(total, 1:2), [deg2rad(trends(total)), deg2rad(plunges(total))], slipmag(total)); + +for i=faultNumbers(2:end) + pressures(i, :)=pressures(faultNumbers(1), :); + tensions(i, :)=tensions(faultNumbers(1), :); +end diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/natsort.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/natsort.m new file mode 100644 index 0000000..74f12e3 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/natsort.m @@ -0,0 +1,331 @@ +function [X,ndx,dbg] = natsort(X,rgx,varargin) +% Alphanumeric / Natural-Order sort the strings in a cell array of strings (1xN char). +% +% (c) 2012-2019 Stephen Cobeldick +% +% Alphanumeric sort a cell array of strings: sorts by character order and +% also by the values of any number substrings. Default: match all integer +% number substrings and perform a case-insensitive ascending sort. +% +%%% Example: +% >> X = {'x2', 'x10', 'x1'}; +% >> sort(X) +% ans = 'x1' 'x10' 'x2' +% >> natsort(X) +% ans = 'x1' 'x2' 'x10' +% +%%% Syntax: +% Y = natsort(X) +% Y = natsort(X,rgx) +% Y = natsort(X,rgx,) +% [Y,ndx,dbg] = natsort(X,...) +% +% To sort filenames or filepaths use NATSORTFILES (FEX 47434). +% To sort the rows of a cell array of strings use NATSORTROWS (FEX 47433). +% +%% Number Substrings %% +% +% By default consecutive digit characters are interpreted as an integer. +% Specifying the optional regular expression pattern allows the numbers to +% include a +/- sign, decimal digits, exponent E-notation, quantifiers, +% or look-around matching. For information on defining regular expressions: +% http://www.mathworks.com/help/matlab/matlab_prog/regular-expressions.html +% +% The number substrings are parsed by SSCANF into numeric values, using +% either the *default format '%f' or the user-supplied format specifier. +% +% This table shows examples of regular expression patterns for some common +% notations and ways of writing numbers, with suitable SSCANF formats: +% +% Regular | Number Substring | Number Substring | SSCANF +% Expression: | Match Examples: | Match Description: | Format Specifier: +% ==============|==================|===============================|================== +% * \d+ | 0, 123, 4, 56789 | unsigned integer | %f %i %u %lu +% --------------|------------------|-------------------------------|------------------ +% [-+]?\d+ | +1, 23, -45, 678 | integer with optional +/- sign| %f %i %d %ld +% --------------|------------------|-------------------------------|------------------ +% \d+\.?\d* | 012, 3.45, 678.9 | integer or decimal | %f +% (\d+|Inf|NaN) | 123, 4, NaN, Inf | integer, Inf, or NaN | %f +% \d+\.\d+e\d+ | 0.123e4, 5.67e08 | exponential notation | %f +% --------------|------------------|-------------------------------|------------------ +% 0[0-7]+ | 012, 03456, 0700 | octal notation & prefix | %o %i +% [0-7]+ | 12, 3456, 700 | octal notation | %o +% --------------|------------------|-------------------------------|------------------ +% 0X[0-9A-F]+ | 0X0, 0X3E7, 0XFF | hexadecimal notation & prefix | %x %i +% [0-9A-F]+ | 0, 3E7, FF | hexadecimal notation | %x +% --------------|------------------|-------------------------------|------------------ +% 0B[01]+ | 0B1, 0B101, 0B10 | binary notation & prefix | %b (not SSCANF) +% [01]+ | 1, 101, 10 | binary notation | %b (not SSCANF) +% --------------|------------------|-------------------------------|------------------ +% +%% Debugging Output Array %% +% +% The third output is a cell array , to check if the numbers have +% been matched by the regular expression and converted to numeric +% by the SSCANF format. The rows of are linearly indexed from , +% even columns contain numbers, odd columns contain split substrings: +% +% >> [~,~,dbg] = natsort(X) +% dbg = +% 'x' [ 2] +% 'x' [10] +% 'x' [ 1] +% +%% Examples %% +% +%%% Multiple integers (e.g. release version numbers): +% >> A = {'v10.6', 'v9.10', 'v9.5', 'v10.10', 'v9.10.20', 'v9.10.8'}; +% >> sort(A) +% ans = 'v10.10' 'v10.6' 'v9.10' 'v9.10.20' 'v9.10.8' 'v9.5' +% >> natsort(A) +% ans = 'v9.5' 'v9.10' 'v9.10.8' 'v9.10.20' 'v10.6' 'v10.10' +% +%%% Integer, decimal, NaN, or Inf numbers, possibly with +/- signs: +% >> B = {'test+NaN', 'test11.5', 'test-1.4', 'test', 'test-Inf', 'test+0.3'}; +% >> sort(B) +% ans = 'test' 'test+0.3' 'test+NaN' 'test-1.4' 'test-Inf' 'test11.5' +% >> natsort(B, '[-+]?(NaN|Inf|\d+\.?\d*)') +% ans = 'test' 'test-Inf' 'test-1.4' 'test+0.3' 'test11.5' 'test+NaN' +% +%%% Integer or decimal numbers, possibly with an exponent: +% >> C = {'0.56e007', '', '43E-2', '10000', '9.8'}; +% >> sort(C) +% ans = '' '0.56e007' '10000' '43E-2' '9.8' +% >> natsort(C, '\d+\.?\d*([eE][-+]?\d+)?') +% ans = '' '43E-2' '9.8' '10000' '0.56e007' +% +%%% Hexadecimal numbers (with '0X' prefix): +% >> D = {'a0X7C4z', 'a0X5z', 'a0X18z', 'a0XFz'}; +% >> sort(D) +% ans = 'a0X18z' 'a0X5z' 'a0X7C4z' 'a0XFz' +% >> natsort(D, '0X[0-9A-F]+', '%i') +% ans = 'a0X5z' 'a0XFz' 'a0X18z' 'a0X7C4z' +% +%%% Binary numbers: +% >> E = {'a11111000100z', 'a101z', 'a000000000011000z', 'a1111z'}; +% >> sort(E) +% ans = 'a000000000011000z' 'a101z' 'a11111000100z' 'a1111z' +% >> natsort(E, '[01]+', '%b') +% ans = 'a101z' 'a1111z' 'a000000000011000z' 'a11111000100z' +% +%%% Case sensitivity: +% >> F = {'a2', 'A20', 'A1', 'a10', 'A2', 'a1'}; +% >> natsort(F, [], 'ignorecase') % default +% ans = 'A1' 'a1' 'a2' 'A2' 'a10' 'A20' +% >> natsort(F, [], 'matchcase') +% ans = 'A1' 'A2' 'A20' 'a1' 'a2' 'a10' +% +%%% Sort order: +% >> G = {'2', 'a', '', '3', 'B', '1'}; +% >> natsort(G, [], 'ascend') % default +% ans = '' '1' '2' '3' 'a' 'B' +% >> natsort(G, [], 'descend') +% ans = 'B' 'a' '3' '2' '1' '' +% >> natsort(G, [], 'num> natsort(G, [], 'char> natsort({'a18446744073709551615z', 'a18446744073709551614z'}, [], '%lu') +% ans = 'a18446744073709551614z' 'a18446744073709551615z' +% +%% Input and Output Arguments %% +% +%%% Inputs (*==default): +% X = CellArrayOfCharRowVectors, to be sorted into natural-order. +% rgx = Regular expression to match number substrings, '\d+'* +% = [] uses the default regular expression, which matches integers. +% can be entered in any order, as many as required: +% = Sort direction: 'descend'/'ascend'* +% = NaN/number order: 'NaN sorted into natural-order. +% ndx = NumericArray, such that Y = X(ndx). The same size as . +% dbg = CellArray of the parsed characters and number values. +% Each row is one input char vector, linear-indexed from . +% +% See also SORT NATSORTFILES NATSORTROWS CELLSTR REGEXP IREGEXP SSCANF +%% Input Wrangling %% +% +assert(iscell(X),'First input must be a cell array.') +tmp = cellfun('isclass',X,'char') & cellfun('size',X,1)<2 & cellfun('ndims',X)<3; +assert(all(tmp(:)),'First input must be a cell array of char row vectors (1xN char).') +% +if nargin<2 || isnumeric(rgx)&&isempty(rgx) + rgx = '\d+'; +else + assert(ischar(rgx)&&ndims(rgx)<3&&size(rgx,1)==1,... + 'Second input must be a regular expression (char row vector).') %#ok +end +% +% Optional arguments: +tmp = cellfun('isclass',varargin,'char') & cellfun('size',varargin,1)<2 & cellfun('ndims',varargin)<3; +assert(all(tmp(:)),'All optional arguments must be char row vectors (1xN char).') +% Character case: +ccm = strcmpi(varargin,'matchcase'); +ccx = strcmpi(varargin,'ignorecase')|ccm; +% Sort direction: +sdd = strcmpi(varargin,'descend'); +sdx = strcmpi(varargin,'ascend')|sdd; +% Char/num order: +chb = strcmpi(varargin,'charnum') +nsAssert(1,varargin,nax,'NaN<->num') +nsAssert(1,varargin,sfx,'SSCANF format') +nsAssert(0,varargin,~(ccx|sdx|chx|nax|sfx)) +% +% SSCANF format: +if nnz(sfx) + fmt = varargin{sfx}; + if strcmpi(fmt,'%b') + cls = 'double'; + else + cls = class(sscanf('0',fmt)); + end +else + fmt = '%f'; + cls = 'double'; +end +% +%% Identify Numbers %% +% +[mat,spl] = regexpi(X(:),rgx,'match','split',varargin{ccx}); +% +% Determine lengths: +nmx = numel(X); +nmn = cellfun('length',mat); +nms = cellfun('length',spl); +mxs = max(nms); +% +% Preallocate arrays: +bon = bsxfun(@le,1:mxs,nmn).'; +bos = bsxfun(@le,1:mxs,nms).'; +arn = zeros(mxs,nmx,cls); +ars = cell(mxs,nmx); +ars(:) = {''}; +ars(bos) = [spl{:}]; +% +%% Convert Numbers to Numeric %% +% +if nmx + tmp = [mat{:}]; + if strcmp(fmt,'%b') + tmp = regexprep(tmp,'^0[Bb]',''); + vec = cellfun(@(s)sum(pow2(s-'0',numel(s)-1:-1:0)),tmp); + else + vec = sscanf(sprintf(' %s',tmp{:}),fmt); + end + assert(numel(vec)==numel(tmp),'The %s format must return one value for each input number.',fmt) +else + vec = []; +end +% +%% Debugging Array %% +% +if nmx && nargout>2 + dbg = cell(mxs,nmx); + dbg(:) = {''}; + dbg(bon) = num2cell(vec); + dbg = reshape(permute(cat(3,ars,dbg),[3,1,2]),[],nmx).'; + idf = [find(~all(cellfun('isempty',dbg),1),1,'last'),1]; + dbg = dbg(:,1:idf(1)); +else + dbg = {}; +end +% +%% Sort Columns %% +% +if ~any(ccm) % ignorecase + ars = lower(ars); +end +% +if nmx && any(chb) % charval + tmp = {'Unknown input arguments',' option may only be specified once. Provided inputs'}; + error('%s:%s',[varargin{:},tmp{1+val}],sprintf('\n''%s''',inp{idx})) +end +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%nsAssert +function grp = nsGroup(vec) +% Groups of a cell array of strings, equivalent to [~,~,grp]=unique(vec); +[vec,idx] = sort(vec); +grp = cumsum([true,~strcmp(vec(1:end-1),vec(2:end))]); +grp(idx) = grp; +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%nsGroup \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/numberedFaults.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/numberedFaults.m new file mode 100644 index 0000000..35e234b --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/numberedFaults.m @@ -0,0 +1,11 @@ +function[]=numberedFaults(all) +ends=cumsum(all.nEl); +begs=[1; ends(1:end-1)+1]; +cols=zeros(size(all.v, 1), 1); +for i=1:length(ends) + cols(begs(i):ends(i)) = i; +end +meshview(all.c, all.v); +text(all.x1, all.y1, num2str(cols)); +end + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/overcount.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/overcount.m new file mode 100644 index 0000000..37e3e13 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/overcount.m @@ -0,0 +1,18 @@ +function[degreeOfFitBoth, degreeOfFit1]=overcount(faultNumbers, anglebetweenP, anglebetweenT, degreeOfFitBoth, degreeOfFit1) +%subtract overcount due to multiple faults associated with 1 region in the +%fault-slip data +if anglebetweenP(faultNumbers(1), 1)<35 + if anglebetweenT(faultNumbers(1), 1)<35 + degreeOfFitBoth=degreeOfFitBoth-length(faultNumbers)+1; + end +end +if anglebetweenP(faultNumbers(1), 1)<35 + if anglebetweenT(faultNumbers(1), 1)>=35 + degreeOfFit1=degreeOfFit1-length(faultNumbers)+1; + end +elseif anglebetweenT(faultNumbers(1), 1)<35 + degreeOfFit1=degreeOfFit1-length(faultNumbers)+1; +end + +end + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/permutationsCheck.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/permutationsCheck.m new file mode 100644 index 0000000..1dc9848 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/permutationsCheck.m @@ -0,0 +1,72 @@ +function[anglesbetween, flips, sigma]=permutationsCheck(modeledVectors, stressAxes, stressAxesTrends, sigma1, sigma2, sigma3) +%checks principal stress axes for any possible stress permutations + +%prepare variables +anglesbetween1=zeros(length(stressAxes), 3); +anglesbetween2=anglesbetween1; anglesbetween3=anglesbetween1; +anglesbetween=anglesbetween1; +toCompare=zeros(length(stressAxes), 9); +flips=[]; + +for i=1:length(stressAxes) + if stressAxes(i, 1)~=0 %if there is comparison data for this fault + %collect vectors for this fault + vector1=modeledVectors(i, 1:3); + vector2=modeledVectors(i, 4:6); + vector3=modeledVectors(i, 7:9); + + %convert comparison data to Cartesian format + toCompare1(i, 1:3)=[(sind(stressAxes(i, 2)+90).* cosd(stressAxesTrends(i, 1))), (sind(stressAxes(i, 2)+90).* sind(stressAxesTrends(i, 1))), cosd(stressAxes(i, 2)+90)]; + toCompare2(i, 1:3)=[(sind(stressAxes(i, 4)+90).* cosd(stressAxesTrends(i, 2))), (sind(stressAxes(i, 4)+90).* sind(stressAxesTrends(i, 2))), cosd(stressAxes(i, 4)+90)]; + toCompare3(i, 1:3)=[(sind(stressAxes(i, 6)+90).* cosd(stressAxesTrends(i, 3))), (sind(stressAxes(i, 6)+90).* sind(stressAxesTrends(i, 3))), cosd(stressAxes(i, 6)+90)]; + + %calculate angles between each of the modeled principal stress axes + %and the axes in the comparison data + anglesbetween1(i,1)=acosd(dot(vector1, toCompare1(i, :))/(norm(vector1)*norm(toCompare1(i, :)))); + anglesbetween1(i,2)=acosd(dot(vector1, toCompare2(i, :))/(norm(vector1)*norm(toCompare2(i, :)))); + anglesbetween1(i,3)=acosd(dot(vector1, toCompare3(i, :))/(norm(vector1)*norm(toCompare3(i, :)))); + anglesbetween2(i,1)=acosd(dot(vector2, toCompare1(i, :))/(norm(vector2)*norm(toCompare1(i, :)))); + anglesbetween2(i,2)=acosd(dot(vector2, toCompare2(i, :))/(norm(vector2)*norm(toCompare2(i, :)))); + anglesbetween2(i,3)=acosd(dot(vector2, toCompare3(i, :))/(norm(vector2)*norm(toCompare3(i, :)))); + anglesbetween3(i,1)=acosd(dot(vector3, toCompare1(i, :))/(norm(vector3)*norm(toCompare1(i, :)))); + anglesbetween3(i,2)=acosd(dot(vector3, toCompare2(i, :))/(norm(vector3)*norm(toCompare2(i, :)))); + anglesbetween3(i,3)=acosd(dot(vector3, toCompare3(i, :))/(norm(vector3)*norm(toCompare3(i, :)))); + + %check that the smallest angle between the axes are being + %considered + for j=1:3 + if anglesbetween1(i, j)>90 + anglesbetween1(i, j)=180-anglesbetween1(i, j); + end + if anglesbetween2(i, j)>90 + anglesbetween2(i, j)=180-anglesbetween2(i, j); + end + if anglesbetween3(i, j)>90 + anglesbetween3(i, j)=180-anglesbetween3(i, j); + end + end + + %check for existence of any stress permutations + %sigma1-sigma2 + if anglesbetween1(i, 1)>anglesbetween1(i, 2) && anglesbetween2(i, 2)>anglesbetween2(i, 1) && anglesbetween1(i, 2)<50 && anglesbetween2(i, 1)<50 + flips=[flips, sprintf('%d (sigma1-sigma2)', i)]; + [sigma1(i, :), sigma2(i, :)]=swap(sigma2(i, :), sigma1(i, :)); + anglesbetween(i, 1)=anglesbetween1(i, 2); + anglesbetween(i, 2)=anglesbetween2(i, 1); + anglesbetween(i, 3)=anglesbetween3(i, 3); + %sigma2-sigma3 + elseif anglesbetween2(i, 2)>anglesbetween2(i, 3) && anglesbetween3(i, 3)>anglesbetween3(i, 2) && anglesbetween2(i, 3)<50 && anglesbetween3(i, 2)<50 + flips=[flips, sprintf('%d (sigma2-sigma3)', i)]; + [sigma2(i, :), sigma3(i, :)]=swap(sigma3(i, :), sigma2(i, :)); + anglesbetween(i, 2)=anglesbetween2(i, 3); + anglesbetween(i, 3)=anglesbetween3(i, 2); + anglesbetween(i, 1)=anglesbetween1(i, 1); + else %no permutation + anglesbetween(i, 1)=anglesbetween1(i,1); + anglesbetween(i, 2)=anglesbetween2(i, 2); + anglesbetween(i, 3)=anglesbetween3(i, 3); + end + end +end +sigma=[sigma1, sigma2, sigma3]; +end diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/rake.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/rake.m new file mode 100644 index 0000000..cbc6f7e --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/rake.m @@ -0,0 +1,6 @@ +function [ totalelements ] = rake(totalelements, slip) %ppositive +%calculates rake on each element of the mesh, given mesh and slip inputs +totalelements.sliprake=totalelements.dip*0; +totalelements.sliprake=atan2d(-slip(:, 2), slip(:, 1)); + + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/raketoTrendPlunge.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/raketoTrendPlunge.m new file mode 100644 index 0000000..4a8fcfc --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/raketoTrendPlunge.m @@ -0,0 +1,29 @@ +function [ trends, plunges ] = raketoTrendPlunge( strikes, dips, rakes ) +%takes series of faults with known strike, dip and rake and outputs the +%trend and plunge for each rake +tanR=zeros(size(rakes)); +cosD=tanR; sinD=tanR; sinR=tanR; beta=tanR; betaTwo=tanR; rawtrend=tanR; +trends=zeros(size(rakes)); +plunges=zeros(size(rakes)); +for i=1:size(rakes) + tanR(i, 1)=tan(degtorad(rakes(i, 1))); + cosD(i, 1)=cos(degtorad(dips(i, 1))); + sinD(i, 1)=sin(degtorad(dips(i, 1))); + sinR(i, 1)=sin(degtorad(rakes(i, 1))); + beta(i, 1)=abs(radtodeg(atan(tanR(i,1)*cosD(i,1)))); + betaTwo(i,1)=180-beta(i, 1); + if rakes(i,1)>90 + rawtrend(i,1)= strikes(i, 1)+ betaTwo(i,1); + else + rawtrend(i,1)=strikes(i, 1)+ beta(i, 1); + end + if rawtrend(i,1)>360 + trends(i,1)=rawtrend(i,1)-360; + else + trends(i,1)=rawtrend(i, 1); + end + plunges(i,1)=radtodeg(asin(sinD(i, 1)*sinR(i, 1))); +end + +end + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/runComparison.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/runComparison.m new file mode 100644 index 0000000..a647e1f --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/runComparison.m @@ -0,0 +1,53 @@ +function [rakes, results, anglesbetween, misfit] = runComparison(faults, faultsHotspot, hotspotContribution, azimuth, faultOpening, comparison, slipData, stressData, eqData, eqDataStress, GPSData) +%prepare inputs for tribemx +d=zeros(sum(faultsHotspot.nEl), 3); +d(sum(faults.nEl)+1:end, 3)=hotspotContribution; +bc=ones(sum(faultsHotspot.nEl), 3); +bc(:, 3)=0; + +if strcmp(faultOpening, 'None')==1 + %standard, do not allow fault opening + bc(:, 3)=0; +elseif strcmp(faultOpening,'All')==1 + %let all faults open + bc(1:sum(faults.nEl), 3)=1; +else + %let poorly fit faults open + for i=1:length(faultOpening) + bc(begs(i):ends(i), 3)=1; + end +end + + +[REMSrotate, ~]=calculateREMS(azimuth); +if comparison==0 + [slip, trac, G] = tribemx(faultsHotspot, d, bc, REMSrotate); + faultsHotspot=rake(faultsHotspot, slip); + rakes=faultsHotspot.sliprake; +end + + + + +if comparison==0 %fault-slip derived, moment tensor axes + [~, ~, misfit, anglebetweenP, anglebetweenT, pressure, tension]=momentTensorsFaults(faults, faultsHotspot, d, bc, azimuth, slipData(:, 1:2), slipData(:, 3:4), G); + anglesbetween=(anglebetweenP(:, 1)+anglebetweenT(:,1))/2; + anglesbetween=nonzeros(unique(anglesbetween, 'rows', 'stable')); + results=[pressure, tension]; + misfit=mean(mean(anglesbetween)); +elseif comparison==1 %fault-slip derived, stress tensor axes + [misfit, anglesbetween, stressAxes, stressRatio, flips, ~, rakes]=stressTensorsFaults(faults, faultsHotspot, d, bc, azimuth,stressData); + results=stressAxes; + anglesbetween=unique(anglesbetween, 'rows', 'stable'); + anglesbetween = anglesbetween(any(anglesbetween,2),:); +elseif comparison==2 %earthquake derived, moment tensor axes + [momAxes, misfit, anglesbetween, rakes] = momentTensorsCoordinates(faults, faultsHotspot, d, bc, azimuth,eqData); + results=momAxes; +elseif comparison==3 %earthquake-derived, stress tensor axes + [stressAxes, anglesbetween, misfit, stressRatio, flips, sigma, rakes] = stressTensorsCoordinates(faults, faultsHotspot, d, bc, azimuth,eqDataStress); + results=stressAxes; +elseif comparison==4 %GPS axes + [anglesbetween, misfit, results, rakes] = GPSCoordinates(faults, faultsHotspot, d, bc, azimuth,hotspotContribution, GPSData); +end + +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/stressTensorsCoordinates.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/stressTensorsCoordinates.m new file mode 100644 index 0000000..486927e --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/stressTensorsCoordinates.m @@ -0,0 +1,210 @@ +function[stressAxes, anglesbetween, misfit, stressRatio, flips, sigmaflipped, rakes] = stressTensorsCoordinates( faults, faultsHotspot, d, bc, alpha, stressGrid) +%stressTensorsCoordinates solves for angular misfit with comparison stress tensor axes +%defined at a series of observation coordinates + +%Inputs: +% faults: meshed fault map faultsHotspot: meshed fault map and spherical mesh hotspot +% d: nelx3 array of boundary conditions & bc: NEL-by-3 array specifying type +% of boundary conditions, see tribemx for specifications +% alpha: angle of uniaxial remote stress, defined clockwise from due east +% stressGrid: comparison data: longitude/latitude (columns 1-2), +% depth (column 3), sigma 1 (columns 4:5), sigma 2 (columns 6:7), +% sigma 3 (columns 8:9) + + +%Outputs: +%stressAxes: stress tensor axes for each observation coordinate defined for +%the model +%anglesbetween: angular misfits between pressure and tension axes for each +%comparison data point +%misfit: average overall angular misfit +%stressRatio: calculated deviatoric stress ratios +%flips: text marking down identified possible stress permutations +%sigmaflipped: stress tensor axes adjusted for possible stress permutations +%rakes: overall rake calculated for each fault from the model + + +%calculate REMS based on desired angle clockwise from due east +rotation=zeros(2,2); +rotation(1,1)=cosd(alpha); rotation(2,2)=cosd(alpha); +rotation(2,1)=sind(alpha); rotation(1,2)=-sind(alpha); +a=[6e6 0; 0 0]; +remsinitial=rotation'*a*rotation; +REMS=zeros(1,6); +REMS(1)=remsinitial(1,1); REMS(2)=remsinitial(2,2); +REMS(4)=-remsinitial(1,2); + +%calculate starting inputs +ends=cumsum(faults.nEl); begs=[1; ends(1:end-1)+1]; +stressesComparison=stressGrid(:,4:9); + +%calculate grid of observation coordinates +stressGrid2=[utmconv(stressGrid(:, 1:2), 0), stressGrid(:,3)]; +obs.x=stressGrid2(:,1); obs.y=stressGrid2(:,2); +obs.z=stressGrid2(:,3)*-1000; +obs.v = 's'; +[slip, trac, out] = tribemx(faultsHotspot, d, bc, REMS, obs); +faultsHotspot=rake(faultsHotspot, slip); +rakes=faultsHotspot.sliprake; +%calculate stress tensor axes +mstress=zeros(length(obs.x), 6); pstresses=[]; magnitudes=[]; +for i=1:length(obs.x) + mstress(i, :)=-out.s(i, 1:6); + pstress = PrincipalStress([mstress(i, 1), mstress(i, 4), mstress(i, 5); mstress(i, 4), mstress(i, 2), mstress(i, 6); mstress(i, 5), mstress(i, 6), mstress(i, 3)], pi/2, 0, pi/2); + pstresses=[pstresses; pstress(:, 2:3)]; + magnitudes=[magnitudes; pstress(:, 1)]; +end + +%calculate stress ratio +magnitudes=reshape(magnitudes, [3, length(magnitudes)/3]).'; +stressRatio=zeros(length(magnitudes), 1); +deviatoricStress=zeros(length(magnitudes), 3); +for i=1:length(magnitudes) + for j=1:3 + meanMag=mean(magnitudes(i, :)); + deviatoricStress(i, j)=magnitudes(i, j)-meanMag; + end +end +for i=1:length(magnitudes) + stressRatio(i, 1)=(deviatoricStress(i, 2)-deviatoricStress(i, 3))/(deviatoricStress(i, 1)-deviatoricStress(i, 3)); +end + +%adjust formatting for plunges (must be positive in order to come out +%correctly), trends must then be switched by 180' to remain consistent +%with which side of plunge is being considered +stressAxes=[]; +for j=1:3 + k=pstresses(j:3:end, :); %take either sigma1, sigma2, or sigma3 + for i=1:length(k) + if k(i, 2)<0 + k(i, 2)=-k(i, 2); + if k(i, 1)90 + anglesbetween(i, j)=180-anglesbetween(i, j); + end + end +end +%------------------------------------------------------------------------- +%calculate degree of similarity with comparison data +%degree of fit as the number of faults that fit well for 1 principal stress +count=0; counts=[]; +for j=1 + for i=1:length(ends) + if anglesbetween(i, (3*j)-2)>0 + angles=anglesbetween(i, (3*j)-2:(3*j)); + if length(nonzeros(logical(angles<35)))==1 + count=count+1; + end + end + end + counts=[counts, count]; +end +fit1=counts; + +%degree of fit as the number of faults that fit well for 2 of 3 principal stresses +count=0; counts=[]; +for j=1 + for i=1:length(ends) + if anglesbetween(i, (3*j)-2)>0 + angles=anglesbetween(i, (3*j)-2:(3*j)); + if length(nonzeros(logical(angles<35)))==2 + count=count+1; + end + end + end + counts=[counts, count]; +end +fit2=counts; + +%degree of fit as the number of faults that fit well for all 3 principal stresses +count=0; counts=[]; +for j=1 + for i=1:length(ends) + if anglesbetween(i, (3*j)-2)>0 && anglesbetween(i, (3*j)-2)<35 && anglesbetween(i, (3*j)-1)<35 && anglesbetween(i, (3*j))<35 + count=count+1; + end + end + counts=[counts, count]; +end +fit3=counts; +fit=[fit1; fit2; fit3]; + + +%degree of misfit as the average angle between principal stresses for the 3 +%vectors +count=0; +count2=0; misfits=[]; +for j=1 + for i=1:length(ends) + if anglesbetween(i, (3*j)-2)~=0 + count=count+anglesbetween(i, (3*j)-2)+anglesbetween(i, (3*j)-1); + count2=count2+2; + end + end + misfit=count/(count2); + misfits=[misfits, misfit]; + count=0; count2=0; +end +misfit=mean(misfits); +anglesbetween=[anglesbetween(:,1), anglesbetween(:,3)]; +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/stressTensorsFaults.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/stressTensorsFaults.m new file mode 100644 index 0000000..8d582de --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/stressTensorsFaults.m @@ -0,0 +1,190 @@ +function[misfit, anglesbetween, stressAxes, stressRatio, flips, sigmaFlipped, rakes] = stressTensorsFaults( faults, faultsHotspot, d, bc, alpha, stressData) +%stressTensorsFaults solves for angular misfit with comparison stress tensor +%defined at a series of faults + +%Inputs: +% faults: meshed fault map faultsHotspot: meshed fault map and spherical mesh hotspot +% d: nelx3 array of boundary conditions & bc: NEL-by-3 array specifying type +% of boundary conditions, see tribemx for specifications +% alpha: angle of uniaxial remote stress, defined clockwise from due east +% G: pre-calculated Green's functions, derived from tribemx +% stressData: comparison data: sigma 1 (columns 1:2), sigma 2(columns 3:4), +% sigma 3(columns 5:6), if data contains multiple comparison points for 1 +% fault: pattern continues, with sigma 1 (columns 7:8), etc. + + +%Outputs: +%misfit: average overall angular misfit +%fit: number of faults for which 1, 2, and all of the principal stress axes +%fit well +%anglesbetween: angular misfits between sigma 1, 2, and 3 axes for each +%comparison data point +%stressAxes: stress tensor axes for each fault defined for +%the model +%stressRatio: calculated deviatoric stress ratios +%flips: text marking down identified possible stress permutations +%sigmaflipped: stress tensor axes adjusted for possible stress permutations + +%calculate REMS based on angle counting clockwise from due East +rotation=zeros(2,2); +rotation(1,1)=cosd(alpha); rotation(2,2)=cosd(alpha); +rotation(2,1)=sind(alpha); rotation(1,2)=-sind(alpha); +a=[6e6 0; 0 0]; +remsinitial=rotation'*a*rotation; +REMS=zeros(1,6); +REMS(1)=remsinitial(1,1); REMS(2)=remsinitial(2,2); +REMS(4)=-remsinitial(1,2); + +%calculate starting inputs +stressesComparison=stressData(:,5:end); +ends=cumsum(faults.nEl); begs=[1; ends(1:end-1)+1]; + +%calculate grid of observation coordinates +stressGrid2=[utmconv(stressData(:, 1:2), 0), stressData(:,3)]; +obs.x=stressGrid2(:,1); obs.y=stressGrid2(:,2); +obs.z=stressGrid2(:,3)*-1000; +obs.v = 's'; +[slip, trac, out, G] = tribemx(faultsHotspot, d, bc, REMS, obs); +faultsHotspot=rake(faultsHotspot, slip); +rakes=faultsHotspot.sliprake; + +%calculate stress tensor axes +mstress=zeros(length(obs.x), 6); pstresses=[]; magnitudes=[]; +for i=1:length(obs.x) + mstress(i, :)=-out.s(i, 1:6); + pstress = PrincipalStress([mstress(i, 1), mstress(i, 4), mstress(i, 5); mstress(i, 4), mstress(i, 2), mstress(i, 6); mstress(i, 5), mstress(i, 6), mstress(i, 3)], pi/2, 0, pi/2); + pstresses=[pstresses; pstress(:, 2:3)]; + magnitudes=[magnitudes; pstress(:, 1)]; +end + +%calculate deviatoric stress ratio +magnitudes=reshape(magnitudes, [3, length(magnitudes)/3]).'; +stressRatio=zeros(length(magnitudes), 1); +deviatoricStress=zeros(length(magnitudes), 3); +for i=1:length(magnitudes) + for j=1:3 + meanMag=mean(magnitudes(i, :)); + deviatoricStress(i, j)=magnitudes(i, j)-meanMag; + end +end +for i=1:length(magnitudes) + stressRatio(i, 1)=(deviatoricStress(i, 2)-deviatoricStress(i, 3))/(deviatoricStress(i, 1)-deviatoricStress(i, 3)); +end + + +%adjust formatting for plunges (must be positive in order to come out +%correctly), trends must then be switched by 180' to remain consistent +%with which side of plunge is being considered +stressAxes=[]; +for j=1:3 + k=pstresses(j:3:end, :); %take either sigma1, sigma2, or sigma3 + for i=1:length(k) + if k(i, 2)<0 + k(i, 2)=-k(i, 2); + if k(i, 1)90 + anglebetween1(i, j)=180-anglebetween1(i, j); + end + if anglebetween2(i, j)>90 + anglebetween2(i, j)=180-anglebetween2(i, j); + end + if anglebetween3(i, j)>90 + anglebetween3(i, j)=180-anglebetween3(i, j); + end + if size(stressesComparison,2)/6==5 + if anglebetween4(i, j)>90 + anglebetween4(i, j)=180-anglebetween4(i, j); + end + if anglebetween5(i, j)>90 + anglebetween5(i, j)=180-anglebetween5(i, j); + end + end + end +end + +anglesbetween=[anglebetween1, anglebetween2, anglebetween3]; +if size(stressesComparison, 2)/6==5 + anglesbetween=[anglebetween1, anglebetween2, anglebetween3, anglebetween4, anglebetween5]; +end +%------------------------------------------------------------------------- +%calculate degree of similarity with comparison data +%degree of misfit as the average angle between principal stresses for the 2 +%vectors +anglesbetween=anglesbetween(:,[1,3,4,6,7,9,10,12,13,15]); +anglesbetween2=anglesbetween; +for i=1:size(stressData,1) + anglesbetween2(i,11)=sum(anglesbetween2(i,1:10))/length(nonzeros(anglesbetween2(i, 1:10))); +end +misfit=sum(anglesbetween2(:,11), 'omitnan')/size(stressData,1); +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/.gitmodules b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/.gitmodules new file mode 100644 index 0000000..c21ca9b --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/.gitmodules @@ -0,0 +1,3 @@ +[submodule "tridisl"] + path = tridisl + url = https://github.com/jploveless/tridisl.git diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/BEM_inputs.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/BEM_inputs.mat new file mode 100644 index 0000000..e2879f2 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/BEM_inputs.mat differ diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/README b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/README new file mode 100644 index 0000000..84db797 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Delano_2017_Geology_Inputs/README @@ -0,0 +1,18 @@ +Boundary element model input files to accompany: + +Delano, J.E., Amos, C.B., Loveless, J.P., Rittenour, T.M., Sherrod, B.L., Lynch, E.M. +2017, Influence of the megathrust earthquake cycle on upper plate deformation in the +Cascadia forearc of Washington State: Geology, doi: 10.1130/G39070.1 + +1. Download tribem package from https://github.com/jploveless/tribem +2. Load the Matlab file "BEM_inputs.mat" into the Matlab workspace +3. Run the command: + +>> [slip, trac] = tribemx(p, d, bc); + +4. Visualize fault slip using "meshview.m" function. For example, to plot dip slip +rates, run: + +>> meshview(p.c, p.v, slip(:, 2)); + +Direct correspondence to Jack Loveless (jloveles@smith.edu) \ No newline at end of file diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/README b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/README new file mode 100644 index 0000000..0af7e21 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/README @@ -0,0 +1,18 @@ +Boundary element model input files to accompany: + +Duckworth, W.C., Amos, C.B., Schermer, E.R., Loveless, J.P., Rittenour, T.M. +2021, Slip and strain accumulation along the Sadie Creek fault, Olympic Peninsula, +Washington: Journal of Geophysical Research, https://doi.org/10.1029/2020JB020276 + +1. Download tribem package from https://github.com/jploveless/tribem +2. Load the Matlab file "BEM_inputs.mat" into the Matlab workspace +3. Run the command: + +>> [slip, trac] = tribemx(p, d, bc); + +4. Visualize fault slip using "meshview.m" function. For example, to plot dip slip +rates, run: + +>> meshview(p.c, p.v, slip(:, 2)); + +Direct correspondence to Jack Loveless (jloveles@smith.edu) \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_05_090.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_05_090.mat new file mode 100644 index 0000000..c6d8ac4 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_05_090.mat differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_05_115.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_05_115.mat new file mode 100644 index 0000000..4a58d4b Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_05_115.mat differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_30_090.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_30_090.mat new file mode 100644 index 0000000..9419d3b Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_30_090.mat differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_30_115.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_30_115.mat new file mode 100644 index 0000000..814e686 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Duckworth_2021_JGR_Inputs/coseismic_30_115.mat differ diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/LICENSE b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/LICENSE new file mode 100644 index 0000000..c41da09 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2019 Jack Loveless + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/ProjectStrainPartialsMats.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/ProjectStrainPartialsMats.m new file mode 100644 index 0000000..9558cfe --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/ProjectStrainPartialsMats.m @@ -0,0 +1,53 @@ +function Gp = ProjectStrainPartials(G, strike, dip, rake); +% PROJECTSTRAINPARTIALS Projects strain partial components onto a fault. +% +% PROJECTSTRAINPARTIALS(G, S, D) projects the matrix of strain partials G onto +% the fault surfaces defined by strike, S, and dip, D, arrays. G is a 6.*n-by-3.*n +% array relating the 6 strain components to the 3 slip components of n faults, and +% S and D are n-by-1 arrays defining each fault's geometry. +% +% GP = PROJECTSTRAINPARTIALS(G, S, D) returns the projected matrix to GP, which is a +% 3.*n-by-3.*n array with rows describing traction in the strike direction, in the dip +% direction, and in the fault-normal direction. +% +% GP = PROJECTSTRAINPARTIALS(G, S, D, R) also uses a rake vector R and, instead of +% returning traction in the strike and dip direction, returns traction in the rake +% direction and the rake perpendicular direction. +% + +% Handle dips > 90 +strike(dip > 90) = wrapTo360(strike(dip > 90) + 180); +dip(dip > 90) = dip(dip > 90) - 90; + +% Check rake +if ~exist('rake', 'var') + rake = zeros(size(dip)); +end + +% Trig. function arrays +sins = repmat(sind(strike), 1, size(G, 2)); +coss = repmat(cosd(strike), 1, size(G, 2)); +sined = repmat(sind(dip), 1, size(G, 2)); +cosed = repmat(cosd(dip), 1, size(G, 2)); +cosr = repmat(cosd(rake), 1, size(G, 2)); +sinr = repmat(sind(rake), 1, size(G, 2)); + +% Extract tensor components +uxx = G(1:6:end, :); +uyy = G(2:6:end, :); +uzz = G(3:6:end, :); +uxy = G(4:6:end, :); +uxz = G(5:6:end, :); +uyz = G(6:6:end, :); + +% Do the rotation, R'*D'*S'*T*S*D*R (used symbolic toolbox) +ud = -sined.*(coss.*(uxz.*(sined) - uxx.*(coss).*(cosed) + uxy.*(cosed).*(sins)) - sins.*(uyz.*(sined) - uxy.*(coss).*(cosed) + uyy.*(cosed).*(sins))) - cosed.*(uzz.*(sined) - uxz.*(coss).*(cosed) + uyz.*(cosed).*(sins)); +us = sined.*(coss.*(uxy.*(coss) + uxx.*(sins)) - sins.*(uyy.*(coss) + uxy.*(sins))) + cosed.*(uyz.*(coss) + uxz.*(sins)); +un = sined.*(coss.*(uxz.*(cosed) + uxx.*(coss).*(sined) - uxy.*(sins).*(sined)) - sins.*(uyz.*(cosed) + uxy.*(coss).*(sined) - uyy.*(sins).*(sined))) + cosed.*(uzz.*(cosed) + uxz.*(coss).*(sined) - uyz.*(sins).*(sined)); + + +% Write the projected partials +Gp = zeros(size(G, 1)/2, size(G, 2)); +Gp(1:3:end, :) = us; +Gp(2:3:end, :) = ud; +Gp(3:3:end, :) = un; \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/README.md b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/README.md new file mode 100644 index 0000000..ecf7b83 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/README.md @@ -0,0 +1,16 @@ +# tribem +### Boundary element code using triangular dislocation elements in Matlab + +Based on algorithms published in: + +Meade, B. J. (2007), Algorithms for the calculation of exact displacements, strains, and stresses for triangular dislocation elements in a uniform elastic half space, *Computers and Geosciences*, **33**, 1064–1075, [doi:10.1016/j.cageo.2006.12.003](http://dx.doi.org/10.1016/j.cageo.2006.12.003). + +__tribem__ uses [__tridisl__](https://github.com/jploveless/tridisl) as a submodule. To clone __tribem__ using `git` on the command line, run + + $ git clone --recursive https://github.com/jploveless/tribem.git + +If not using `git` on the command line, use the following workflow to access the necessary subfunctions: +- Download __tribem__ as a `.zip` file and unzip +- Download [__tridisl__](https://github.com/jploveless/tridisl) as a `.zip` file and unzip +- Move the contents of the `tridisl` folder to empty `tribem/tridisl` folder +- Add the `tribem` and `tribem/tridisl` directories to your MATLAB path diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/StrainToStressComp.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/StrainToStressComp.m new file mode 100644 index 0000000..adf3704 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/StrainToStressComp.m @@ -0,0 +1,24 @@ +function s = StrainToStressComp(e, lambda, mu) +% StressToStrain.m +% +% Calculate stress components given a strain tensor and elastic +% moduli lambda and mu. +% +% Stress and strain are n-by-6 arrays structured as: +% [xx yy zz xy xz yz] +% +% Strain can also be a n-by-m*6 array, giving multiple strain tensors. +% + +net = size(e, 2)./6; % number of strain tensors +s = e; +en = e(:, 1:6:end) + e(:, 2:6:end) + e(:, 3:6:end); % normal strains summed + +s(:, 1:6:end) = 2.*mu.*e(:, 1:6:end) + lambda.*en; +s(:, 2:6:end) = 2.*mu.*e(:, 2:6:end) + lambda.*en; +s(:, 3:6:end) = 2.*mu.*e(:, 3:6:end) + lambda.*en; +s(:, 4:6:end) = 2.*mu.*e(:, 4:6:end); +s(:, 5:6:end) = 2.*mu.*e(:, 5:6:end); +s(:, 6:6:end) = 2.*mu.*e(:, 6:6:end); + + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/StressToStrainComp.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/StressToStrainComp.m new file mode 100644 index 0000000..3b3fdaa --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/StressToStrainComp.m @@ -0,0 +1,24 @@ +function e = StressToStrainComp(s, lambda, mu) +% StressToStrain.m +% +% Calculate strain components given a stress tensor and elastic +% moduli lambda and mu. +% +% Stress and strain are n-by-6 arrays structured as: +% [xx yy zz xy xz yz] +% +% Stress can also be a n-by-m*6 array, giving a tensor in each row. +% + +net = size(s, 2)./6; % number of stress tensors +e = s; +sn = s(:, 1:6:end) + s(:, 2:6:end) + s(:, 3:6:end); % trace of stress tensor + +ncoef = lambda./(2*mu*(3*lambda + 2*mu)); % Normal coefficient + +e(:, 1:6:end) = 0.5./mu.*s(:, 1:6:end) - ncoef.*sn; +e(:, 2:6:end) = 0.5./mu.*s(:, 2:6:end) - ncoef.*sn; +e(:, 3:6:end) = 0.5./mu.*s(:, 3:6:end) - ncoef.*sn; +e(:, 4:6:end) = 0.5./mu.*s(:, 4:6:end); +e(:, 5:6:end) = 0.5./mu.*s(:, 5:6:end); +e(:, 6:6:end) = 0.5./mu.*s(:, 6:6:end); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/example.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/example.mat new file mode 100644 index 0000000..b3c44e6 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/example.mat differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/example_opp_dips.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/example_opp_dips.mat new file mode 100644 index 0000000..e89b413 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/example_opp_dips.mat differ diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/.gitignore b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/.gitignore new file mode 100644 index 0000000..3042c7e --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/.gitignore @@ -0,0 +1,2 @@ +.DS_Store +gmshfaultsprefs.mat \ No newline at end of file diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/OrderedEdges.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/OrderedEdges.m new file mode 100644 index 0000000..08ed58e --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/OrderedEdges.m @@ -0,0 +1,11 @@ +function elo = OrderedEdges(c, v); +% OrderedEdges returns the edges +el = boundedges(c, v); +elo = [el(1, :)]; +for i = 2:length(el); + [next, col] = find(el == elo(i-1, 2)); % find all of the boundary lines containing the second entry of the current ordered boundary line + n = find(sum(el(next, :), 2) ~= sum(elo(i-1, :), 2)); % choose that which is not the current boundary line + next = next(n); col = col(n); + elo = [elo; [el(next, col) el(next, setdiff([1 2], col))]]; % order the endpoints of the next boundary line +end +elo = elo'; \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/PatchEdges.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/PatchEdges.m new file mode 100644 index 0000000..660d098 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/PatchEdges.m @@ -0,0 +1,18 @@ +function ec = PatchEdges(p) +% PatchEdges Determines coordinates of fault edges in patch structure. +% EC = PatchEdges(P) determines the 3-D coordinates of the outlines of +% faults as specified in structure P. The output EC is 3 column array +% containing [x, y, z] (or [lon, lat, z]) coordinates of the edges, with +% [NaN NaN NaN] rows separating edges of distinct entities so that all +% edges can be plotted with a simple plot or plot3 command. +% + +ends = cumsum(p.nEl); +begs = [1; ends(1:end-1)+1]; +cc = [0; cumsum(p.nc)]; +ec = []; + +for i = 1:length(p.nEl) % For each entity, + oe = OrderedEdges(p.c, p.v(begs(i):ends(i), :)); + ec = [ec; p.c([oe(1, :), oe(end)], :); nan(1, 3)]; +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/README.md b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/README.md new file mode 100644 index 0000000..2cc56b3 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/README.md @@ -0,0 +1,2 @@ +# meshing +Codes for triangular dislocation element meshing with Gmsh diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/arbrot.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/arbrot.m new file mode 100644 index 0000000..8c670b7 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/arbrot.m @@ -0,0 +1,57 @@ +function fcoords = arbrot(coords,strike,dip) +% +% ARBROT carries out an arbitrary rotation of points in x,y,z space. +% +% FCOORDS = ARBROT(COORDS,STRIKE,DIP) uses the x, y, z coordinate +% triplets contained in the n x 3 array COORDS and the STRIKE and +% DIP of the desired rotation (i.e. the vertical axis and horizontal +% axis rotation, respectively) in ordre to determine the new final +% coordinates, which are output as coordinate triplets in FCOORDS. +% To return the points to their original strike, specify [] for +% STRIKE. To rotate a vertical plane counterclockwise (east dip), +% specify a positive DIP, and specify a negative DIP for clockwise +% dip rotation. +% +% The program carries out 5 coordinate transformations: +% 1) After determining the southernmost point, the points are +% TRANSLATED so that the southernmost point lies at the origin, +% 2) The points are rotated about their AVERAGE strike so that +% they lie in an approximately N-S striking line (plane). +% 3) The points are rotated about the specified DIP. +% 4) The points are rotated about the specified STRIKE. +% 5) The points are re-translated such that the x,y coordinates +% of the southernmost point are the same as before the +% transformations. +% + +warning('off','MATLAB:singularMatrix') + +% place the coords into an appropriately shaped array for transformations +coords = [coords'; ones(1, size(coords, 1))]; + +% find the center point +or = mean(coords, 2); +% create the translation matrix +shift = [[1 0 0;0 1 0;0 0 1;0 0 0] [-or(1:2);0; 1]]; + +% determine the mean strike of the points +b = [coords(1, :)' ones(size(coords, 2), 1)]\coords(2, :)'; +str = 90 - atand(b(1)); +north = [cosd(str) -sind(str) 0 0;sind(str) cosd(str) 0 0;0 0 1 0;0 0 0 1]; + +% create the specified strike matrix +if length(strike) == 0; + strike = str; +end +strikem = [cosd(strike) sind(strike) 0 0;-sind(strike) cosd(strike) 0 0;0 0 1 0;0 0 0 1]; +% dip matrix +di = sign(dip)*(90-abs(dip)); +dipm = [cosd(di) 0 -sind(di) 0;0 1 0 0;sind(di) 0 cosd(di) 0;0 0 0 1]; +% re-translation matrix +rshift = [[1 0 0;0 1 0;0 0 1;0 0 0] [or(1:2); 0; 1]]; + +% make the composite transformation +fcoords = rshift*strikem*dipm*north*shift*coords; +fcoords = fcoords(1:3,:)'; + +warning('on','MATLAB:singularMatrix') \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/boundedges.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/boundedges.m new file mode 100644 index 0000000..045b579 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/boundedges.m @@ -0,0 +1,23 @@ +function e=boundedges(p,t) +%BOUNDEDGES Find boundary edges from triangular mesh +% E=BOUNDEDGES(P,T) + +% Copyright (C) 2004-2006 Per-Olof Persson. See COPYRIGHT.TXT for details. + +% Form all edges, non-duplicates are boundary edges +edges=[t(:,[1,2]); + t(:,[1,3]); + t(:,[2,3])]; +node3=[t(:,3);t(:,2);t(:,1)]; +edges=sort(edges,2); +[foo,ix,jx]=unique(edges,'rows'); +vec=histc(jx,1:max(jx)); +qx=find(vec==1); +e=edges(ix(qx),:); +node3=node3(ix(qx)); + +% Orientation +v1=p(e(:,2),:)-p(e(:,1),:); +v2=p(node3,:)-p(e(:,1),:); +ix=find(v1(:,1).*v2(:,2)-v1(:,2).*v2(:,1)>0); +e(ix,[1,2])=e(ix,[2,1]); diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2geo.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2geo.m new file mode 100644 index 0000000..7ff65ea --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2geo.m @@ -0,0 +1,58 @@ +function contour2geo(lon, lat, dep, esize, file, gvers) +% contour2geo Converts contour lines to a .geo file for Gmsh. +% contour2geo(lon, lat, dep, esize, file) converts the contour +% lines whose coordinates are defined by vectors lon, lat, dep +% into a .geo file for meshing using Gmsh. esize specifies the +% element size, and file gives the filename with full path. +% +% The lon, lat of contour lines are assumed to be ordered, +% and contour lines are separated based on changes in depth. +% +% The geographic coordinates are converted to geocentric +% coordinates before writing to the file. These can be +% converted back to lon, lat, dep using mshxyz2geo.m. + +% Identify breaks in contour lines based on depth +dd = diff(dep); +maxdd = max(abs(dd)); +breaks = find(abs(dd) > 0.2*maxdd); +begs = [1; breaks+1]; +ends = [breaks; size(dep, 1)]; + +% Check for Gmsh version ID +if exist('gvers', 'var') + if gvers >= 4 + surfname = 'Surface'; + else + surfname = 'Ruled Surface'; + end +else + surfname = 'Surface'; % Assume newer version +end + +% Convert all coordinates to geocentric Cartesian +[x, y, z] = long_lat_to_xyz(deg2rad(lon), deg2rad(lat), 6371-abs(dep)); + +% Prep file for writing +fid = fopen([file '.geo'], 'w'); +fprintf(fid, 'esize = %g;\n', esize); +% Write .geo points +fprintf(fid, 'Point(%g) = {%g, %g, %g, esize};\n', [1:size(lon, 1); x'; y'; z']); +% Write contour lines +for i = 1:length(begs) + fprintf(fid, 'CatmullRom(%g) = {%g:%g};\n', i, begs(i), ends(i)); +end +j = i; +% Write end lines, circulations, and surfaces +for i = 1:length(begs)-1 + % Depth connection 1 + fprintf(fid, 'CatmullRom(%g) = {%g,%g};\n', j+(2*i-1), begs(i), begs(i+1)); + % Depth connection 2 + fprintf(fid, 'CatmullRom(%g) = {%g,%g};\n', j+(2*i-0), ends(i), ends(i+1)); + % Line loop + fprintf(fid, 'Line Loop(%g) = {%g, %g, -%g, -%g};\n', i, i, j+(2*i-0), i+1, j+(2*i-1)); + % Surface + fprintf(fid, '%s(%g) = {%g};\n', surfname, i, i); +end + +fclose(fid); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2p.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2p.m new file mode 100644 index 0000000..9159cce --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2p.m @@ -0,0 +1,52 @@ +function p = contour2p(lon, lat, dep, esize) +% contour2p Converts contour lines to mesh structure. +% p = contour2p(lon, lat, depth, esize, geofile) converts the +% ordered contour lines with coordinates lon, lat, depth into a +% mesh structure p, with elements of size esize, meshed using +% Gmsh. +% + +% Check for preferences file +if exist('gmshfaultspref.mat', 'file') ~= 0 % If this .mat file exists, + load('gmshfaultspref.mat', 'gmshpath') % Load it +else % If not, + if ismac + if exist('/Applications/Gmsh.app/Contents/MacOS/gmsh', 'file') % Check for default install location + gmshpath = '/Applications/Gmsh.app/Contents/MacOS/'; + else + gmshpath = ''; % Or ask for install location + while ~exist([gmshpath filesep 'gmsh'], 'file') + gmshpath = input('Enter path to Gmsh application: '); + end + end + % Save Gmsh path to preferences file, to be read in future runs + gmfp = fileparts(which('gmshfaults')); + save([gmfp filesep 'gmshfaultspref.mat'], 'gmshpath'); + elseif ispc || (isunix && ~ismac) + gmshpath = ''; % Or ask for install location + while ~exist([gmshpath filesep 'gmsh.exe'], 'file') + gmshpath = input('Enter path to Gmsh application: '); + end + % Save Gmsh path to preferences file, to be read in future runs + gmfp = fileparts(which('gmshfaults')); + save([gmfp filesep 'gmshfaultspref.mat'], 'gmshpath'); + end +end + +% Write geo file, first checking version +geofile = 'from_contour2p'; +[~, gvers] = system(sprintf('%s/gmsh -version', gmshpath)); +gvers = regexp(gvers, '\d+.\d+.\d+', 'match'); +gvers = str2num(gvers{end}(1)); +contour2geo(lon, lat, dep, esize, geofile, gvers) + +% Do the meshing +system(sprintf('%s/gmsh -2 %s.geo -o %s.msh -v 0 > junk', gmshpath, geofile, geofile)); + +% Read in the mesh coordinates +p = ReadPatches([geofile '.msh']); + +% Convert from geocentric to geographic +[lon, lat] = xyz_to_long_lat(p.c(:, 1), p.c(:, 2), p.c(:, 3)); % Long, lat +cdis = mag(p.c, 2); % Distance from earth center +p.c = [rad2deg(lon), rad2deg(lat), cdis-6371]; \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2xyz.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2xyz.m new file mode 100644 index 0000000..5b040b8 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/contour2xyz.m @@ -0,0 +1,36 @@ +function varargout = contour2xyz(c) +% contour2xyz Converts contour array to x, y, z +% [x, y, z] = contour2xyz(c) converts the contour array c +% to vectors x, y, and z. +% +% xyz = contour2xyz(c) converts the contour array to the +% 3-column array xyz. +% +% + +% Allocate space for arrays +[x, y, z] = deal(zeros(size(c, 2), 1)); + +i = 0; % Counting variable along columns of contours +j = 1; % Count number of contour lines +while i < size(c, 2) + cn = c(2, i+1); % Get length of contour + dep = c(1, i+1); % Get contour interval + x(i+(1:cn)) = c(1, i+(2:cn+1)); % Insert x coordinates + y(i+(1:cn)) = c(2, i+(2:cn+1)); % Insert y coordinates + z(i+(1:cn)) = dep; % Replicate z coordinate + i = i+1+cn; % Increment counter + j = j+1; % Increment number of contour lines +end +keep = x ~= 0; +x = x(keep); +y = y(keep); +z = z(keep); + +if nargout == 1 + varargout{1} = [x(:), y(:), z(:)]; +elseif nargout == 3 + varargout{1} = x; + varargout{2} = y; + varargout{3} = z; +end diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults.txt new file mode 100644 index 0000000..0c8ad4e --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults.txt @@ -0,0 +1,116 @@ +-18.63010257,66.25470531,0 +-17.74118039,66.12228332,0 +-17.44645753,66.06449194,0 +-17.30860329,66.03940814,0 +-17.21353140,65.99690228,0 +-17.13272029,65.96400827,0 +-17.08043075,65.92525514,0 +-21.52000848,63.92916700,1 +-21.23275568,64.18084898,1 +-21.14719344,64.27390757,1 +-20.96636202,64.42926655,1 +-20.64865203,64.65791818,1 +-20.54772643,64.72094451,1 +-20.69914836,63.95120622,2 +-20.67321534,64.02421587,2 +-20.58324672,63.94737367,3 +-20.56327064,64.04165796,3 +-20.52486892,64.09425718,3 +-20.26454584,63.94048160,4 +-20.27053336,64.01523136,4 +-16.32350081,66.13214507,5 +-16.62194754,65.49970506,5 +-16.86837519,65.07581282,5 +-17.02462693,64.88103145,5 +-22.40331825,63.96304261,6 +-22.43659341,63.94843264,6 +-22.46986857,63.93903649,6 +-22.63149079,63.86689457,6 +-22.72893948,63.82498819,6 +-21.80911893,64.07653123,7 +-22.05155225,63.92023474,7 +-22.07532023,63.90455697,7 +-22.20129048,63.83966253,7 +-17.16336804,64.81495078,8 +-19.38129974,63.97962612,8 +-16.09187425,65.06443163,9 +-16.40088948,64.88492441,9 +-16.60380407,64.74335270,9 +-19.07709697,65.23372953,10 +-19.02384852,65.12263194,10 +-18.94875958,65.03554334,10 +-19.21428937,65.06917950,11 +-19.15486349,64.94625513,11 +-17.06560572,66.19757781,12 +-17.02684976,65.92087938,12 +-17.08586228,65.75703847,12 +-17.13728425,65.61085854,12 +-16.50270513,65.22405543,13 +-16.39684426,65.35236359,13 +-16.28817988,65.58036060,13 +-16.21500078,65.83813275,13 +-16.06891552,66.09467139,13 +-19.94336941,64.00841501,14 +-19.96892093,63.92638587,14 +-21.08104872,65.47219586,15 +-21.00974480,65.33865276,15 +-20.23728569,65.89789869,16 +-20.34424157,65.59033101,16 +-21.30684446,64.68608034,17 +-21.33061244,64.49741799,17 +-16.22049829,64.12652624,18 +-15.43615519,64.31259605,18 +-14.81818790,64.43082027,19 +-15.07963560,64.30229163,19 +-14.40224838,64.89361548,20 +-14.55674020,64.72162628,20 +-15.88774667,64.92888894,21 +-15.98281856,64.77232531,21 +-17.88425638,66.08646796,22 +-18.09816814,65.97542904,22 +-18.26454395,66.14901525,23 +-18.33584787,65.98993984,23 +-18.58541158,66.17303086,24 +-18.72801942,66.02859500,24 +-18.81120732,66.22578507,25 +-18.81120732,66.09128477,25 +-19.53613049,65.79578305,26 +-19.52424651,65.64429761,26 +-19.58366644,65.85904534,27 +-19.69062231,65.69815216,27 +-18.24077598,65.82500037,28 +-18.31207989,65.68347566,28 +-18.00309625,65.79091027,29 +-18.02686422,65.64919811,29 +-14.66369608,65.78116195,30 +-14.75876797,65.64429761,30 +-14.55674020,65.39314131,31 +-14.60427614,65.21937585,31 +-15.84021073,64.79257830,32 +-15.69760289,64.92888894,32 +-19.47671056,64.30744432,33 +-19.61931840,64.16280452,33 +-20.39177751,64.09539284,34 +-20.05902589,64.14726249,34 +-20.22540170,64.32804545,35 +-20.04714191,64.44107662,35 +-19.64150184,64.13447697,36 +-19.90770313,64.09296989,36 +-14.93528478,64.69099184,37 +-14.63105473,64.59735101,37 +-17.88251340,65.86763052,38 +-19.60331463,66.16134611,38 +-18.29517104,66.08080968,39 +-17.98479909,66.03433778,39 +-16.58806687,66.27176015,40 +-16.61183485,66.22197713,40 +-17.07768711,66.30807794,41 +-17.08719430,66.26410762,41 +-17.07768711,66.23538992,41 +-17.06817992,66.22772634,41 +-17.37716357,66.44902736,42 +-17.40568514,66.40340088,42 +-17.73843675,66.58918573,43 +-17.67664002,66.51731110,43 +-18.12823151,66.82882968,44 +-17.99275406,66.72761761,44 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long.txt new file mode 100644 index 0000000..858d5a3 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long.txt @@ -0,0 +1,118 @@ +0 +451114.3713 5243050.767 0 +451134.4797 5243102.625 0 +451163.0547 5243156.6 0 +451213.8548 5243223.275 0 +451256.1882 5243246.559 0 +451351.4384 5243329.638 0 +451416.6429 5243369.066 0 +451584.2722 5243453.463 0 +451625.5473 5243468.28 0 +451735.3496 5243495.797 0 +451822.6623 5243512.465 0 +451868.6999 5243529.928 0 +451932.9938 5243545.803 0 +451987.7626 5243567.234 0 +452025.7738 5243594.616 0 +452025.7738 5243594.616 0 +452034.2168 5243599.619 0 +452068.0835 5243617.611 0 +452098.9124 5243634.271 0 +452107.8064 5243639.078 0 +452158.0773 5243665.536 0 +452221.5774 5243691.994 0 +452282.4317 5243721.099 0 +452327.411 5243735.651 0 +452363.1298 5243740.942 0 +452398.8486 5243742.265 0 +452432.2305 5243743.758 0 +452475.9205 5243747.9 0 +452475.9205 5243747.9 0 +452599.7462 5243793.946 0 +452739.1815 5243845.796 0 +453208.8178 5244001.901 0 +453226.0158 5244004.546 0 +453298.7764 5244023.067 0 +453491.8123 5244093.733 0 +453711.4169 5244179.723 0 +END +1 +440273.9193 5233384.48 0 +442106.1626 5234647.868 0 +443442.3111 5235712.818 0 +444044.2393 5236546.257 0 +444746.0486 5237139.905 0 +445611.2378 5237929.688 0 +446476.4601 5238959.138 0 +446530.4353 5239033.221 0 +446636.798 5239195.147 0 +446691.8314 5239252.297 0 +446902.5908 5239449.944 0 +447217.9748 5239787.553 0 +447313.0743 5239920.106 0 +447357.8224 5239959.571 0 +447408.6225 5240023.071 0 +447449.8976 5240077.84 0 +447481.6477 5240123.083 0 +447503.079 5240144.515 0 +447526.8915 5240168.327 0 +447550.7041 5240187.377 0 +447742.792 5240377.878 0 +448023.78 5240556.472 0 +448344.5332 5240790.299 0 +448528.2205 5240931.058 0 +448715.6227 5241073.425 0 +448756.6332 5241108.482 0 +448783.7531 5241127.003 0 +448815.1062 5241145.524 0 +448838.2573 5241158.753 0 +449126.6537 5241338.67 0 +449213.3208 5241446.202 0 +449327.0918 5241552.036 0 +449450.3886 5241661.132 0 +449519.445 5241723.044 0 +449541.293 5241729.676 0 +449680.1996 5241797.145 0 +449844.0887 5241857.366 0 +450030.7732 5241926.791 0 +450247.732 5242043.208 0 +450347.5724 5242086.059 0 +450388.9252 5242103.807 0 +450410.5426 5242117.065 0 +450535.0978 5242191.63 0 +450615.9686 5242262.188 0 +450672.6814 5242310.031 0 +450784.9288 5242410.753 0 +450865.6269 5242474.253 0 +450883.6961 5242487.966 0 +450947.1872 5242519.714 0 +450962.3732 5242530.931 0 +450977.1899 5242543.631 0 +450996.2399 5242557.389 0 +451007.8816 5242573.264 0 +451034.34 5242589.139 0 +451050.215 5242600.781 0 +451081.7724 5242621.212 0 +451065.0317 5242611.364 0 +END +2 +455312.8596 5243707.058 0 +455973.261 5243823.475 0 +456320.395 5243922.959 0 +456707.7458 5244069.009 0 +457054.8798 5244215.059 0 +END +3 +454330.2745 5241822.582 0 +463035.0835 5246346.966 0 +END +4 +455098.8906 5243775.211 0 +457067.3945 5244558.379 0 +460962.5508 5246855.263 0 +463672.7306 5248416.012 0 +466948.7607 5250360.999 0 +469991.4751 5252643.035 0 +472835.7517 5253469.859 0 +480471.1601 5256903.862 0 +END \ No newline at end of file diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f1.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f1.txt new file mode 100644 index 0000000..7c48119 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f1.txt @@ -0,0 +1,36 @@ + 4.5111437e+05 5.2430508e+06 -1.0000000e+04 + 4.5113448e+05 5.2431026e+06 -1.0000000e+04 + 4.5116305e+05 5.2431566e+06 -1.0000000e+04 + 4.5121385e+05 5.2432233e+06 -1.0000000e+04 + 4.5125619e+05 5.2432466e+06 -1.0000000e+04 + 4.5135144e+05 5.2433296e+06 -1.0000000e+04 + 4.5141664e+05 5.2433691e+06 -1.0000000e+04 + 4.5158427e+05 5.2434535e+06 -1.0000000e+04 + 4.5162555e+05 5.2434683e+06 -1.0000000e+04 + 4.5173535e+05 5.2434958e+06 -1.0000000e+04 + 4.5182266e+05 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5.2440045e+06 -1.0000000e+04 + 4.5329878e+05 5.2440231e+06 -1.0000000e+04 + 4.5349181e+05 5.2440937e+06 -1.0000000e+04 + 4.5371142e+05 5.2441797e+06 -1.0000000e+04 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f2.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f2.txt new file mode 100644 index 0000000..68b1e15 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f2.txt @@ -0,0 +1,57 @@ + 4.4027392e+05 5.2333845e+06 -1.0000000e+04 + 4.4210616e+05 5.2346479e+06 -1.0000000e+04 + 4.4344231e+05 5.2357128e+06 -1.0000000e+04 + 4.4404424e+05 5.2365463e+06 -1.0000000e+04 + 4.4474605e+05 5.2371399e+06 -1.0000000e+04 + 4.4561124e+05 5.2379297e+06 -1.0000000e+04 + 4.4647646e+05 5.2389591e+06 -1.0000000e+04 + 4.4653044e+05 5.2390332e+06 -1.0000000e+04 + 4.4663680e+05 5.2391951e+06 -1.0000000e+04 + 4.4669183e+05 5.2392523e+06 -1.0000000e+04 + 4.4690259e+05 5.2394499e+06 -1.0000000e+04 + 4.4721797e+05 5.2397876e+06 -1.0000000e+04 + 4.4731307e+05 5.2399201e+06 -1.0000000e+04 + 4.4735782e+05 5.2399596e+06 -1.0000000e+04 + 4.4740862e+05 5.2400231e+06 -1.0000000e+04 + 4.4744990e+05 5.2400778e+06 -1.0000000e+04 + 4.4748165e+05 5.2401231e+06 -1.0000000e+04 + 4.4750308e+05 5.2401445e+06 -1.0000000e+04 + 4.4752689e+05 5.2401683e+06 -1.0000000e+04 + 4.4755070e+05 5.2401874e+06 -1.0000000e+04 + 4.4774279e+05 5.2403779e+06 -1.0000000e+04 + 4.4802378e+05 5.2405565e+06 -1.0000000e+04 + 4.4834453e+05 5.2407903e+06 -1.0000000e+04 + 4.4852822e+05 5.2409311e+06 -1.0000000e+04 + 4.4871562e+05 5.2410734e+06 -1.0000000e+04 + 4.4875663e+05 5.2411085e+06 -1.0000000e+04 + 4.4878375e+05 5.2411270e+06 -1.0000000e+04 + 4.4881511e+05 5.2411455e+06 -1.0000000e+04 + 4.4883826e+05 5.2411588e+06 -1.0000000e+04 + 4.4912665e+05 5.2413387e+06 -1.0000000e+04 + 4.4921332e+05 5.2414462e+06 -1.0000000e+04 + 4.4932709e+05 5.2415520e+06 -1.0000000e+04 + 4.4945039e+05 5.2416611e+06 -1.0000000e+04 + 4.4951945e+05 5.2417230e+06 -1.0000000e+04 + 4.4954129e+05 5.2417297e+06 -1.0000000e+04 + 4.4968020e+05 5.2417971e+06 -1.0000000e+04 + 4.4984409e+05 5.2418574e+06 -1.0000000e+04 + 4.5003077e+05 5.2419268e+06 -1.0000000e+04 + 4.5024773e+05 5.2420432e+06 -1.0000000e+04 + 4.5034757e+05 5.2420861e+06 -1.0000000e+04 + 4.5038893e+05 5.2421038e+06 -1.0000000e+04 + 4.5041054e+05 5.2421171e+06 -1.0000000e+04 + 4.5053510e+05 5.2421916e+06 -1.0000000e+04 + 4.5061597e+05 5.2422622e+06 -1.0000000e+04 + 4.5067268e+05 5.2423100e+06 -1.0000000e+04 + 4.5078493e+05 5.2424108e+06 -1.0000000e+04 + 4.5086563e+05 5.2424743e+06 -1.0000000e+04 + 4.5088370e+05 5.2424880e+06 -1.0000000e+04 + 4.5094719e+05 5.2425197e+06 -1.0000000e+04 + 4.5096237e+05 5.2425309e+06 -1.0000000e+04 + 4.5097719e+05 5.2425436e+06 -1.0000000e+04 + 4.5099624e+05 5.2425574e+06 -1.0000000e+04 + 4.5100788e+05 5.2425733e+06 -1.0000000e+04 + 4.5103434e+05 5.2425891e+06 -1.0000000e+04 + 4.5105022e+05 5.2426008e+06 -1.0000000e+04 + 4.5108177e+05 5.2426212e+06 -1.0000000e+04 + 4.5106503e+05 5.2426114e+06 -1.0000000e+04 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f3.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f3.txt new file mode 100644 index 0000000..f38ffa8 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f3.txt @@ -0,0 +1,5 @@ + 4.5531286e+05 5.2437071e+06 -1.0000000e+04 + 4.5597326e+05 5.2438235e+06 -1.0000000e+04 + 4.5632040e+05 5.2439230e+06 -1.0000000e+04 + 4.5670775e+05 5.2440690e+06 -1.0000000e+04 + 4.5705488e+05 5.2442151e+06 -1.0000000e+04 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f4.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f4.txt new file mode 100644 index 0000000..a560925 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f4.txt @@ -0,0 +1,2 @@ + 4.5433027e+05 5.2418226e+06 -1.0000000e+04 + 4.6303508e+05 5.2463470e+06 -1.0000000e+04 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f5.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f5.txt new file mode 100644 index 0000000..f40320c --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords/f5.txt @@ -0,0 +1,8 @@ + 4.5509889e+05 5.2437752e+06 -1.0000000e+04 + 4.5706739e+05 5.2445584e+06 -1.0000000e+04 + 4.6096255e+05 5.2468553e+06 -1.0000000e+04 + 4.6367273e+05 5.2484160e+06 -1.0000000e+04 + 4.6694876e+05 5.2503610e+06 -1.0000000e+04 + 4.6999148e+05 5.2526430e+06 -1.0000000e+04 + 4.7283575e+05 5.2534699e+06 -1.0000000e+04 + 4.8047116e+05 5.2569039e+06 -1.0000000e+04 diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f1.geo b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f1.geo new file mode 100644 index 0000000..d484477 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f1.geo @@ -0,0 +1,79 @@ +charl = 500; +Point(1) = {451114, 5.24305e+06, 0, charl}; +Point(2) = {451134, 5.2431e+06, 0, charl}; +Point(3) = {451163, 5.24316e+06, 0, charl}; +Point(4) = {451214, 5.24322e+06, 0, charl}; +Point(5) = {451256, 5.24325e+06, 0, charl}; +Point(6) = {451351, 5.24333e+06, 0, charl}; +Point(7) = {451417, 5.24337e+06, 0, charl}; +Point(8) = {451584, 5.24345e+06, 0, charl}; +Point(9) = {451626, 5.24347e+06, 0, charl}; +Point(10) = {451735, 5.2435e+06, 0, charl}; +Point(11) = {451823, 5.24351e+06, 0, charl}; +Point(12) = {451869, 5.24353e+06, 0, charl}; +Point(13) = {451933, 5.24355e+06, 0, charl}; +Point(14) = {451988, 5.24357e+06, 0, charl}; +Point(15) = {452026, 5.24359e+06, 0, charl}; +Point(16) = {452026, 5.24359e+06, 0, charl}; +Point(17) = {452034, 5.2436e+06, 0, charl}; +Point(18) = {452068, 5.24362e+06, 0, charl}; +Point(19) = {452099, 5.24363e+06, 0, charl}; +Point(20) = {452108, 5.24364e+06, 0, charl}; +Point(21) = {452158, 5.24367e+06, 0, charl}; +Point(22) = {452222, 5.24369e+06, 0, charl}; +Point(23) = {452282, 5.24372e+06, 0, charl}; +Point(24) = {452327, 5.24374e+06, 0, charl}; +Point(25) = {452363, 5.24374e+06, 0, charl}; +Point(26) = {452399, 5.24374e+06, 0, charl}; +Point(27) = {452432, 5.24374e+06, 0, charl}; +Point(28) = {452476, 5.24375e+06, 0, charl}; +Point(29) = {452476, 5.24375e+06, 0, charl}; +Point(30) = {452600, 5.24379e+06, 0, charl}; +Point(31) = {452739, 5.24385e+06, 0, charl}; +Point(32) = {453209, 5.244e+06, 0, charl}; +Point(33) = {453226, 5.244e+06, 0, charl}; +Point(34) = {453299, 5.24402e+06, 0, charl}; +Point(35) = {453492, 5.24409e+06, 0, charl}; +Point(36) = {453711, 5.24418e+06, 0, charl}; +Point(37) = {451825, 5.24882e+06, -8695.73, charl}; +Point(38) = {451606, 5.24873e+06, -8694.23, charl}; +Point(39) = {451413, 5.24866e+06, -8690.59, charl}; +Point(40) = {451341, 5.24864e+06, -8685.51, charl}; +Point(41) = {451324, 5.24864e+06, -8683.48, charl}; +Point(42) = {450856, 5.24848e+06, -8667.37, charl}; +Point(43) = {450717, 5.24843e+06, -8665.17, charl}; +Point(44) = {450593, 5.24838e+06, -8663.16, charl}; +Point(45) = {450593, 5.24838e+06, -8663.16, charl}; +Point(46) = {450550, 5.24838e+06, -8656.84, charl}; +Point(47) = {450517, 5.24837e+06, -8651.25, charl}; +Point(48) = {450482, 5.24837e+06, -8645.17, charl}; +Point(49) = {450447, 5.24836e+06, -8640.86, charl}; +Point(50) = {450402, 5.24835e+06, -8639.15, charl}; +Point(51) = {450341, 5.24832e+06, -8641.18, charl}; +Point(52) = {450277, 5.24829e+06, -8641.5, charl}; +Point(53) = {450227, 5.24827e+06, -8644.26, charl}; +Point(54) = {450218, 5.24826e+06, -8644.81, charl}; +Point(55) = {450187, 5.24825e+06, -8646.74, charl}; +Point(56) = {450153, 5.24823e+06, -8648.71, charl}; +Point(57) = {450144, 5.24822e+06, -8649.43, charl}; +Point(58) = {450144, 5.24822e+06, -8649.43, charl}; +Point(59) = {450106, 5.2482e+06, -8654.97, charl}; +Point(60) = {450051, 5.24818e+06, -8654.57, charl}; +Point(61) = {449987, 5.24816e+06, -8649.83, charl}; +Point(62) = {449941, 5.24814e+06, -8649.23, charl}; +Point(63) = {449855, 5.24812e+06, -8640.53, charl}; +Point(64) = {449746, 5.24809e+06, -8632.6, charl}; +Point(65) = {449705, 5.24808e+06, -8631.68, charl}; +Point(66) = {449536, 5.248e+06, -8639.22, charl}; +Point(67) = {449470, 5.24796e+06, -8645.24, charl}; +Point(68) = {449373, 5.24788e+06, -8665.76, charl}; +Point(69) = {449331, 5.24786e+06, -8668.58, charl}; +Point(70) = {449278, 5.2478e+06, -8689.91, charl}; +Point(71) = {449247, 5.24775e+06, -8709.55, charl}; +Point(72) = {449225, 5.2477e+06, -8729.76, charl}; +CatmullRom(1) = {1:36}; +CatmullRom(2) = {37:72}; +CatmullRom(3) = {36,37}; +CatmullRom(4) = {72,1}; +Line Loop(1) = {1, 3, 2, 4}; +Ruled Surface(1) = {1}; diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f1.msh b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f1.msh new file mode 100644 index 0000000..db69ec5 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f1.msh @@ -0,0 +1,681 @@ +$MeshFormat +2.2 0 8 +$EndMeshFormat +$Nodes +246 +1 451114 5243050 0 +2 451134 5243100 0 +3 451163 5243160 0 +4 451214 5243220 0 +5 451256 5243250 0 +6 451351 5243330 0 +7 451417 5243370 0 +8 451584 5243450 0 +9 451626 5243470 0 +10 451735 5243500 0 +11 451823 5243510 0 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Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f2.txt new file mode 100644 index 0000000..aff6561 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f2.txt @@ -0,0 +1,57 @@ + 4.3698794e+05 5.2371729e+06 -8.7160538e+03 + 4.3879858e+05 5.2384612e+06 -8.8391269e+03 + 4.4012849e+05 5.2395333e+06 -8.8746479e+03 + 4.4075107e+05 5.2403430e+06 -8.7570279e+03 + 4.4145188e+05 5.2409378e+06 -8.7627435e+03 + 4.4231968e+05 5.2417246e+06 -8.7478781e+03 + 4.4320339e+05 5.2427326e+06 -8.6425228e+03 + 4.4325918e+05 5.2428046e+06 -8.6322191e+03 + 4.4337016e+05 5.2429612e+06 -8.6059130e+03 + 4.4342582e+05 5.2430177e+06 -8.6023367e+03 + 4.4363756e+05 5.2432142e+06 -8.5967495e+03 + 4.4395719e+05 5.2435470e+06 -8.5725202e+03 + 4.4405561e+05 5.2436756e+06 -8.5536298e+03 + 4.4410041e+05 5.2437151e+06 -8.5533711e+03 + 4.4415250e+05 5.2437771e+06 -8.5460294e+03 + 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Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f3.geo b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f3.geo new file mode 100644 index 0000000..cf2bd26 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f3.geo @@ -0,0 +1,17 @@ +charl = 500; +Point(1) = {455313, 5.24371e+06, 0, charl}; +Point(2) = {455973, 5.24382e+06, 0, charl}; +Point(3) = {456320, 5.24392e+06, 0, charl}; +Point(4) = {456708, 5.24407e+06, 0, charl}; +Point(5) = {457055, 5.24422e+06, 0, charl}; +Point(6) = {455607, 5.249e+06, -8645.39, charl}; +Point(7) = {455258, 5.24886e+06, -8665, charl}; +Point(8) = {454870, 5.24871e+06, -8678.75, charl}; +Point(9) = {454523, 5.24861e+06, -8676.06, charl}; +Point(10) = {453866, 5.24849e+06, -8636.07, charl}; +CatmullRom(1) = {1:5}; +CatmullRom(2) = 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Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f3.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f3.txt new file mode 100644 index 0000000..019a2ce --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_-60dip/f3.txt @@ -0,0 +1,5 @@ + 4.5386574e+05 5.2484863e+06 -8.6360707e+03 + 4.5452303e+05 5.2486130e+06 -8.6760601e+03 + 4.5486997e+05 5.2487132e+06 -8.6787455e+03 + 4.5525838e+05 5.2488557e+06 -8.6650050e+03 + 4.5560704e+05 5.2489967e+06 -8.6453889e+03 diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.geo b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.geo new file mode 100644 index 0000000..b4740b4 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.geo @@ -0,0 +1,79 @@ +charl = 100; +Point(1) = {451114, 5.24305e+06, 0, charl}; +Point(2) = {451134, 5.2431e+06, 0, charl}; +Point(3) = {451163, 5.24316e+06, 0, charl}; +Point(4) = {451214, 5.24322e+06, 0, charl}; +Point(5) = {451256, 5.24325e+06, 0, charl}; +Point(6) = {451351, 5.24333e+06, 0, charl}; +Point(7) = {451417, 5.24337e+06, 0, charl}; +Point(8) = {451584, 5.24345e+06, 0, charl}; +Point(9) = {451626, 5.24347e+06, 0, charl}; +Point(10) = {451735, 5.2435e+06, 0, charl}; +Point(11) = {451823, 5.24351e+06, 0, charl}; +Point(12) = {451869, 5.24353e+06, 0, charl}; +Point(13) = {451933, 5.24355e+06, 0, charl}; +Point(14) = {451988, 5.24357e+06, 0, charl}; +Point(15) = {452026, 5.24359e+06, 0, charl}; +Point(16) = {452026, 5.24359e+06, 0, charl}; +Point(17) = {452034, 5.2436e+06, 0, charl}; +Point(18) = {452068, 5.24362e+06, 0, charl}; +Point(19) = {452099, 5.24363e+06, 0, charl}; +Point(20) = {452108, 5.24364e+06, 0, charl}; +Point(21) = {452158, 5.24367e+06, 0, charl}; +Point(22) = {452222, 5.24369e+06, 0, charl}; +Point(23) = {452282, 5.24372e+06, 0, charl}; +Point(24) = {452327, 5.24374e+06, 0, charl}; +Point(25) = {452363, 5.24374e+06, 0, charl}; +Point(26) = {452399, 5.24374e+06, 0, charl}; +Point(27) = {452432, 5.24374e+06, 0, charl}; +Point(28) = {452476, 5.24375e+06, 0, charl}; +Point(29) = {452476, 5.24375e+06, 0, charl}; +Point(30) = {452600, 5.24379e+06, 0, charl}; +Point(31) = {452739, 5.24385e+06, 0, charl}; +Point(32) = {453209, 5.244e+06, 0, charl}; +Point(33) = {453226, 5.244e+06, 0, charl}; +Point(34) = {453299, 5.24402e+06, 0, charl}; +Point(35) = {453492, 5.24409e+06, 0, charl}; +Point(36) = {453711, 5.24418e+06, 0, charl}; +Point(37) = {455590, 5.23956e+06, -8624.78, charl}; +Point(38) = {455371, 5.23947e+06, -8626.28, charl}; +Point(39) = {455178, 5.2394e+06, -8629.92, charl}; +Point(40) = {455106, 5.23938e+06, -8635, charl}; +Point(41) = {455089, 5.23938e+06, -8637.03, charl}; +Point(42) = {454621, 5.23922e+06, -8653.14, charl}; +Point(43) = {454482, 5.23916e+06, -8655.34, charl}; +Point(44) = {454358, 5.23912e+06, -8657.35, charl}; +Point(45) = {454358, 5.23912e+06, -8657.35, charl}; +Point(46) = {454315, 5.23911e+06, -8663.67, charl}; +Point(47) = {454282, 5.23911e+06, -8669.26, charl}; +Point(48) = {454247, 5.23911e+06, -8675.34, charl}; +Point(49) = {454212, 5.2391e+06, -8679.65, charl}; +Point(50) = {454167, 5.23908e+06, -8681.36, charl}; +Point(51) = {454106, 5.23906e+06, -8679.33, charl}; +Point(52) = {454042, 5.23903e+06, -8679.01, charl}; +Point(53) = {453992, 5.239e+06, -8676.24, charl}; +Point(54) = {453983, 5.239e+06, -8675.7, charl}; +Point(55) = {453952, 5.23898e+06, -8673.76, charl}; +Point(56) = {453918, 5.23896e+06, -8671.8, charl}; +Point(57) = {453909, 5.23896e+06, -8671.08, charl}; +Point(58) = {453909, 5.23896e+06, -8671.08, charl}; +Point(59) = {453871, 5.23893e+06, -8665.54, charl}; +Point(60) = {453816, 5.23891e+06, -8665.94, charl}; +Point(61) = {453752, 5.2389e+06, -8670.67, charl}; +Point(62) = {453706, 5.23888e+06, -8671.28, charl}; +Point(63) = {453620, 5.23886e+06, -8679.98, charl}; +Point(64) = {453511, 5.23883e+06, -8687.91, charl}; +Point(65) = {453470, 5.23881e+06, -8688.83, charl}; +Point(66) = {453301, 5.23873e+06, -8681.29, charl}; +Point(67) = {453235, 5.23869e+06, -8675.27, charl}; +Point(68) = {453138, 5.23862e+06, -8654.75, charl}; +Point(69) = {453096, 5.23859e+06, -8651.93, charl}; +Point(70) = {453043, 5.23853e+06, -8630.6, charl}; +Point(71) = {453012, 5.23848e+06, -8610.96, charl}; +Point(72) = {452990, 5.23844e+06, -8590.75, charl}; +CatmullRom(1) = {1:36}; +CatmullRom(2) = {37:72}; +CatmullRom(3) = {36,37}; +CatmullRom(4) = {72,1}; +Line Loop(1) = {1, 3, 2, 4}; +Ruled Surface(1) = {1}; diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.msh b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.msh new file mode 100644 index 0000000..6018cdb --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.msh @@ -0,0 +1,10662 @@ +$MeshFormat +4 0 8 +$EndMeshFormat +$Entities +72 4 1 0 +1 451114 5243050 0 451114 5243050 0 0 +2 451134 5243100 0 451134 5243100 0 0 +3 451163 5243160 0 451163 5243160 0 0 +4 451214 5243220 0 451214 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Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.txt new file mode 100644 index 0000000..fe5b50f --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f1.txt @@ -0,0 +1,36 @@ + 4.5298984e+05 5.2384360e+06 -8.5907521e+03 + 4.5301199e+05 5.2384827e+06 -8.6109606e+03 + 4.5304254e+05 5.2385319e+06 -8.6305957e+03 + 4.5309550e+05 5.2385933e+06 -8.6519287e+03 + 4.5313812e+05 5.2386159e+06 -8.6547510e+03 + 4.5323544e+05 5.2386938e+06 -8.6752667e+03 + 4.5330125e+05 5.2387318e+06 -8.6812896e+03 + 4.5346964e+05 5.2388143e+06 -8.6888283e+03 + 4.5351083e+05 5.2388293e+06 -8.6879129e+03 + 4.5361983e+05 5.2388588e+06 -8.6799815e+03 + 4.5370626e+05 5.2388777e+06 -8.6712811e+03 + 4.5375224e+05 5.2388952e+06 -8.6706740e+03 + 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4.5537087e+05 5.2394700e+06 -8.6262831e+03 + 4.5559033e+05 5.2395564e+06 -8.6247778e+03 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f2.geo b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f2.geo new file mode 100644 index 0000000..0b6e51b --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f2.geo @@ -0,0 +1,121 @@ +charl = 100; +Point(1) = {440274, 5.23338e+06, 0, charl}; +Point(2) = {442106, 5.23465e+06, 0, charl}; +Point(3) = {443442, 5.23571e+06, 0, charl}; +Point(4) = {444044, 5.23655e+06, 0, charl}; +Point(5) = {444746, 5.23714e+06, 0, charl}; +Point(6) = {445611, 5.23793e+06, 0, charl}; +Point(7) = {446476, 5.23896e+06, 0, charl}; +Point(8) = {446530, 5.23903e+06, 0, charl}; +Point(9) = {446637, 5.2392e+06, 0, charl}; +Point(10) = {446692, 5.23925e+06, 0, charl}; +Point(11) = {446903, 5.23945e+06, 0, charl}; +Point(12) = {447218, 5.23979e+06, 0, charl}; +Point(13) = {447313, 5.23992e+06, 0, charl}; +Point(14) = {447358, 5.23996e+06, 0, charl}; +Point(15) = {447409, 5.24002e+06, 0, charl}; +Point(16) = {447450, 5.24008e+06, 0, charl}; +Point(17) = {447482, 5.24012e+06, 0, charl}; +Point(18) = {447503, 5.24014e+06, 0, charl}; +Point(19) = {447527, 5.24017e+06, 0, charl}; +Point(20) = {447551, 5.24019e+06, 0, charl}; +Point(21) = {447743, 5.24038e+06, 0, charl}; +Point(22) = {448024, 5.24056e+06, 0, charl}; +Point(23) = {448345, 5.24079e+06, 0, charl}; +Point(24) = {448528, 5.24093e+06, 0, charl}; +Point(25) = {448716, 5.24107e+06, 0, charl}; +Point(26) = {448757, 5.24111e+06, 0, charl}; +Point(27) = {448784, 5.24113e+06, 0, charl}; +Point(28) = {448815, 5.24115e+06, 0, charl}; +Point(29) = {448838, 5.24116e+06, 0, charl}; +Point(30) = {449127, 5.24134e+06, 0, charl}; 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Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f3.geo b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f3.geo new file mode 100644 index 0000000..ef28334 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_botcoords_60dip/f3.geo @@ -0,0 +1,17 @@ +charl = 100; +Point(1) = {455313, 5.24371e+06, 0, charl}; +Point(2) = {455973, 5.24382e+06, 0, charl}; +Point(3) = {456320, 5.24392e+06, 0, charl}; +Point(4) = {456708, 5.24407e+06, 0, charl}; +Point(5) = {457055, 5.24422e+06, 0, charl}; +Point(6) = {458505, 5.23943e+06, -8675.12, charl}; +Point(7) = {458156, 5.23928e+06, -8655.5, charl}; +Point(8) = {457768, 5.23914e+06, -8641.76, charl}; +Point(9) = {457421, 5.23904e+06, -8644.45, charl}; +Point(10) = {456764, 5.23892e+06, -8684.44, charl}; +CatmullRom(1) = {1:5}; +CatmullRom(2) = 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Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f1.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f1.txt new file mode 100644 index 0000000..0793ebe --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f1.txt @@ -0,0 +1,36 @@ + 4.5111437e+05 5.2430508e+06 0.0000000e+00 + 4.5113448e+05 5.2431026e+06 0.0000000e+00 + 4.5116305e+05 5.2431566e+06 0.0000000e+00 + 4.5121385e+05 5.2432233e+06 0.0000000e+00 + 4.5125619e+05 5.2432466e+06 0.0000000e+00 + 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0.0000000e+00 + 4.5247592e+05 5.2437479e+06 0.0000000e+00 + 4.5259975e+05 5.2437939e+06 0.0000000e+00 + 4.5273918e+05 5.2438458e+06 0.0000000e+00 + 4.5320882e+05 5.2440019e+06 0.0000000e+00 + 4.5322602e+05 5.2440045e+06 0.0000000e+00 + 4.5329878e+05 5.2440231e+06 0.0000000e+00 + 4.5349181e+05 5.2440937e+06 0.0000000e+00 + 4.5371142e+05 5.2441797e+06 0.0000000e+00 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f2.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f2.txt new file mode 100644 index 0000000..3b62a54 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f2.txt @@ -0,0 +1,57 @@ + 4.4027392e+05 5.2333845e+06 0.0000000e+00 + 4.4210616e+05 5.2346479e+06 0.0000000e+00 + 4.4344231e+05 5.2357128e+06 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4.5094719e+05 5.2425197e+06 0.0000000e+00 + 4.5096237e+05 5.2425309e+06 0.0000000e+00 + 4.5097719e+05 5.2425436e+06 0.0000000e+00 + 4.5099624e+05 5.2425574e+06 0.0000000e+00 + 4.5100788e+05 5.2425733e+06 0.0000000e+00 + 4.5103434e+05 5.2425891e+06 0.0000000e+00 + 4.5105022e+05 5.2426008e+06 0.0000000e+00 + 4.5108177e+05 5.2426212e+06 0.0000000e+00 + 4.5106503e+05 5.2426114e+06 0.0000000e+00 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f3.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f3.txt new file mode 100644 index 0000000..ea18629 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f3.txt @@ -0,0 +1,5 @@ + 4.5531286e+05 5.2437071e+06 0.0000000e+00 + 4.5597326e+05 5.2438235e+06 0.0000000e+00 + 4.5632040e+05 5.2439230e+06 0.0000000e+00 + 4.5670775e+05 5.2440690e+06 0.0000000e+00 + 4.5705488e+05 5.2442151e+06 0.0000000e+00 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f4.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f4.txt new file mode 100644 index 0000000..73fdd0c --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f4.txt @@ -0,0 +1,2 @@ + 4.5433027e+05 5.2418226e+06 0.0000000e+00 + 4.6303508e+05 5.2463470e+06 0.0000000e+00 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f5.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f5.txt new file mode 100644 index 0000000..9e0426c --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faults_long_topcoords/f5.txt @@ -0,0 +1,8 @@ + 4.5509889e+05 5.2437752e+06 0.0000000e+00 + 4.5706739e+05 5.2445584e+06 0.0000000e+00 + 4.6096255e+05 5.2468553e+06 0.0000000e+00 + 4.6367273e+05 5.2484160e+06 0.0000000e+00 + 4.6694876e+05 5.2503610e+06 0.0000000e+00 + 4.6999148e+05 5.2526430e+06 0.0000000e+00 + 4.7283575e+05 5.2534699e+06 0.0000000e+00 + 4.8047116e+05 5.2569039e+06 0.0000000e+00 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faultsutm.txt b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faultsutm.txt new file mode 100644 index 0000000..c9f5aca --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/faultsutm.txt @@ -0,0 +1,116 @@ + -1.8630103e+01 6.6254705e+01 0.0000000e+00 + -1.7741180e+01 6.6122283e+01 0.0000000e+00 + -1.7446458e+01 6.6064492e+01 0.0000000e+00 + -1.7308603e+01 6.6039408e+01 0.0000000e+00 + -1.7213531e+01 6.5996902e+01 0.0000000e+00 + -1.7132720e+01 6.5964008e+01 0.0000000e+00 + -1.7080431e+01 6.5925255e+01 0.0000000e+00 + -2.1520008e+01 6.3929167e+01 1.0000000e+00 + -2.1232756e+01 6.4180849e+01 1.0000000e+00 + -2.1147193e+01 6.4273908e+01 1.0000000e+00 + -2.0966362e+01 6.4429267e+01 1.0000000e+00 + -2.0648652e+01 6.4657918e+01 1.0000000e+00 + -2.0547726e+01 6.4720945e+01 1.0000000e+00 + -2.0699148e+01 6.3951206e+01 2.0000000e+00 + -2.0673215e+01 6.4024216e+01 2.0000000e+00 + -2.0583247e+01 6.3947374e+01 3.0000000e+00 + -2.0563271e+01 6.4041658e+01 3.0000000e+00 + -2.0524869e+01 6.4094257e+01 3.0000000e+00 + -2.0264546e+01 6.3940482e+01 4.0000000e+00 + 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-1.9214289e+01 6.5069180e+01 1.1000000e+01 + -1.9154863e+01 6.4946255e+01 1.1000000e+01 + -1.7065606e+01 6.6197578e+01 1.2000000e+01 + -1.7026850e+01 6.5920879e+01 1.2000000e+01 + -1.7085862e+01 6.5757038e+01 1.2000000e+01 + -1.7137284e+01 6.5610859e+01 1.2000000e+01 + -1.6502705e+01 6.5224055e+01 1.3000000e+01 + -1.6396844e+01 6.5352364e+01 1.3000000e+01 + -1.6288180e+01 6.5580361e+01 1.3000000e+01 + -1.6215001e+01 6.5838133e+01 1.3000000e+01 + -1.6068916e+01 6.6094671e+01 1.3000000e+01 + -1.9943369e+01 6.4008415e+01 1.4000000e+01 + -1.9968921e+01 6.3926386e+01 1.4000000e+01 + -2.1081049e+01 6.5472196e+01 1.5000000e+01 + -2.1009745e+01 6.5338653e+01 1.5000000e+01 + -2.0237286e+01 6.5897899e+01 1.6000000e+01 + -2.0344242e+01 6.5590331e+01 1.6000000e+01 + -2.1306844e+01 6.4686080e+01 1.7000000e+01 + -2.1330612e+01 6.4497418e+01 1.7000000e+01 + -1.6220498e+01 6.4126526e+01 1.8000000e+01 + -1.5436155e+01 6.4312596e+01 1.8000000e+01 + -1.4818188e+01 6.4430820e+01 1.9000000e+01 + -1.5079636e+01 6.4302292e+01 1.9000000e+01 + -1.4402248e+01 6.4893615e+01 2.0000000e+01 + -1.4556740e+01 6.4721626e+01 2.0000000e+01 + -1.5887747e+01 6.4928889e+01 2.1000000e+01 + -1.5982819e+01 6.4772325e+01 2.1000000e+01 + -1.7884256e+01 6.6086468e+01 2.2000000e+01 + -1.8098168e+01 6.5975429e+01 2.2000000e+01 + -1.8264544e+01 6.6149015e+01 2.3000000e+01 + -1.8335848e+01 6.5989940e+01 2.3000000e+01 + -1.8585412e+01 6.6173031e+01 2.4000000e+01 + -1.8728019e+01 6.6028595e+01 2.4000000e+01 + -1.8811207e+01 6.6225785e+01 2.5000000e+01 + -1.8811207e+01 6.6091285e+01 2.5000000e+01 + -1.9536130e+01 6.5795783e+01 2.6000000e+01 + -1.9524247e+01 6.5644298e+01 2.6000000e+01 + -1.9583666e+01 6.5859045e+01 2.7000000e+01 + -1.9690622e+01 6.5698152e+01 2.7000000e+01 + -1.8240776e+01 6.5825000e+01 2.8000000e+01 + -1.8312080e+01 6.5683476e+01 2.8000000e+01 + -1.8003096e+01 6.5790910e+01 2.9000000e+01 + -1.8026864e+01 6.5649198e+01 2.9000000e+01 + -1.4663696e+01 6.5781162e+01 3.0000000e+01 + -1.4758768e+01 6.5644298e+01 3.0000000e+01 + -1.4556740e+01 6.5393141e+01 3.1000000e+01 + -1.4604276e+01 6.5219376e+01 3.1000000e+01 + -1.5840211e+01 6.4792578e+01 3.2000000e+01 + -1.5697603e+01 6.4928889e+01 3.2000000e+01 + -1.9476711e+01 6.4307444e+01 3.3000000e+01 + -1.9619318e+01 6.4162805e+01 3.3000000e+01 + -2.0391778e+01 6.4095393e+01 3.4000000e+01 + -2.0059026e+01 6.4147262e+01 3.4000000e+01 + -2.0225402e+01 6.4328045e+01 3.5000000e+01 + -2.0047142e+01 6.4441077e+01 3.5000000e+01 + -1.9641502e+01 6.4134477e+01 3.6000000e+01 + -1.9907703e+01 6.4092970e+01 3.6000000e+01 + -1.4935285e+01 6.4690992e+01 3.7000000e+01 + -1.4631055e+01 6.4597351e+01 3.7000000e+01 + -1.7882513e+01 6.5867631e+01 3.8000000e+01 + -1.9603315e+01 6.6161346e+01 3.8000000e+01 + -1.8295171e+01 6.6080810e+01 3.9000000e+01 + -1.7984799e+01 6.6034338e+01 3.9000000e+01 + -1.6588067e+01 6.6271760e+01 4.0000000e+01 + -1.6611835e+01 6.6221977e+01 4.0000000e+01 + -1.7077687e+01 6.6308078e+01 4.1000000e+01 + -1.7087194e+01 6.6264108e+01 4.1000000e+01 + -1.7077687e+01 6.6235390e+01 4.1000000e+01 + -1.7068180e+01 6.6227726e+01 4.1000000e+01 + -1.7377164e+01 6.6449027e+01 4.2000000e+01 + -1.7405685e+01 6.6403401e+01 4.2000000e+01 + -1.7738437e+01 6.6589186e+01 4.3000000e+01 + -1.7676640e+01 6.6517311e+01 4.3000000e+01 + -1.8128232e+01 6.6828830e+01 4.4000000e+01 + -1.7992754e+01 6.6727618e+01 4.4000000e+01 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmsh.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmsh.m new file mode 100644 index 0000000..f603a04 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmsh.m @@ -0,0 +1,52 @@ +function p = gmsh(geofile) +% gmsh Calls gmsh to mesh a 2-D surface. +% p = gmsh(geofile) will call Gmsh to mesh a 2-D fault +% surface from the geometry file geofile and return the +% fault to structure p. +% + +% Make sure the .geo file has .geo extension +[p, f, e] = fileparts(geofile); +if isempty(e) + geofile = [geofile '.geo']; +else + if ~startsWith(e, 'geo') + geofile = [p, f, '.geo']; + end +end + +% Check for preferences file +if exist('gmshfaultspref.mat', 'file') ~= 0 % If this .mat file exists, + load('gmshfaultspref.mat', 'gmshpath') % Load it +else % If not, + if ismac + if exist('/Applications/Gmsh.app/Contents/MacOS/gmsh', 'file') % Check for default install location + gmshpath = '/Applications/Gmsh.app/Contents/MacOS/'; + else + gmshpath = ''; % Or ask for install location + while ~exist([gmshpath filesep 'gmsh'], 'file') + gmshpath = input('Enter path to Gmsh application: '); + end + end + % Save Gmsh path to preferences file, to be read in future runs + gmfp = fileparts(which('gmshfaults')); + save([gmfp filesep 'gmshfaultspref.mat'], 'gmshpath'); + elseif ispc || (isunix && ~ismac) + gmshpath = ''; % Or ask for install location + while ~exist([gmshpath filesep 'gmsh.exe'], 'file') + gmshpath = input('Enter path to Gmsh application: '); + end + % Save Gmsh path to preferences file, to be read in future runs + gmfp = fileparts(which('gmshfaults')); + save([gmfp filesep 'gmshfaultspref.mat'], 'gmshpath'); + end +end + +% Do the meshing +system(sprintf('%s/gmsh -2 %s -o %s.msh -v 0 > junk', gmshpath, geofile, geofile(1:end-4))); + +% Read the mesh +p = ReadPatches(sprintf('%s.msh', geofile(1:end-4))); + +% Remove temp files +system('rm junk'); diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshfaults.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshfaults.m new file mode 100644 index 0000000..1d79907 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshfaults.m @@ -0,0 +1,86 @@ +function allstring = gmshfaults(topdir, botdir, sz) +% gmshfaults Meshes faults in 3D using Gmsh. +% gmshfaults(BOTDIR, ELSIZE) meshes all faults whose bottom coordinates +% are contained in text files within the folder BOTDIR, using the +% element size specified using ELSIZE. Geometry (.geo) and mesh (.msh) +% files are saved to the bottom coordinate directory. +% +% ALL = gmshfaults(...) returns a string to the command line that can be +% used to read all faults in using ReadPatches.m, i.e. +% >> p = ReadPatches(ALL); +% +% + +% Hard code full path to top coordinates directory here +%topdir = ['~' filesep, 'Desktop', filesep,'chile', filesep,'Manual_Faultloc_All', filesep,'Manual_Faultloc_Originals', filesep,'Manual_Faultloc_16km']; + +% List all bottom coordinate files +files = dir([botdir filesep '*.txt']); +% Sort files numerically +files = sortnumfilenames(files); + +for i = 1:size(files, 1) + % Read bottom coordinates + botcoords = load([botdir filesep files(i).name]); + % Get number of coordinates + nc = size(botcoords, 1); + % Read top coordinates + topcoords = load([topdir filesep files(i).name]); + % Write the Gmsh geometry file + geofile = [botdir filesep files(i).name(1:end-4) '.geo']; + fid = fopen(geofile, 'w'); + fprintf(fid, 'charl = %g;\n', sz); + fprintf(fid, 'Point(%g) = {%g, %g, %g, charl};\n', [1:2*nc; [topcoords(:, 1); flipud(botcoords(:, 1))]'; [topcoords(:, 2); flipud(botcoords(:, 2))]'; [topcoords(:, 3); flipud(botcoords(:, 3))]']); + fprintf(fid, 'CatmullRom(%g) = {%g:%g};\n', [1:2; [1 nc+1; nc 2*nc]]); + fprintf(fid, 'CatmullRom(%g) = {%g,%g};\n', [3:4; [nc 2*nc; nc+1 1]]); + fprintf(fid, 'Line Loop(1) = {1, 3, 2, 4};\nRuled Surface(1) = {1};\n'); + fclose(fid); + + % Mesh using Gmsh + + % Check for preferences file + if exist('gmshfaultspref.mat', 'file') ~= 0 % If this .mat file exists, + load('gmshfaultspref.mat', 'gmshpath') % Load it + else % If not, + if ismac + if exist('/Applications/Gmsh.app/Contents/MacOS/gmsh', 'file') % Check for default install location + gmshpath = '/Applications/Gmsh.app/Contents/MacOS/'; + else + gmshpath = ''; % Or ask for install location + while ~exist([gmshpath filesep 'gmsh'], 'file') + gmshpath = input('Enter path to Gmsh application: '); + end + end + % Save Gmsh path to preferences file, to be read in future runs + gmfp = fileparts(which('gmshfaults')); + save([gmfp filesep 'gmshfaultspref.mat'], 'gmshpath'); + elseif ispc || (isunix && ~ismac) + gmshpath = ''; % Or ask for install location + while ~exist([gmshpath filesep 'gmsh.exe'], 'file') + gmshpath = input('Enter path to Gmsh application: '); + end + % Save Gmsh path to preferences file, to be read in future runs + gmfp = fileparts(which('gmshfaults')); + save([gmfp filesep 'gmshfaultspref.mat'], 'gmshpath'); + end + end + % Do the meshing + system(sprintf('%s/gmsh -2 %s -o %s.msh -v 0 > junk', gmshpath, geofile, geofile(1:end-4))); +end +% Remove report file +if isunix + system('rm junk'); +elseif ispc + %system('del junk'); +end + +% Make a space-separated string of all .msh files +alldir = dir([botdir '/*.msh']); +% Sort files numerically +alldir = sortnumfilenames(alldir); + +allstring = ''; +for i = 1:length(alldir) + allstring = sprintf('%s %s/%s', allstring, alldir(i).folder, alldir(i).name); +end +allstring = allstring(2:end); % Remove leading space \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshfaults_anna.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshfaults_anna.m new file mode 100644 index 0000000..0c9783b --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshfaults_anna.m @@ -0,0 +1,54 @@ +function allstring = gmshfaults_anna(topdir, botdir, sz) +% gmshfaults Meshes faults in 3D using Gmsh. +% gmshfaults(BOTDIR, ELSIZE) meshes all faults whose bottom coordinates +% are contained in text files within the folder BOTDIR, using the +% element size specified using ELSIZE. Geometry (.geo) and mesh (.msh) +% files are saved to the bottom coordinate directory. +% +% ALL = gmshfaults(...) returns a string to the command line that can be +% used to read all faults in using ReadPatches.m, i.e. +% >> p = ReadPatches(ALL); +% +% + +% Hard code full path to top coordinates directory here +%topdir = ['~' filesep, 'Desktop', filesep,'chile', filesep,'Manual_Faultloc_All', filesep,'Manual_Faultloc_Originals', filesep,'Manual_Faultloc_16km']; + +% List all bottom coordinate files +files = dir([botdir filesep '*.txt']); + +for i = 1:size(files, 1) + % Read bottom coordinates + botcoords = load([botdir filesep files(i).name]); + % Get number of coordinates + nc = size(botcoords, 1); + % Read top coordinates + topcoords = load([topdir filesep files(i).name]); + % Write the Gmsh geometry file + geofile = [botdir filesep files(i).name(1:end-4) '.geo']; + fid = fopen(geofile, 'w'); + fprintf(fid, 'charl = %g;\n', sz); + fprintf(fid, 'Point(%g) = {%g, %g, %g, charl};\n', [1:2*nc; [topcoords(:, 1); flipud(botcoords(:, 1))]'; [topcoords(:, 2); flipud(botcoords(:, 2))]'; [topcoords(:, 3); flipud(botcoords(:, 3))]']); + fprintf(fid, 'CatmullRom(%g) = {%g:%g};\n', [1:2; [1 nc+1; nc 2*nc]]); + fprintf(fid, 'CatmullRom(%g) = {%g,%g};\n', [3:4; [nc 2*nc; nc+1 1]]); + fprintf(fid, 'Line Loop(1) = {1, 3, 2, 4};\nRuled Surface(1) = {1};\n'); + fclose(fid); + fid = fopen('infile.txt','rt') ; + + % Mesh using Gmsh (default) + % system(sprintf('/Applications/Gmsh/Gmsh.app/Contents/MacOS/gmsh -2 %s -o %s.msh -v 0 > junk', geofile, geofile(1:end-4))); + % Mesh using Gmsh (Linux) +% system(sprintf('gmsh -2 %s -o %s.msh -v 0 > junk', geofile, geofile(1:end-4))); + % Mesh using Gmsh (Windows) + system(sprintf('C:/Users/apearson/Documents/gmsh/gmsh -2 %s -o %s.msh -v 0 > junk', geofile, geofile(1:end-4))); + +end +system('del junk'); + +% Make a space-separated string of all .msh files +alldir = dir([botdir '/*.msh']); +xlsfiles={alldir.name}; +[~,idx]=natsort(xlsfiles); +alldir=alldir(idx); +allstring = sprintf('%s ', alldir.name); +allstring = allstring(1:end-1); % Remove trailing space \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshlistric.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshlistric.m new file mode 100644 index 0000000..c37133e --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshlistric.m @@ -0,0 +1,50 @@ +function p = gmshlistric(edgex, edgey, edgez, top, bot, ls1, ls2, fs1, fs2, sz) +% gmshplane Makes a triangulated listric fault in Gmsh. +% p = gmshsurface(edgex, edgey, edgez, top, bot, ls1, ls2, fs1, fs2, sz) +% creates a triangulated mesh structure using Gmsh for the surface defined +% by the edge coordiantes input variables. edgex, edgey, edgez are +% vectors giving all edge coordinates. top, bot, ls1, ls2, fs1, and fs2 are +% vectors giving the indices of the edge coordinate arrays to define +% the top, bottom, listric sides, and flat sides of the surface. The element +% size is given by sz. +% + +np = length(edgex); % Number of points +nrows = size(ls1, 2)/2; % Number of listric rows +alledge = [top(:); ls1(:); fs1(:); bot(:); fs2(:); ls2(:)]; % All edges +nedge = size(alledge, 1)/2; % Number of edges + +% Write coordinates to Gmsh .geo file +%fn = sprintf('junk%g', rem(now, 1)); +fn = 'junk'; +fid = fopen([fn '.geo'], 'w'); +charl = sz*ones(1, np); % Create vector of element size +charl(bot) = 10*sz; % Make nodes along bottom have a larger size +% Write points: top then bottom +fprintf(fid, 'Point(%g) = {%g, %g, %g, %g};\n', [1:np; edgex(:)'; edgey(:)'; edgez(:)'; charl]); +% Write lines: top, listric side 1, flat side 1, bottom, flat side 2, listric side 2 +for i = 1:nedge + fprintf(fid, 'Line(%g) = {%g, %g};\n', i, alledge(2*i-1), alledge(2*i)); +end + +% Extra lines that separate panels +for i = 1:nrows + fprintf(fid, 'Line(%g) = {%g, %g};\n', nedge+i, ls1(length(ls1)-2*(i-1)), ls2(2*i-1)); +end + +% Circulate lines and create surfaces +fprintf(fid, 'Line Loop(1) = {%g, %g, %g, %g};\nSurface(1) = {1};\n', [nrows+(2:4), -(2*nrows+5)]); % Flat part of fault +for i = 1:nrows % Listric panels + if i == 1 + fprintf(fid, 'Line Loop(%g) = {%g, %g, %g, %g};\nSurface(%g) = {%g};\n', 1+i, 2, nedge+nrows, nedge, 1, 1+i, 1+i); + else + fprintf(fid, 'Line Loop(%g) = {%g, %g, %g, %g};\nSurface(%g) = {%g};\n', 1+i, nrows+3-i, 2*nrows+i+3, nrows+i+3, -(2*nrows+i+4), 1+i, 1+i); + end +end +fclose(fid); + +% Mesh using Gmsh +p = gmsh([fn '.geo']); + +% Remove temp files +%system(sprintf('rm %s*', fn)); diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshplane.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshplane.m new file mode 100644 index 0000000..1e4ef0d --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshplane.m @@ -0,0 +1,35 @@ +function p = gmshplane(tx, ty, tz, maxz, dip, sz) +% gmshplane Makes a triangulated planar fault in Gmsh. +% p = gmshplane(tx, ty, tz, L, W, strike, dip, size) creates a +% triangulated mesh structure using Gmsh for the plane defined +% by the input variables. tx, ty, tz are 2-element vectors giving +% the coordinates of the end points of the tip line; maxz gives +% the maximum depth; dip gives the dip, with positive to the right +% looking from endpoint 1 to endpoint 2; and size gives the nominal +% element size ("characteristic length") in Gmsh. +% + +% Determine deep coordinates based on dip and maximum depth +strike = atan2d(diff(tx), diff(ty)); +horzd = (abs(maxz) - abs(tz))./tand(dip); +dx = tx + cosd(strike).*horzd; +dy = ty + sind(strike).*horzd; +dz = [maxz; maxz]; + +% Write coordinates to Gmsh .geo file +fid = fopen('junk.geo', 'w'); +fprintf(fid, 'charl%g = %g;\n', [1:length(sz); sz(:)']); % Write element size +szi = [1 1 length(sz) length(sz)]; % Element size index array +% Write points: top then bottom +fprintf(fid, 'Point(%g) = {%g, %g, %g, charl%g};\n', [1:4; [tx(:)', dx(:)']; [ty(:)', dy(:)']; [tz(:)', dz(:)']; szi]); +% Write lines: top, side 1, bottom, side 2 +fprintf(fid, 'Line(%g) = {%g,%g};\n', [1, 1, 2, 2, 2, 4, 3, 4, 3, 4, 3, 1]); +% Circulate lines and create plane +fprintf(fid, 'Line Loop(1) = {1, 2, 3, 4};\nRuled Surface(1) = {1};\n'); +fclose(fid); + +% Mesh using Gmsh +p = gmsh('junk.geo'); + +% Remove temp files +system('rm junk*'); diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshsurface.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshsurface.m new file mode 100644 index 0000000..44cf2b0 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/gmshsurface.m @@ -0,0 +1,38 @@ +function p = gmshsurface(edgex, edgey, edgez, top, bot, s1, s2, sz) +% gmshplane Makes a triangulated nonplanar fault in Gmsh. +% p = gmshsurface(edgex, edgey, edgez, top, bot, s1, s2, sz) creates a +% triangulated mesh structure using Gmsh for the surface defined +% by the edge coordiantes input variables. edgex, edgey, edgez are +% vectors giving all edge coordinates. top, bot, s1, and s2 are +% vectors giving the indices of the edge coordinate arrays to define +% the top, bottom, and sides of the surface. The element size is given +% by sz. +% + +np = length(edgex); % Number of points +alledge = [top(:); s1(:); bot(:); s2(:)]; % All edges +edgeend = cumsum([length(top), length(s1), length(bot), length(s2)]); % Edge indices +edgebeg = [1 edgeend(1:end-1)]; + +% Write coordinates to Gmsh .geo file +fn = sprintf('junk%g', rem(now, 1)); +fid = fopen([fn '.geo'], 'w'); +fprintf(fid, 'charl = %g;\n', sz); % Write element size +% Write points: top then bottom +fprintf(fid, 'Point(%g) = {%g, %g, %g, charl};\n', [1:np; edgex(:)'; edgey(:)'; edgez(:)']); +% Write lines: top, side 1, bottom, side 2 +for i = 1:4, + edge = alledge(edgebeg(i):edgeend(i)); + fprintf(fid, 'BSpline(%g) = {%g', i, edge(1)); + fprintf(fid, ', %g', edge(2:end)); + fprintf(fid, '};\n'); +end +% Circulate lines and create plane +fprintf(fid, 'Line Loop(1) = {1, 2, 3, 4};\nSurface(1) = {1};\n'); +fclose(fid); + +% Mesh using Gmsh +p = gmsh([fn '.geo']); + +% Remove temp files +system(sprintf('rm %s*', fn)); diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/maketopbotcoords.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/maketopbotcoords.m new file mode 100644 index 0000000..e538d1f --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/maketopbotcoords.m @@ -0,0 +1,63 @@ +function maketopbotcoords(file, depth) +% maketopbotcoords Makes files for top and bottom coordinates from an ArcGIS text file. +% maketopbotcoords(FILE, DEPTH) makes folders containing x, y, z coordinates for +% the top of a fault and the bottom (with uniform z coordinate specified by input +% arugment DEPTH), based on a FILE containing surface trace coordinates exported from +% ArcGIS. Individual text files will be generated for distinct features within the +% coordinate file. Folders will be generated to hold the top and bottom coordiante files, +% named FILE_topcoords and FILE_botcoords, respectively. +% +% Use the function rotatefaultcoords to assign dips to each fault (by changing the +% bottom coordinates) and function gmshfaults to create triangulated meshes of all +% faults. +% + +% ArcGIS file style 1: Feature coordinates start with FID and end with "END" +a = opentxt(file); +ends = strfind(a(:, 1)', 'E') - 1; +if ~isempty(ends) + astyle = 1; + if diff(ends(end), ends(end-1)) == 1 + ends = ends(1:end-1); + end + begs = [2 ends(1:end-1) + 3]; +else +% ArcGIS file style 2: Each line contains feature x, y, FID + astyle = 2; + if a(1) == 'X' + fl = 2; + else + fl = 1; + end + a = str2num(a(fl:end, :)); + d3 = diff(a(:, 3)); + ends = [find(d3==1); size(a, 1)]; + begs = [1; ends(1:end-1)+1]; +end + +topdir = [file(1:end-4), '_topcoords']; +botdir = [file(1:end-4), '_botcoords']; +if ~exist(topdir, 'dir') + mkdir(topdir) +end + +if ~exist(botdir, 'dir') + mkdir(botdir) +end + +for i = 1:numel(begs) + if astyle == 1 + tout = str2num(a(begs(i):ends(i), :)); + else + tout = [a(begs(i):ends(i), 1:2), zeros(ends(i)-begs(i)+1, 1)]; + end + + tout = unique(tout, 'rows', 'stable'); + % Try to sort coordinates along a single direction +% [~, di] = sort(mag(tout, 2)); +% tout = tout(di, :); + + bout = [tout(:, 1:2) -abs(depth)*ones(size(tout, 1), 1)]; + save(sprintf('%s/f%g.txt', topdir, i), 'tout', '-ascii'); + save(sprintf('%s/f%g.txt', botdir, i), 'bout', '-ascii'); +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/mshfilenames.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/mshfilenames.m new file mode 100644 index 0000000..6cd638b --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/mshfilenames.m @@ -0,0 +1,15 @@ +function mnames = mshfilenames(dir) +% mshfilenames Makes a space-separated string of a directory's .msh filenames +% mnames = mshfilenames(dir) creates a space-delimited string of the .msh +% filenames within folder dir. mnames is a string suitable for use with +% ReadPatches.m. +% + +mnames = ''; +files = dir('*.msh')' + +for i = 1:numel(files) + mnames = sprintf('%s %s/%s', name, files(i).folder, files(i).name); +end + +mnames = mnames(2:end); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/opentxt.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/opentxt.m new file mode 100644 index 0000000..b9d19db --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/opentxt.m @@ -0,0 +1,14 @@ +function in = opentxt(infile); +% +% IN = OPENTXT(INFILE) returns a character array IN by reading the text file +% INFILE. +% + +fid1 = fopen(infile); frewind(fid1); + +in = textscan(fid1, '%s', 'delimiter', '\n', 'whitespace', ' '); +in = in{1}; +in = char(in); +szin = size(in); + +fclose(fid1); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/patchcat.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/patchcat.m new file mode 100644 index 0000000..f837c1c --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/patchcat.m @@ -0,0 +1,11 @@ +function pn = patchcat(p1, p2) +% PATCHCAT Concatenates two patch structures. +% PN = PATCHCAT(P1, P2) concatenates patch structures +% P1 and P2 and returns the combined structure to PN. +% + +% Concatenate all fields +pn = structmath(p1, p2, 'vertcat'); + +% Adjust the vertex ordering +pn.v(sum(p1.nEl)+1:end, :) = p2.v + size(p1.c, 1); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/rad2deg.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/rad2deg.m new file mode 100644 index 0000000..c4fd83d --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/rad2deg.m @@ -0,0 +1,3 @@ +function [angle_deg] = rad2deg( angle_rad ) + +angle_deg = (angle_rad*360) / (2*pi); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/rotatefaultcoords_dir.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/rotatefaultcoords_dir.m new file mode 100644 index 0000000..899dd39 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/rotatefaultcoords_dir.m @@ -0,0 +1,37 @@ +function rotcoords=rotatefaultcoords(dirname, dip) +% rotatefaultcoords Rotates a set of fault coordinates to a specified dip. +% +% rotatefaultcoords(DIRNAME, DIP) rotates the coordinates contained in +% all text files within directory DIRNAME to represent a fault of a +% specified DIP. Negative DIP values give westward dips, positive give +% eastward dips. The text files are assumed to contain X, Y, and Z +% coordinates of the trace of a vertical fault at depth. The rotated +% coordinates will be saved to a text file within a newly created +% directory with "_DIPdip" appended. +% + +% Create a new directory into which rotated coordinate files will be placed +rotdirname = sprintf('%s_truedip', dirname); +if ~exist(rotdirname, 'dir') + mkdir(rotdirname); +end +% Get a listing of all files in the specified directory +files = dir([dirname filesep '*.txt']); +% Sort files numerically +files = sortnumfilenames(files); + +% Expand scalar dip to one value per file +if numel(dip) == 1 + dip = dip.*ones(numel(files), 1); +end + +% For each file... +for i = 1:size(files, 1) + % Load the coordinates + coords = load([dirname filesep files(i).name]); + % Rotate the coordinates by the specified dip + rotcoords = arbrot(coords, [], dip(i)); + % Save the rotated coordinates to the newly created directory + save([rotdirname filesep files(i).name], 'rotcoords', '-ascii'); +end + \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/sortnumfilenames.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/sortnumfilenames.m new file mode 100644 index 0000000..7162b93 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/sortnumfilenames.m @@ -0,0 +1,25 @@ +function sfiles = sortnumfilenames(files) +% SORTNUMFILENAMES Sorts filenames in true numerical order. +% SORTFNUMFILENAMES(FILES) sorts a structure of filenames returned from +% DIR, given as FILES, in true numerical order (i.e., file1.txt, file2.txt,...) +% rather than the default result from DIR of file1.txt, file10.txt,... +% +% Any filenames containing a number will be properly sorted. Filenames +% containing no digits will be placed at the end of the list but will +% remain in the same order relative to each other as they appear in FILES. +% +% SFILES = SORTNUMFILENAMES(FILES) returns the sorted file structure to SFILES. +% + +nf = numel(files); % Number of files +N = zeros(nf, 1); % Allocate space for sorting matrix +for i = 1:nf + ns = regexp(files(i).name, '\d+', 'match'); % Check for number as string + if ~isempty(ns) % If a number exists, + N(i) = str2num(ns{:}); % Convert it to numeric + else % If it's entirely text, + N(i) = 1e10+i; % Give this file a large value so it appears at the end of the list + end +end +[~, Ns] = sort(N); % Find indices of sorted numerical values. Text-only names are placed last, but in the original order relative to each other +sfiles = files(Ns); % Sort files diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/structmath.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/structmath.m new file mode 100644 index 0000000..e314301 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/structmath.m @@ -0,0 +1,51 @@ +function ns = structmath(s1, s2, op) +% STRUCTMATH Carries out simple operations on structures. +% NS = STRUCTMATH(S1, S2, OPERATION) carries out simple math operations +% on structures S1 and S2. Fields of common name and size will be related +% using OPERATION, which can be any number of operations that acts column- +% wise on an array, such as PLUS, MINUS, MTIMES, LDIVIDE, RDIVIDE, POWER. +% OPERATION should be given as a string. For example, to add the fields +% of common name and size in structures S1 and S2 and return the results +% to new structure NS, use NS = structmath(S1, S2, 'plus'). +% +% S2 can be a scalar, which can be used with selected operations, for +% example, added to each field. +% + +% Make sure operation is a real operation +w = which(op); +if isempty(w) + return +end + +% If both arguments are structures +if isstruct(s2) + % Check for common fields + fn1 = fieldnames(s1); + fn2 = fieldnames(s2); + [junk, cf1] = ismember(fn2, fn1); + [junk, cf2] = ismember(fn1, fn2); + cf1 = cf1(find(cf1)); + cf2 = cf2(find(cf2)); + cfn = length(cf1); + cf2 = sort(cf2); + + % Loop through fields, checking for common size + for i = 1:cfn + f1 = getfield(s1, fn1{cf1(i)}); + f2 = getfield(s2, fn2{cf2(i)}); + %if isequal(size(f1), size(f2)) + nf = eval(sprintf('%s(f1, f2)', op)); + eval(sprintf('ns.%s = nf;', fn1{cf1(i)})); + %end + end +else + fn1 = fieldnames(s1); + % Loop through fields, checking for common size + for i = 1:length(fn1) + f1 = getfield(s1, fn1{i}); + nf = eval(sprintf('%s(f1, s2)', op)); + eval(sprintf('ns.%s = nf;', fn1{i})); + %end + end +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/trendsort.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/trendsort.m new file mode 100644 index 0000000..a9b57d4 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/trendsort.m @@ -0,0 +1,15 @@ +function sorted = trendsort(coords, thresh) +% trendsort Sorts x, y coordinates along a similar trend direction +% sorted = trendsort(coords) sorts the n-by-2 array coords, containing +% x, y coordinate pairs so that they follow a single general trend (i.e., +% east to west, or south to north). +% + +% First sort based on distance from a common origin +[~, di] = sort(mag(coords, 2)); +sorted = coords(di, :); + +% Calculate trends of sorted coordinate pairs +dc = diff(sorted); +trends = atan2d(dc(:, 1), dc(:, 1)); + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/uniqueels.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/uniqueels.m new file mode 100644 index 0000000..6c0301f --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/uniqueels.m @@ -0,0 +1,16 @@ +function pu = uniqueels(p) +% uniqueels Cleans a patch structure retaining unique elements. +% pu = uniqueels(p) cleans patch structure p leaving only unique +% elements, returning them to structure pu. + +% Get node coordinates +px = unstack3(p.c(p.v, 1)); +py = unstack3(p.c(p.v, 2)); +pz = unstack3(p.c(p.v, 3)); + +% Check unique nodes +[uc, ic] = unique([px, py, pz], 'rows'); + +% Extract unique structure +pu = patchsubset(p, ic); + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/wrapTo360.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/wrapTo360.m new file mode 100644 index 0000000..0cb03d8 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/meshing-master/meshing-master/wrapTo360.m @@ -0,0 +1,15 @@ +function lon = wrapTo360(lon) +%wrapTo360 Wrap angle in degrees to [0 360] +% +% lonWrapped = wrapTo360(LON) wraps angles in LON, in degrees, to the +% interval [0 360] such that zero maps to zero and 360 maps to 360. +% (In general, positive multiples of 360 map to 360 and negative +% multiples of 360 map to zero.) +% +% See also wrapTo180, wrapToPi, wrapTo2Pi. + +% Copyright 2007-2008 The MathWorks, Inc. + +positiveInput = (lon > 0); +lon = mod(lon, 360); +lon((lon == 0) & positiveInput) = 360; diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/opentxt.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/opentxt.m new file mode 100644 index 0000000..b9d19db --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/opentxt.m @@ -0,0 +1,14 @@ +function in = opentxt(infile); +% +% IN = OPENTXT(INFILE) returns a character array IN by reading the text file +% INFILE. +% + +fid1 = fopen(infile); frewind(fid1); + +in = textscan(fid1, '%s', 'delimiter', '\n', 'whitespace', ' '); +in = in{1}; +in = char(in); +szin = size(in); + +fclose(fid1); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/poly3d2tribem.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/poly3d2tribem.m new file mode 100644 index 0000000..06b171c --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/poly3d2tribem.m @@ -0,0 +1,52 @@ +function [p, d, bc, rems, obs] = poly3d2tribem(file) + + + +% Read .in file as text +a = opentxt(file); + +% Find indices of objects, nodes, and elements +objects = findstr(a(:, 1)', 'o'); +nodes = findstr(a(:, 1)', 'v'); +els1 = findstr(a(:, 1)', 'e'); +els2 = findstr(a(:, 2)', ' '); +els = intersect(els1, els2); + +% Index differences +dnode = diff(nodes); +dels = diff(els); + +% Beginning and end of node, element series +nbegs = [nodes(1), nodes(find(dnode > 1) + 1)]; +nends = [nodes(find(dnode > 1)), nodes(end)]; + +ebegs = [els(1), els(find(dels > 1) + 1)]; +eends = [els(find(dels > 1)), els(end)]; + +% Define number of elements +no = size(objects, 2); +p.nc = (nends - nbegs + 1)'; +p.nEl = (eends - ebegs +1)'; + +% Gather nodes, elements, and boundary conditions +p.c = zeros(sum(p.nc), 3); +p.v = zeros(sum(p.nEl), 3); +d = p.v; +bc = p.v; + +elcount = 1; +for i = 1:length(nbegs) + for j = nbegs(i):nends(i) + nline = textscan(a(j, :), 'v %f global %f %f %f\r'); + p.c(nline{1}, :) = [nline{2}, nline{3}, nline{4}]; + end + for j = ebegs(i):eends(i) + eline = textscan(a(j, :), 'e 3 elocal %s %f %f %f %f %f %f\r'); + p.v(elcount, :) = [eline{5}, eline{6}, eline{7}]; + bctext = char(eline{1}); bctext1 = bctext; bctext(1) = bctext1(2); bctext(2) = bctext1(1); + bct = strfind(bctext, 't'); + bc(elcount, bct) = 1; + d(elcount, :) = [eline{3}, -eline{2}, eline{4}]; % Reverse order of strike and dip directions + elcount = elcount + 1; + end +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/remote_stress_examples.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/remote_stress_examples.m new file mode 100644 index 0000000..29d6196 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/remote_stress_examples.m @@ -0,0 +1,41 @@ +% tribem simple remote stress example + +% Establish fault geometry +[bx, bz] = meshgrid(0:2.5:50, 0:2.5:25); +b.c = [bx(:), zeros(size(bx(:))), -bz(:)]; +b.nc = length(b.c); +b.v = delaunay(bx(:), bz(:)); +b.nEl = length(b.v); + +% Data and boundary conditions arrays (zero traction everywhere) +d = zeros(size(b.v)); % All zero values +bc = ones(size(b.v)); % All traction conditions + +% Observation grid +[x, y] = meshgrid(-10.1:1:60, -15.1:1:15); +obs.x = x(:); obs.y = y(:); obs.z = -15*ones(size(obs.x)); +% Calculate stress, displacement, and strain +obs.v = 'sde'; + +% Run tribem with remote stress tensor of 490 units in the s_yy direction +% (Tension perpendicular to fault) +[slip, trac, out, G] = tribemx(b, d, bc, [0 490 0 0 0 0], obs); + +% Visualize traction and slip in the element-normal direction +meshview(b.c, b.v, trac(:, 3)); +view([0 0]); axis square; axis equal; title('Element-normal traction') +meshview(b.c, b.v, slip(:, 3)); +view([0 0]); axis square; axis equal; title('Element-normal slip') +ca = caxis; + + +% Run tribem with remote stress tensor of 490 units in the s_yy direction +% and lithostatic loading (density of 2, corresponding to 490 units of +% compression at bottom of fault (25 km depth), canceling out remote stress) +% (Tension perpendicular to fault) +[lslip, ltrac, lout] = tribemx(b, d, bc, [0 490 0 0 0 0], obs, G, 2); +meshview(b.c, b.v, ltrac(:, 3)); +view([0 0]); axis square; axis equal; title('Element-normal traction, lithostatic') +meshview(b.c, b.v, lslip(:, 3)); +view([0 0]); axis square; axis equal; title('Element-normal slip, lithostatic') +caxis(ca); colormap(bluewhitered); % Set color scale equal to other slip figure diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/signconventions.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/signconventions.m new file mode 100644 index 0000000..bf0a473 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/signconventions.m @@ -0,0 +1,56 @@ +function signconventions() +% signconventions Tests relationships in sighs of traction, slip, and stress/strain. +% + +% Establish fault geometry +[bx, bz] = meshgrid(0:2.5:50, 0:2.5:25); +b.c = [bx(:), -bz(:)*cosd(60), -bz(:)]; % 60 degree south dip +b.nc = length(b.c); +b.v = delaunay(bx(:), bz(:)); +b.v = fliplr(b.v); % Enforce counterclockwise circulation, upward normal vector +b.nEl = length(b.v); + +% Data and boundary conditions arrays (zero traction everywhere) +d = repmat([0 0 0], size(b.v, 1), 1); % All zero values +bc = repmat([1 1 0], size(b.v, 1), 1); % All traction conditions + +% Observation grid +[x, y] = meshgrid(-10.1:1:60, -15.1:1:15); +obs.x = x(:); obs.y = y(:); obs.z = 0*ones(size(obs.x)); +% Calculate stress, displacement, and strain +obs.v = 'sde'; + +% Run tribem with remote stress tensor of 1 unit in the s_yy direction +% (Tension perpendicular to fault) +[slip, trac, out, G] = tribemx(b, d, bc, [0 1 0 0 0 0], obs); + +% Plot slips +meshview(b.c, b.v, slip(:, 1)); title('Strike slip (sinistral +)') +meshview(b.c, b.v, slip(:, 2)); title('Dip slip (reverse +)') +meshview(b.c, b.v, slip(:, 3)); title('Normal slip (opening +)') + +% Plot tractions +meshview(b.c, b.v, trac(:, 1)); title('Strike traction (sinistral +)') +meshview(b.c, b.v, trac(:, 2)); title('Dip traction (reverse +)') +meshview(b.c, b.v, trac(:, 3)); title('Normal traction (tension +)') + +% Plot displacements as vectors +figure +quiver3(obs.x, obs.y, obs.z, out.u(:, 1), out.u(:, 2), out.u(:, 3)); +title('Displacements due to fault slip') + +% Plot stress components as pcolors +figure; pcolor(x, y, reshape(out.s(:, 1), size(x))); colormap(bluewhitered); title(['\sigma_{xx}']) +figure; pcolor(x, y, reshape(out.s(:, 2), size(x))); colormap(bluewhitered); title(['\sigma_{yy}']) +figure; pcolor(x, y, reshape(out.s(:, 3), size(x))); colormap(bluewhitered); title(['\sigma_{zz}']) +figure; pcolor(x, y, reshape(out.s(:, 4), size(x))); colormap(bluewhitered); title(['\sigma_{xy}']) +figure; pcolor(x, y, reshape(out.s(:, 5), size(x))); colormap(bluewhitered); title(['\sigma_{xz}']) +figure; pcolor(x, y, reshape(out.s(:, 6), size(x))); colormap(bluewhitered); title(['\sigma_{yz}']) + +% Check stress component signs by showing displacement gradients +figure; pcolor(x(:, 1:end-1), y(:, 1:end-1), diff(reshape(out.u(:, 1), size(x)), 1, 2)); colormap(bluewhitered); title(['\delta{u}_{x}/\delta{x}']) +figure; pcolor(x(1:end-1, :), y(1:end-1, :), diff(reshape(out.u(:, 2), size(x)))); colormap(bluewhitered); title(['\delta{u}_{y}/\delta{y}']) +dxy = diff(reshape(out.u(:, 1), size(x))); +dyx = diff(reshape(out.u(:, 2), size(x)), 1, 2); +exy = 0.5*(dxy(:, 1:end-1) + dyx(1:end-1, :)); +figure; pcolor(x(1:end-1, 1:end-1), y(1:end-1, 1:end-1), exy); colormap(bluewhitered); title(['\delta{u}_{x}/\delta{y}']) \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/signconventions_live.mlx b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/signconventions_live.mlx new file mode 100644 index 0000000..c03f2ca Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/signconventions_live.mlx differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tribem.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tribem.m new file mode 100644 index 0000000..52c34f4 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tribem.m @@ -0,0 +1,285 @@ +function [slip, trac, o, G] = tribem(patch, d, bc, varargin) +% TRIBEM Triangular element boundary element solver using geographic coordinates. +% [SLIP, TRAC] = TRIBEM(PATCH, D, BC) estimates slip or traction on triangular +% elements given a mesh in structure PATCH, a set of slip and traction +% boundary conditions D and a boundary condition identifer matrix, BC. +% +% PATCH can either be a string giving the full patch to a Gmsh .msh file +% or a structure given as PATCH = READPATCHES(PATCHFILE). Given NEL +% triangular elements, D should be an NEL-by-3 array of boundary conditions, +% giving either the slip or traction conditions on each element. For elements +% with slip prescribed, the corresponding line of D should be: +% +% [strike slip, dip slip, tensile slip] +% +% and for elements whose traction conditions are specified, D should read: +% +% [shear stress (strike), shear stress (dip), normal stress]. +% +% The NEL-by-3 array BC specifies the type of boundary conditions for each +% element, given as 0 for slip conditions and 1 for traction conditions. +% +% [SLIP, TRAC, O] = TRIBEM(PATCH, D, BC, OBS) will also calculate values at a set of +% observation coordinates defined by input argument OBS. OBS can be a structure +% containing fields lon, lat, dep, and v, where lon, lat, and dep are N-by-1 arrays +% giving the coordinates of N observation points (dep in km), and v is an integer +% specifying what will be calculated at these points: +% v = 1: Calculate displacement only (returned to O.u as a 3N-by-1 vector) +% v = 2: Calculate stress only (returned to O.s as a 6N-by-1 vector) +% v = 3: Calculate displacement and stress +% +% [SLIP, TRAC, G] = TRIBEM(PATCH, D, BC) will output the structure G containing +% fields of Green's functions relating slip to displacement and/or traction. This +% structure can be reused as an input argument, speeding computation when only the +% boundary conditions and not the problem geometry have changed. +% +% [SLIP, TRAC, O, G] = TRIBEM(PATCH, D, BC, OBS) will output both O and G, when OBS +% is specified as an input argument. +% +% [...] = TRIBEM(PATCH, D, BC, REMS) allows specification of a remote stress tensor, +% REMS. The tensor components, assuming Cartesian coordinates, should be given as +% +% REMS = [sigma_xx, sigma_yy, 0, sigma_xy, 0, 0]'; % 0 values for components involving z +% +% [...] = TRIBEM(PATCH, D, BC, G) uses a structure G of already-calculated +% traction (G.sp) and displacement partials (G.u). No checking is done to assure +% that the sizes of G fields are appropriate for the problem; this must be done +% externally. Therefore, this option is best used when only the boundary conditions +% change from one model run to the next, i.e., all of the problem geometry remains +% consistent. +% +% [...] = TRIBEM(PATCH, D, BC, CHOP) accepts CHOP as a flag to indicate whether +% or not the components of slip should be chopped according to element geometry. If +% CHOP > 0, only strike-slip and dip-slip will be considered for dipping faults, and +% only strike-slip and tensile motion will be considered for vertical faults. +% +% [...] = TRIBEM(PATCH, D, BC, G, CHOP) accepts both G and CHOP as input arguments. +% If the input G fields are already chopped, no additional trimming will be done. +% +% +% SIGN CONVENTIONS: +%------------------ +% +% SLIP: +% + | - +% ------------------------------- +% 1. Strike: Sinistral | Dextral +% 2. Dip: Reverse | Normal +% 3. Tensile: Opening | Closing +% +% TRACTION: +% + | - +% ---------------------------------------- +% 1. Strike shear: Strike | Strike + 180 +% 2. Dip shear: Updip | Downdip +% 3. Normal: Tensile | Compressional +% +% For comparison, Poly3D's sign conventions are: +% +% SLIP: +% + | - +% ------------------------------- +% 1. Dip: Normal | Reverse +% 2. Strike: Sinistral | Dextral +% 3. Tensile: Opening | Closing +% +% TRACTION: +% + | - +% ---------------------------------------- +% 1. Dip shear: Downdip | Updip +% 2. Strike shear: Strike | Strike + 180 +% 3. Normal: Tensile | Compressional +% + +chop = 0; + +% Parse optional inputs +noa = length(varargin); +if noa > 0 + for i = 1:noa % Loop through optional arguments + if isstruct(varargin{i}) % If it's a structure, it's either observations or partials + if isfield(varargin{i}, 'lon') % If field lon exists, it's observations + obs = varargin{i}; + else % If not, + G = varargin{i}; % It's partials + end + else + if length(varargin{i}) == 1 % If a single value was entered, it's either chop flag or Poisson's ratio + if varargin{i} <= 0.5 % If it's less than or equal to 0.5, it's PR + pr = varargin{i}; + else + chop = varargin{i}; % If not, it's chop flag + end + elseif length(varargin{i}) == 2 % If a 2-element vector was specified, + lame = varargin{i}; % Lame parameters were specified + elseif length(varargin{i}) == 6 + rems = varargin{i}; % Remote stress tensor + end + end + end +end + +% Read patch file, if necessary +if ischar(patch) + patch = ReadPatches(patch); + patch = PatchCoords(patch); +end + +% Calculate patch coordinates, if necessary +if ~isfield(patch, 'lonc') + patch = PatchCoords(patch); +end + +% Total number of elements +tne = sum(patch.nEl); + +% Project remote stress tensor onto elements +if exist('rems', 'var') + rems([3 5 6]) = 0; % Make sure traction-free surface of half space condition is met + remsp = ProjectStrainPartialsMats(repmat(rems(:), sum(patch.nEl), 1), patch.strike, patch.dip); +end + +% Make a structure containing perturbed element centroid coordinates +% Centroids are perturbed toward the half-space surface along the normal vector +psc = 1e3; % Centroid perturbation scaling factor +[cent.lon, cent.lat, cent.dep] = deal(patch.lonc+psc.*patch.nv(:, 1), patch.latc+psc.*patch.nv(:, 2), patch.zc+psc.*patch.nv(:, 3)); + +% Augment this structure with any observation coordinates +if exist('obs', 'var') + obs.lon = obs.lon(:); + obs.lat = obs.lat(:); + obs.dep = obs.dep(:); + if ~isfield(obs, 'v') % Default behavior is to calculate displacements only at observation coordinates + obs.v = 1; + end + if obs.v == 1 % Calculate displacements at observation coordinates + opt = repmat([1 0], length(obs.lon), 1); + elseif obs.v == 2 % Calculate stresses at observation coordinates + opt = repmat([0 1], length(obs.lon), 1); + elseif obs.v == 3 % Calculate displacements and stresses at observation coordinates + opt = repmat([1 1], length(obs.lon), 1); + else + opt = zeros(0, 2); + end +else + [obs.lon, obs.lat, obs.dep] = deal([]); + obs.v = 999; + opt = zeros(0, 2); +end + +% Augmented calculation coordinates +cc.lon = [cent.lon; obs.lon]; +cc.lat = [cent.lat; obs.lat]; +cc.dep = [cent.dep; obs.dep]; +% Set partials calculation option; this will be adjusted if need be when observations are considered +opt = logical([repmat([0 1], tne, 1); opt]); + +% Call GetTriCombinedPartials for elements and coordinates +if ~exist('G', 'var') + % Check for existence of specified Lame parameters + if ~exist('lame', 'var') + mu = 3e10; lambda = 3e10; % Defaults + else + mu = lame(1); lambda = lame(2); + end + % Check for existence of specified Poisson's ratio + if ~exist('pr', 'var') + pr = 0.25; + end + [G.u, G.e, G.tz] = GetTriCombinedPartials(patch, cc, opt, pr); + G.e = G.e./1e6; % Internal conversion assuming mm is unit of slip + G.e = StrainToStressComp(G.e', mu, lambda)'; + G.sp = ProjectStrainPartialsMats(G.e(1:6*tne, :), patch.strike, patch.dip); +end + +% Trim arrays for slip components, if requested and if not already done +if chop > 0 + triD = find(G.tz == 2); + triT = find(G.tz == 3); + colkeep = setdiff(1:3*tne, [3*triD-0; 3*triT-1]); % Define columns to keep + if size(G.sp, 2) == numel(patch.v) % If the columns have not already been trimmed... + G.e = G.e(:, colkeep); % ...trim them + G.sp = G.sp(:, colkeep); + if size(G.u, 2) > size(G.e, 2) + G.u = G.u(:, colkeep); + end + end +else + colkeep = 1:3*tne; % All columns retained if no chopping is requested +end + +% Determine which elements need slip estimated, and which have slip prescribed +c3 = 0; % Flag to indicate that the arrays came in as 3 column arrays +if max([size(bc, 2), size(d, 2)]) == 3 + c3 = 1; + d = reshape(d', numel(d), 1); + bc = reshape(bc', numel(bc), 1); +end +bc = logical(bc(:)); +islip = find(~bc(colkeep)); % Indices of prescribed slips +pslip = d(colkeep); pslip = pslip(islip); % Actual prescribed slips +itrac = find(bc); % Indices of prescibed tractions +ptrac = d(itrac); % Actual prescribed tractions +esidx = find(bc(colkeep)); % Indices of the slip components that will be estimated + +% Determine traction induced by any input displacement boundary conditions +dstress = G.sp(:, islip)*pslip; + +if ~exist('remsp', 'var') % If there is no remote stress + % Corrected traction is prescribed traction minus contribution from displacement b.c. + elstress = ptrac - dstress(itrac); + % Estimate slips that produce corrected traction + m = G.sp(itrac, esidx)\elstress; + % Assemble full slip vector (prescribed and estimated) + slip = zeros(3*tne, 1); + slip(islip) = pslip; + slip(itrac) = m; + % Assemble full traction vector (prescribed and estimated) + trac = zeros(3*tne, 1); + trac(islip) = dstress(islip); + trac(itrac) = ptrac; +else + elstress = 0*d; % Full element stress vector + elstress(itrac) = ptrac; % Corrected traction is prescribed traction minus contribution from displacement b.c. + elstress = elstress - dstress - remsp; % Also corrected for remote stress projected onto elements + g = G.sp; seye = eye(size(G.sp, 1)); + g(:, islip) = seye(:, islip); + m = g\elstress; + % Assemble full slip vector (prescribed and estimated) + slip = m; + slip(islip) = pslip; + % Assemble full traction vector (prescribed and estimated) + trac = elstress; +end + +% Forward calculation for observations +if obs.v == 1 | obs.v == 3 + o.u = G.u*slip(:); +else + o.u = []; +end +if obs.v == 2 | obs.v == 3 + o.s = G.e(6*tne+1:end, :)*slip(:); +else + o.s = []; +end + +% Reshape if original boundary condition array was n-by-3 +if c3 == 1 + slip = reshape(slip, 3, tne)'; + trac = reshape(trac, 3, tne)'; +end + +% Process optional output arguments +if nargout == 3 % 3rd argument could be o or G + if obs.v == 999 % If no observation points are specified, it must be G + varargout{:} = G; + else + varargout{:} = o; + end +end + +if nargout == 4 + varargout{1} = o; + varargout{2} = G; +end diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tribemx.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tribemx.m new file mode 100644 index 0000000..a9dca99 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tribemx.m @@ -0,0 +1,317 @@ +function [slip, trac, varargout] = tribemx(patch, d, bc, varargin) +% TRIBEMX Triangular element boundary element solver. +% [SLIP, TRAC] = TRIBEMX(PATCH, D, BC) estimates slip or traction on triangular +% elements given a mesh in structure PATCH, a set of slip and traction +% boundary conditions D and a boundary condition identifer matrix, BC. +% +% PATCH can either be a string giving the full patch to a Gmsh .msh file +% or a structure given as PATCH = READPATCHES(PATCHFILE). Given NEL +% triangular elements, D should be an NEL-by-3 array of boundary conditions, +% giving either the slip or traction conditions on each element. For elements +% with slip prescribed, the corresponding line of D should be: +% +% [strike slip, dip slip, tensile slip] +% +% and for elements whose traction conditions are specified, D should read: +% +% [shear stress (strike), shear stress (dip), normal stress]. +% +% The NEL-by-3 array BC specifies the type of boundary conditions for each +% element, given as 0 for slip conditions and 1 for traction conditions. +% +% [SLIP, TRAC, O] = TRIBEMX(PATCH, D, BC, OBS) will also calculate values at a set of +% observation coordinates defined by input argument OBS. OBS can be a structure +% containing fields x, y, z, and v, where x, y, and z are N-by-1 arrays giving +% the coordinates of N observation points, and v is a character specifying what +% will be calculated at these points: +% u: Calculate displacement (returned to O.u as a 3N-by-1 vector) +% s: Calculate stress (returned to O.s as a 6N-by-1 vector) +% e: Calculate strain (returned to O.e as 6N-by-1 vector) +% +% [SLIP, TRAC, G] = TRIBEMX(PATCH, D, BC) will output the structure G containing +% fields of Green's functions relating slip to displacement and/or traction. This +% structure can be reused as an input argument, speeding computation when only the +% boundary conditions and not the problem geometry have changed. +% +% [SLIP, TRAC, O, G] = TRIBEMX(PATCH, D, BC, OBS) will output both O and G, when OBS +% is specified as an input argument. +% +% [...] = TRIBEMX(PATCH, D, BC, REMS) allows specification of a remote stress tensor, +% REMS. The tensor components, assuming Cartesian coordinates, should be given as +% +% REMS = [sigma_xx, sigma_yy, 0, sigma_xy, 0, 0]'; % 0 values for components involving z +% +% [...] = TRIBEMX(PATCH, D, BC, RHO) allows specification of a density (assumed kg/m^3) +% that will be used to apply lithostatic stress to the problem. RHO must be greater than +% 1; if you wish to ignore lithostatic stress, don't prescribe a density. +% +% [...] = TRIBEMX(PATCH, D, BC, G) uses a structure G of already-calculated +% traction (G.sp) and displacement partials (G.u). No checking is done to assure +% that the sizes of G fields are appropriate for the problem; this must be done +% externally. Therefore, this option is best used when only the boundary conditions +% change from one model run to the next, i.e., all of the problem geometry remains +% consistent. +% +% [...] = TRIBEMX(PATCH, D, BC, CHOP) accepts CHOP as a flag to indicate whether +% or not the components of slip should be chopped according to element geometry. If +% CHOP = 1, only strike-slip and dip-slip will be considered for dipping faults, and +% only strike-slip and tensile motion will be considered for vertical faults. +% +% [...] = TRIBEMX(PATCH, D, BC, G, CHOP) accepts both G and CHOP as input arguments. +% If the input G fields are already chopped, no additional trimming will be done. +% +% +% SIGN CONVENTIONS: +%------------------ +% +% SLIP: +% + | - +% ------------------------------- +% 1. Strike: Sinistral | Dextral +% 2. Dip: Reverse | Normal +% 3. Tensile: Opening | Closing +% +% TRACTION: +% + | - +% ---------------------------------------- +% 1. Strike shear: Strike | Strike + 180 +% 2. Dip shear: Updip | Downdip +% 3. Normal: Tensile | Compressional +% +% For comparison, Poly3D's sign conventions are: +% +% SLIP: +% + | - +% ------------------------------- +% 1. Dip: Normal | Reverse +% 2. Strike: Sinistral | Dextral +% 3. Tensile: Opening | Closing +% +% TRACTION: +% + | - +% ---------------------------------------- +% 1. Dip shear: Downdip | Updip +% 2. Strike shear: Strike | Strike + 180 +% 3. Normal: Tensile | Compressional +% + +chop = 0; + +% Parse optional inputs +noa = length(varargin); +if noa > 0 + for i = 1:noa % Loop through optional arguments + if isstruct(varargin{i}) % If it's a structure, it's either observations or partials + if isfield(varargin{i}, 'x') % If field x exists, it's observations + obs = varargin{i}; + else % If not, + G = varargin{i}; % It's partials + end + else + if length(varargin{i}) == 1 % If a single value was entered, it's either chop flag or Poisson's ratio + if varargin{i} <= 0.5 % If it's less than or equal to 0.5, it's PR + pr = varargin{i}; + elseif double(varargin{i}) == 1 + chop = varargin{i}; % If it's a 1 or true, it's chop flag + elseif varargin{i} > 1 + lith = varargin{i}; % If it's greater than one, it's a density for lithostatic stress + end + elseif length(varargin{i}) == 2 % If a 2-element vector was specified, + lame = varargin{i}; % Lame parameters were specified + elseif length(varargin{i}) >= 4 + rems = varargin{i}; % Remote stress tensor + end + end + end +end + +% Read patch file, if necessary +if ischar(patch) + patch = ReadPatches(patch); + patch = PatchCoordsx(patch); +end + +% Calculate patch coordinates, if necessary +if ~isfield(patch, 'xc') + patch = PatchCoordsx(patch); +end + +% Total number of elements +tne = sum(patch.nEl); +% Project remote stress tensor onto elements +if exist('rems', 'var') + rems([5 6]) = 0; % Make sure traction-free surface of half space condition is met + remsp = ProjectStrainPartialsMats(repmat(rems(:), sum(patch.nEl), 1), patch.strike, patch.dip); +end + +% Add lithostatic stress, if requested +if exist('lith', 'var') + lstress = -abs(lith.*9.8*patch.zc); % Magnitude of lithostatic load; assumes meters and compression + lstress = stack6([lstress, lstress, lstress, zeros(sum(patch.nEl), 3)]); % Full stress tensor + ltrac = ProjectStrainPartialsMats(lstress, patch.strike, patch.dip); % Lithostatic tractions + if exist('remsp', 'var') + remsp = remsp + ltrac; % Add lithostatic to existing remote stress + else + remsp = ltrac; % Or consider lithostatic as the only remote stress + end +end + +% Check for existence of specified Lame parameters +if ~exist('lame', 'var') + mu = 3e10; lambda = 3e10; % Defaults +else + mu = lame(1); lambda = lame(2); +end + + +% Make a structure containing perturbed element centroid coordinates +% Centroids are perturbed toward the half-space surface along the normal vector +psc = 1e-5; % Centroid perturbation scaling factor +[cent.x, cent.y, cent.z] = deal(patch.xc+psc.*patch.nv(:, 1), patch.yc+psc.*patch.nv(:, 2), patch.zc+psc.*patch.nv(:, 3)); + +% Augment this structure with any observation coordinates +if exist('obs', 'var') + obs.x = obs.x(:); + obs.y = obs.y(:); + obs.z = obs.z(:); + if ~isfield(obs, 'v') % Default behavior is to calculate displacements only at observation coordinates + obs.v = 'd'; + end + opt = zeros(length(obs.x), 2); % Initialize observation coordinate calculation option array + if contains(obs.v, 'd') % Calculate displacements at observation coordinates + opt(:, 1) = 1; + end + if contains(obs.v, 's') | contains(obs.v, 'e') % Calculate stresses/strains at observation coordinates + opt(:, 2) = 1; + end +else + [obs.x, obs.y, obs.z] = deal([]); + obs.v = 'x'; + opt = zeros(0, 2); +end + +% Augmented calculation coordinates +cc.x = [cent.x; obs.x]; +cc.y = [cent.y; obs.y]; +cc.z = [cent.z; obs.z]; +% Set partials calculation option; this will be adjusted if need be when observations are considered +opt = logical([repmat([0 1], tne, 1); opt]); + +% Call GetTriCombinedPartials for elements and coordinates +if ~exist('G', 'var') + % Check for existence of specified Poisson's ratio + if ~exist('pr', 'var') + pr = 0.25; + end + [G.u, G.e, G.tz] = GetTriCombinedPartialsx(patch, cc, opt, pr); + G.s = StrainToStressComp(G.e', mu, lambda)'; + G.sp = ProjectStrainPartialsMats(G.s(1:6*tne, :), patch.strike, patch.dip); +end +% Trim arrays for slip components, if requested and if not already done +if chop > 0 + triD = find(G.tz == 2); + triT = find(G.tz == 3); + colkeep = setdiff(1:3*tne, [3*triD-0; 3*triT-1]); % Define columns to keep + if size(G.sp, 2) == numel(patch.v) % If the columns have not already been trimmed... + G.s = G.s(:, colkeep); % ...trim them + G.e = G.e(:, colkeep); + G.sp = G.sp(:, colkeep); + if size(G.u, 2) > size(G.e, 2) + G.u = G.u(:, colkeep); + end + end +else + colkeep = 1:3*tne; % All columns retained if no chopping is requested +end + +% Determine which elements need slip estimated, and which have slip prescribed +c3 = 0; % Flag to indicate that the arrays came in as 3 column arrays +if max([size(bc, 2), size(d, 2)]) == 3 + c3 = 1; + d = reshape(d', numel(d), 1); + bc = reshape(bc', numel(bc), 1); +end +bc = logical(bc(:)); +islip = find(~bc(colkeep)); % Indices of prescribed slips +pslip = d(colkeep); pslip = pslip(islip); % Actual prescribed slips +itrac = find(bc); % Indices of prescibed tractions +ptrac = d(itrac); % Actual prescribed tractions +esidx = find(bc(colkeep)); % Indices of the slip components that will be estimated + +% Determine traction induced by any input displacement boundary conditions +dstress = G.sp(:, islip)*pslip; + +if ~exist('remsp', 'var') % If there is no remote stress + % Corrected traction is prescribed traction minus contribution from displacement b.c. + elstress = ptrac - dstress(itrac); + % Estimate slips that produce corrected traction + m = G.sp(itrac, esidx)\elstress; + % Assemble full slip vector (prescribed and estimated) + slip = zeros(3*tne, 1); + slip(islip) = pslip; + slip(itrac) = m; + % Assemble full traction vector (prescribed and estimated) + trac = zeros(3*tne, 1); + trac(islip) = dstress(islip); % Traction from prescribed slip + trac(itrac) = ptrac; % Prescribed traction +else + elstress = 0*d; % Full element stress vector + elstress(itrac) = ptrac; % Corrected traction is prescribed traction minus contribution from displacement b.c. + elstress = elstress - dstress - remsp; % Also corrected for remote stress projected onto elements + g = G.sp; seye = eye(size(G.sp, 1)); % Set up design matrix + g(:, islip) = seye(:, islip); % Substitute identity matrix for prescribed slip columns + m = g\elstress; + % Assemble full slip vector (prescribed and estimated) + slip = m; + slip(islip) = pslip; + % Assemble full traction vector (prescribed and estimated) + trac = -elstress; +end +% Forward calculation for observations +if contains(obs.v, 'd') + o.u = G.u*slip(:); +else + o.u = []; +end +if contains(obs.v, 'e') + if exist('rems', 'var') %%includes REMS in calculations of strains + oreme = StressToStrainComp(rems, mu, lambda); + else + oreme = 0; + end + o.e = G.e(6*tne+1:end, :)*slip(:) + repmat(oreme(:), length(obs.x), 1); +else + o.e = []; +end +if contains(obs.v, 's') + if exist('rems', 'var') + orems = repmat(rems(:), length(obs.x), 1); + else + orems = 0; + end + o.s = G.s(6*tne+1:end, :)*slip(:) + orems; +else + o.s = []; +end + + +% Reshape if original boundary condition array was n-by-3 +if c3 == 1 + slip = reshape(slip, 3, tne)'; + trac = reshape(trac, 3, tne)'; +end + +% Process optional output arguments +if nargout == 3 % 3rd argument could be o or G + if contains(obs.v, 'x') % If no observation points are specified, it must be G + varargout{:} = G; + else + varargout{:} = o; + end +end + +if nargout == 4 + varargout{1} = o; + varargout{2} = G; +end + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/GetTriCombinedPartials.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/GetTriCombinedPartials.m new file mode 100644 index 0000000..6c0c4c1 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/GetTriCombinedPartials.m @@ -0,0 +1,87 @@ +function [Gu, Ge, Patches, Station] = GetTriCombinedPartials(Patches, Station, op) +% Calculate elastic displacement and/or strain partial derivatives for triangular elements +% +% [Gu, Ge, tz] = GetTriCombinedPartials(Patches, Station, option) +% +% Output arguments: +% Gu : Displacement partials +% Ge : Strain partials +% tz : Zeroing array +% +% Input arguments: +% Patches : Patches structure +% Station : Station structure +% option : Flag vector indicating which partials should be calculated +% The first element indicates whether displacement partials should be calculated, +% and the second whether strain partials should be calculated, using the convention +% 0 = don't calculate, 1 = calculate. +% +% option can also be an n-by-2 array, with each row corresponding to a row in the +% Station structure's fields. This may cut down on calculation time, only calculating +% the partials at the specified observation coordinates +% + +% Initialize variables +nStations = numel(Station.lon); +% Process options variable +op = logical(op); +if size(op, 1) == 1 + op = repmat(op, nStations, 1); +end +nPatches = numel(Patches.lon1); +Gu = zeros(3*sum(op(:, 1)), 3*nPatches); +Ge = zeros(6*sum(op(:, 2)), 3*nPatches); +Patches.tz = zeros(nPatches, 1); +Patches.tz(abs(Patches.dip - 90) > 1) = 2; +Patches.tz(Patches.tz == 0) = 3; +[v1u, v2u, v3u] = deal(cell(max(op(:, 1)), nPatches)); +[v1e, v2e, v3e] = deal(cell(max(op(:, 2)), nPatches)); +projstrikes = zeros(sum(Patches.nEl), 1); + +% Calculate the requested partials +if nPatches > 0 +% parfor_progress(nPatches); + parfor (iPatches = 1:nPatches) + % Do local oblique Mercator projection + [p, s] = ProjectTriCoords([Patches.lon1(iPatches) Patches.lat1(iPatches) Patches.z1(iPatches) Patches.lon2(iPatches) Patches.lat2(iPatches) Patches.z2(iPatches) Patches.lon3(iPatches) Patches.lat3(iPatches) Patches.z3(iPatches)], Station); + projstrikes(iPatches) = p.Strike; + % If displacement partials are requested... + if sum(op(:, 1)) > 0 + % Calculate elastic displacement for strike slip component + [uxs, uys, uzs,... + uxd, uyd, uzd,... + uxt, uyt, uzt] = tri_dislz_partials([p.px1, p.px2, p.px3], [p.py1, p.py2, p.py3], abs([p.z1, p.z2, p.z3]), s.tpx(op(:, 1)), s.tpy(op(:, 1)), abs(s.dep(op(:, 1))), 0.25); + v1u{iPatches} = reshape(-[uxs uys -uzs]', 3*sum(op(:, 1)), 1); + v2u{iPatches} = reshape(-[uxd uyd -uzd]', 3*sum(op(:, 1)), 1); + v3u{iPatches} = reshape(-[uxt uyt -uzt]', 3*sum(op(:, 1)), 1); + end + + % If strain partials are requested... + if sum(op(:, 2)) > 0 + [uxxs, uyys, uzzs, uxys, uxzs, uyzs,... + uxxd, uyyd, uzzd, uxyd, uxzd, uyzd,... + uxxt, uyyt, uzzt, uxyt, uxzt, uyzt] = tri_strain_fast_partials([p.px1, p.px2, p.px3], [p.py1, p.py2, p.py3], abs([p.z1, p.z2, p.z3]), s.tpx(op(:, 2)), s.tpy(op(:, 2)), abs(s.dep(op(:, 2))), 0.25); + v1e{iPatches} = reshape(-[uxxs uyys uzzs uxys -uxzs -uyzs]', 6*sum(op(:, 2)), 1); + v2e{iPatches} = reshape(-[uxxd uyyd uzzd uxyd -uxzd -uyzd]', 6*sum(op(:, 2)), 1); + v3e{iPatches} = reshape(-[uxxt uyyt uzzt uxyt -uxzt -uyzt]', 6*sum(op(:, 2)), 1); + end +% parfor_progress; + end +% parfor_progress(0); + % Place cells for each slip component into matrices + if ~isempty(Gu) + Gu(:, 1:3:end) = cell2mat(v1u); + Gu(:, 2:3:end) = cell2mat(v2u); + Gu(:, 3:3:end) = cell2mat(v3u); + % Project using element strike to eliminate effects of local oblique projection + Gu = xyz2enumat(Gu, -projstrikes + 90); + end + if ~isempty(Ge) + Ge(:, 1:3:end) = cell2mat(v1e); + Ge(:, 2:3:end) = cell2mat(v2e); + Ge(:, 3:3:end) = cell2mat(v3e); + % Project using element strike to eliminate effects of local oblique projection + Ge = xyz2enumat_strain(Ge, -projstrikes + 90); + end + Patches.Strike = projstrikes; +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/GetTriCombinedPartialsx.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/GetTriCombinedPartialsx.m new file mode 100644 index 0000000..d69fae2 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/GetTriCombinedPartialsx.m @@ -0,0 +1,76 @@ +function [Gu, Ge, tz] = GetTriCombinedPartialsx(Patches, Station, op, pr) +% Calculate elastic displacement and/or strain partial derivatives for triangular elements +% +% [Gu, Ge, tz] = GetTriCombinedPartials(Patches, Station, option) +% +% Output arguments: +% Gu : Displacement partials +% Ge : Strain partials +% tz : Zeroing array +% +% Input arguments: +% Patches : Patches structure +% Station : Station structure +% option : Flag vector indicating which partials should be calculated +% The first element indicates whether displacement partials should be calculated, +% and the second whether strain partials should be calculated, using the convention +% 0 = don't calculate, 1 = calculate. +% +% option can also be an n-by-2 array, with each row corresponding to a row in the +% Station structure's fields. This may cut down on calculation time, only calculating +% the partials at the specified observation coordinates +% + +% Initialize variables +nStations = numel(Station.x); +% Process options variable +op = logical(op); +if size(op, 1) == 1 + op = repmat(op, nStations, 1); +end +nPatches = numel(Patches.x1); +Gu = zeros(3*sum(op(:, 1)), 3*nPatches); +Ge = zeros(6*sum(op(:, 2)), 3*nPatches); +tz = zeros(nPatches, 1); +tz(abs(Patches.dip - 90) > 1) = 2; +tz(tz == 0) = 3; +[v1u v2u v3u] = deal(cell(max(op(:, 1)), nPatches)); +[v1e v2e v3e] = deal(cell(max(op(:, 2)), nPatches)); + +% Calculate the requested partials +if nPatches > 0 +% parfor_progress(nPatches); + parfor (iPatches = 1:nPatches) + if sum(op(:, 1)) > 0 + % Calculate elastic displacement for strike slip component + [uxs uys uzs... + uxd uyd uzd... + uxt uyt uzt] = tri_dislz_partials([Patches.x1(iPatches), Patches.x2(iPatches), Patches.x3(iPatches)], [Patches.y1(iPatches), Patches.y2(iPatches), Patches.y3(iPatches)], abs([Patches.z1(iPatches), Patches.z2(iPatches), Patches.z3(iPatches)]), Station.x(op(:, 1)), Station.y(op(:, 1)), abs(Station.z(op(:, 1))), 0.25); + v1u{iPatches} = reshape(-[uxs uys -uzs]', 3*sum(op(:, 1)), 1); + v2u{iPatches} = reshape(-[uxd uyd -uzd]', 3*sum(op(:, 1)), 1); + v3u{iPatches} = reshape(-[uxt uyt -uzt]', 3*sum(op(:, 1)), 1); + end + + if sum(op(:, 2)) > 0 + [uxxs uyys uzzs uxys uxzs uyzs... + uxxd uyyd uzzd uxyd uxzd uyzd... + uxxt uyyt uzzt uxyt uxzt uyzt] = tri_strain_fast_partials([Patches.x1(iPatches) Patches.x2(iPatches) Patches.x3(iPatches)], [Patches.y1(iPatches) Patches.y2(iPatches) Patches.y3(iPatches)], abs([Patches.z1(iPatches) Patches.z2(iPatches) Patches.z3(iPatches)]), Station.x(op(:, 2)), Station.y(op(:, 2)), abs(Station.z(op(:, 2))), 0.25); + v1e{iPatches} = reshape(-[uxxs uyys uzzs uxys -uxzs -uyzs]', 6*sum(op(:, 2)), 1); + v2e{iPatches} = reshape(-[uxxd uyyd uzzd uxyd -uxzd -uyzd]', 6*sum(op(:, 2)), 1); + v3e{iPatches} = reshape(-[uxxt uyyt uzzt uxyt -uxzt -uyzt]', 6*sum(op(:, 2)), 1); + end +% parfor_progress; + end +% parfor_progress(0); + % Place cells for each slip component into matrices + if ~isempty(Gu) + Gu(:, 1:3:end) = cell2mat(v1u); + Gu(:, 2:3:end) = cell2mat(v2u); + Gu(:, 3:3:end) = cell2mat(v3u); + end + if ~isempty(Ge) + Ge(:, 1:3:end) = cell2mat(v1e); + Ge(:, 2:3:end) = cell2mat(v2e); + Ge(:, 3:3:end) = cell2mat(v3e); + end +end \ No newline at end of file diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/PatchCoordsx.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/PatchCoordsx.m new file mode 100644 index 0000000..bbff0b5 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/PatchCoordsx.m @@ -0,0 +1,57 @@ +function Patches = PatchCoordsx(Patches); +% +% PatchCoords.m +% +% This function creates new arrays of longitude, latitude, and depth +% coordinates for each of the 3 vertices of each triangular element. +% +% Arguments: +% Patches : a structure containing Patches.c and Patches.v, as +% extracted by ReadPatches.m (and adjusted by +% PatchEndAdjust.m) +% +% Returned variables: +% Patches : an updated structure containing: +% .x1 : Geocentric x coordinate of all first vertices +% .y1 : Geocentric y coordinate of all first vertices +% .z1 : depth of all first vertices +% .x2 : Geocentric x coordinate of all second vertices +% .y2 : Geocentric y coordinate of all second vertices +% .z2 : depth of all second vertices +% .x3 : Geocentric x coordinate of all third vertices +% .y3 : Geocentric y coordinate of all third vertices +% .z3 : depth of all third vertices +% .zc : depth of element centroid +% + +Patches.z1 = []; +Patches.z2 = []; +Patches.z3 = []; +Patches.zc = []; +Patches.x1 = []; +Patches.y1 = []; +Patches.x2 = []; +Patches.y2 = []; +Patches.x3 = []; +Patches.y3 = []; +Patches.xc = []; +Patches.yc = []; + +Patches.x1 = [Patches.x1; Patches.c(Patches.v(:, 1), 1)]; +Patches.y1 = [Patches.y1; Patches.c(Patches.v(:, 1), 2)]; +Patches.z1 = [Patches.z1 ; Patches.c(Patches.v(:, 1), 3)]; +Patches.x2 = [Patches.x2; Patches.c(Patches.v(:, 2), 1)]; +Patches.y2 = [Patches.y2; Patches.c(Patches.v(:, 2), 2)]; +Patches.z2 = [Patches.z2 ; Patches.c(Patches.v(:, 2), 3)]; +Patches.x3 = [Patches.x3; Patches.c(Patches.v(:, 3), 1)]; +Patches.y3 = [Patches.y3; Patches.c(Patches.v(:, 3), 2)]; +Patches.z3 = [Patches.z3 ; Patches.c(Patches.v(:, 3), 3)]; +[cx,cy,cz] = centroid3([Patches.x1 Patches.x2 Patches.x3],... + [Patches.y1 Patches.y2 Patches.y3],... + [Patches.z1 Patches.z2 Patches.z3]); +Patches.xc = [Patches.xc; cx]; +Patches.yc = [Patches.yc; cy]; +Patches.zc = [Patches.zc; cz]; + +[Patches.strike, Patches.dip, Patches.nv] = tristrikedip(Patches.c, Patches.v); +Patches.up = ones(size(Patches.nEl)); diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/README.md b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/README.md new file mode 100644 index 0000000..058b723 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/README.md @@ -0,0 +1,6 @@ +# tridisl +Triangular dislocation element wrapper functions in Matlab + +Based on algorithms published in: + +Meade, B. J. (2007), Algorithms for the calculation of exact displacements, strains, and stresses for triangular dislocation elements in a uniform elastic half space, *Computers and Geosciences*, **33**, 1064–1075, [doi:10.1016/j.cageo.2006.12.003](http://dx.doi.org/10.1016/j.cageo.2006.12.003). diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/ReadPatches.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/ReadPatches.m new file mode 100644 index 0000000..b0e3c6d --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/ReadPatches.m @@ -0,0 +1,52 @@ +function Patches = ReadPatches(filenames); +% +% ReadPatches.m +% +% This function reads in any triangulated patch files specified by +% Segment.other1 and returns their coordinates to Patches. +% +% Arguments: +% filenames : string containing all filenames of patch files +% +% Returned variables: +% Patches : a structure containing: +% .c : all vertex coordinates (n x 3) +% .v : element vertex indices (m x 3) +% .nEl : number of elements in each patch file +% .nc : number of coordinates in each patch file +% +Patches.c = []; +Patches.v = []; +Patches.nEl = []; +Patches.nc = []; + +if numel(filenames) > 0 + if size(filenames, 1) == 1 + spaces = [0 findstr(filenames, ' ') length(filenames)+1]; + nfiles = length(spaces) - 1; + else + nfiles = size(filenames, 1); + end + + for i = 1:nfiles + if exist('spaces', 'var') + filename = filenames(spaces(i)+1:spaces(i+1)-1); + else + filename = strtrim(filenames(i, :)); + end + + if filename(end-3:end) == '.msh' + [c, v] = msh2coords(filename); + elseif filename(end-3:end) == '.mat' + load(filename, 'c', 'v') + end + crossd = cross([c(v(:, 2), :) - c(v(:, 1), :)], [c(v(:, 3), :) - c(v(:, 1), :)]); + negp = find(crossd(:, 3) < 0); + [v(negp, 2), v(negp, 3)] = swap(v(negp, 2), v(negp, 3)); + Patches.v = [Patches.v; v + sum(size(Patches.c, 1))]; + c = [str2num(num2str(c(:, 1), '%3.3f')), str2num(num2str(c(:, 2), '%3.3f')), str2num(num2str(c(:, 3), '%3.3f'))]; % Consistent with precision of station, segment files. We need a consistent precision when checking for existing kernels + Patches.c = [Patches.c; c]; + Patches.nEl = [Patches.nEl; size(v, 1)]; + Patches.nc = [Patches.nc; size(c, 1)]; + end +end \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/bluewhitered.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/bluewhitered.m new file mode 100644 index 0000000..e56f19b --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/bluewhitered.m @@ -0,0 +1,126 @@ +function newmap = bluewhitered(m, varargin) +%BLUEWHITERED Blue, white, and red color map. +% BLUEWHITERED(M) returns an M-by-3 matrix containing a blue to white +% to red colormap, with white corresponding to the CAXIS value closest +% to zero. This colormap is most useful for images and surface plots +% with positive and negative values. BLUEWHITERED, by itself, is the +% same length as the current colormap. +% +% Examples: +% ------------------------------ +% figure +% imagesc(peaks(250)); +% colormap(bluewhitered(256)), colorbar +% +% figure +% imagesc(peaks(250), [0 8]) +% colormap(bluewhitered), colorbar +% +% figure +% imagesc(peaks(250), [-6 0]) +% colormap(bluewhitered), colorbar +% +% figure +% surf(peaks) +% colormap(bluewhitered) +% axis tight +% +% See also HSV, HOT, COOL, BONE, COPPER, PINK, FLAG, +% COLORMAP, RGBPLOT. + + +if nargin < 1 + m = size(get(gcf,'colormap'),1); +end + + +bottom = [0 0 0.5]; +botmiddle = [0 0.5 1]; +middle = [1 1 1]; +topmiddle = [1 0 0]; +top = [0.5 0 0]; + +% Find middle +if nargin == 2; + lims = varargin{:}; +else + lims = get(gca, 'CLim'); +end + +% Find ratio of negative to positive +if (lims(1) < 0) & (lims(2) > 0) + % It has both negative and positive + % Find ratio of negative to positive + ratio = abs(lims(1)) / (abs(lims(1)) + lims(2)); + neglen = round(m*ratio); + poslen = m - neglen; + + % Just negative + new = [bottom; botmiddle; middle]; + len = length(new); + oldsteps = linspace(0, 1, len); + newsteps = linspace(0, 1, neglen); + newmap1 = zeros(neglen, 3); + + for i=1:3 + % Interpolate over RGB spaces of colormap + newmap1(:,i) = min(max(interp1(oldsteps, new(:,i), newsteps)', 0), 1); + end + + % Just positive + new = [middle; topmiddle; top]; + len = length(new); + oldsteps = linspace(0, 1, len); + newsteps = linspace(0, 1, poslen); + newmap = zeros(poslen, 3); + + for i=1:3 + % Interpolate over RGB spaces of colormap + newmap(:,i) = min(max(interp1(oldsteps, new(:,i), newsteps)', 0), 1); + end + + % And put 'em together + newmap = [newmap1; newmap]; + +elseif lims(1) >= 0 + % Just positive + new = [middle; topmiddle; top]; + len = length(new); + oldsteps = linspace(0, 1, len); + newsteps = linspace(0, 1, m); + newmap = zeros(m, 3); + + for i=1:3 + % Interpolate over RGB spaces of colormap + newmap(:,i) = min(max(interp1(oldsteps, new(:,i), newsteps)', 0), 1); + end + +else + % Just negative + new = [bottom; botmiddle; middle]; + len = length(new); + oldsteps = linspace(0, 1, len); + newsteps = linspace(0, 1, m); + newmap = zeros(m, 3); + + for i=1:3 + % Interpolate over RGB spaces of colormap + newmap(:,i) = min(max(interp1(oldsteps, new(:,i), newsteps)', 0), 1); + end + +end +% +% m = 64; +% new = [bottom; botmiddle; middle; topmiddle; top]; +% % x = 1:m; +% +% oldsteps = linspace(0, 1, 5); +% newsteps = linspace(0, 1, m); +% newmap = zeros(m, 3); +% +% for i=1:3 +% % Interpolate over RGB spaces of colormap +% newmap(:,i) = min(max(interp1(oldsteps, new(:,i), newsteps)', 0), 1); +% end +% +% % set(gcf, 'colormap', newmap), colorbar \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/centroid3.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/centroid3.m new file mode 100644 index 0000000..6e99ff5 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/centroid3.m @@ -0,0 +1,23 @@ +function [cx, cy, cz] = centroid3(x, y, z, varargin) +% +% [cx, cy, cz] = centroid3(x, y, z) +% +% Function centroid3 calculates the three-dimensional centroid (center of +% mass) coordinates of an n-sided polygon given the x,y,z coordinates of +% its vertices, assuming equal masses located at each vertex. x, y, and z +% can either be 1 x n or k x n arrays of coordinates. +% +% [cx, cy, cz] = centroid3(x, y, z, m) +% +% Function centroid3 calculates the centroid coordinates as above, but +% considering different masses at each vertex. m should be the same +% size as x, y, and z. +% +if nargin == 4; + m = varargin{:}; +else + m = ones(size(x)); +end + +cc = [sum(m.*x, 2) sum(m.*y, 2) sum(m.*z, 2)]./repmat(sum(m, 2), 1, 3); +cx = cc(:, 1); cy = cc(:, 2); cz = cc(:, 3); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/mag.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/mag.m new file mode 100644 index 0000000..1aa8dbb --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/mag.m @@ -0,0 +1,21 @@ +function m = mag(x,varargin); +% +% MAG calculates the magnitude of a vector. +% +% M = MAG(X) determines the magnitude of the vector X. X is one +% dimensional, either a row or column vector. +% +% M = MAG(X,DIM) determines the magnitude along the dimension DIM. +% To calculate the magnitude of the vectors whose components are +% contained in the columns of X, prescribe DIM = 2. To calculate +% the magnitude of the vectors whose components are in the rows of +% X, DIM = 1. +% + +if nargin == 2; + dim = varargin{1}; +else + dim = 1; +end + +m = sqrt(sum(x.^2,dim)); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/meshview.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/meshview.m new file mode 100644 index 0000000..5cf02a4 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/meshview.m @@ -0,0 +1,71 @@ +function h = meshview(c, v, varargin) +% +% MESHVIEW plots a triangulated mesh in a new figure. +% +% MESHVIEW(C, V) plots the triangulated mesh using the vertex coordinates +% contained in C and the element vertex indices contained in V. C is an +% n x 2 or n x 3 array of values containing the x, y or x, y, and z values +% of each of the n vertices. V is an m x 3 array, each line of which contains +% the indices of the 3 vertices that make up each of the m triangular elements. +% If C is n x 2, a 2-D representation of the mesh will be plotted and if C is +% n x 3, the full 3-D mesh will be plotted. +% +% MESHVIEW(C, V, COLOR) plots the mesh and colors the elements using the information +% in array COLOR. COLOR can either be a 1 x 3 vector specifying the RGB color values +% used to plot all elements, or an m x 1 array providing values characterizing the +% elements, i.e. slip magnitudes. If COLOR is an m x 3 array, it is assumed that +% the values contained in the columns of COLOR represent some characteristic of the +% element in the x, y, and z directions, e.g., slip magnitude in three directions. In +% this case, the total magnitude of slip is automatically calculated and used to color +% the elements; to color the elements by a particular component, specify that component +% as the m x 1 vector COLOR. +% +% MESHVIEW(C, V, FIGURE) plots the mesh in the figure window specified with FIGURE. The +% default behavior is to plot the mesh in a new figure window. +% +% MESHVIEW(C, V, COLOR, FIGURE) uses both optional inputs. +% +% H = MESHVIEW(...) returns the patch objects to the handle H. +% + +% parse optional color input +if nargin == 3; + if numel(varargin{1}) == 1 % figure flag is specified + fign = varargin{1}; + color = repmat([1 1 1], size(v, 1), 1); % color the elements white if no color is given + else + color = varargin{1}; + if size(color, 2) == 3 % an array of x, y, z, values were given + color = mag(color, 2); + end + fign = []; + end +elseif nargin == 4; + color = varargin{1}; + if size(color, 2) == 3 % an array of x, y, z, values were given + color = mag(color, 2); + end + fign = varargin{2}; +else + color = repmat([1 1 1], size(v, 1), 1); % color the elements white if no color is given + fign = []; +end + +% make the plot +if numel(fign) == 0; + figure + ax = gca; +else + if round(fign) == fign; % if it's actually a figure number + figure(fign); + ax = gca; + hold on + else % otherwise it's an axis handle + ax = fign; + hold on + end +end +h = patch('Vertices', c, 'faces', v, 'facevertexcdata', color, 'facecolor', 'flat', 'edgecolor', 'black', 'parent', ax); +%caxis = [min(color), max(color)]; +axis equal; +colormap(bluewhitered); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/msh2coords.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/msh2coords.m new file mode 100644 index 0000000..407ef95 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/msh2coords.m @@ -0,0 +1,30 @@ +function [c,v] = msh2coords(file) +% +% MSH2COORDS extracts coordinate and vertex information from a Gmsh .msh file. +% +% [C,V] = MSH2COORDS(FILE) extracts the coordinates and vertex ordering of +% triangular elements from the Gmsh .msh file named FILE. The coordinates +% are returned to the n x 3 array C, arranged with the x, y, and z locations +% of coordinates in the three columns. V is an m x 3 array containing the +% indices of the 3 vertices making up each of the m triangular elements. +% + +% open file as character array +in = opentxt(file); + +% extract number of nodes and elements +nnode = str2double(in(5,:)); +ne = str2double(in(8+nnode,:)); + +c = str2num(in(6:5+nnode,:)); +c = c(:,2:end); + +% find 1-D elements and ignore +d1 = 9+nnode; % start at line of first element listing +sp = strfind(in(d1,:),' '); % find the locations of spaces in that line +while str2double(in(d1,sp(1)+1)) == 1; % while the first char. after the first space = 1... + d1 = d1+1; % skip that line: it's a one-dimensional element + sp = strfind(in(d1,:),' '); % make a new index of space locations +end +v = str2num(in(d1:8+nnode+ne,:)); +v = v(:,end-2:end); diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/stack2.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/stack2.m new file mode 100644 index 0000000..237af55 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/stack2.m @@ -0,0 +1,11 @@ +function b = stack2(a) +% stack2 Converts an n-by-2 array to a 2n-by-1 column vector. +% stack2(A) converts the n-by-2 array A to a 2n-by-1 column vector +% with order [A(1, 1) A(1, 2)...A(n, 1) A(n, 2)]' +% +% B = stack2(A) returns the output to vector B. +% +% See also: stack3, unstack3, unstack2 +% + +b = reshape(a', 2*size(a, 1), 1); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/stack3.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/stack3.m new file mode 100644 index 0000000..9c1d411 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/stack3.m @@ -0,0 +1,11 @@ +function b = stack3(a) +% stack3 Converts an n-by-3 array to a 3n-by-1 column vector. +% stack3(A) converts the n-by-3 array A to a 3n-by-1 column vector +% with order [A(1, 1) A(1, 2) A(1, 3)...A(n, 1) A(n, 2) A(n, 3)]' +% +% B = stack3(A) returns the output to vector B. +% +% See also: unstack3, stack2, unstack2 +% + +b = reshape(a', 3*size(a, 1), 1); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/swap.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/swap.m new file mode 100644 index 0000000..0f7109a --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/swap.m @@ -0,0 +1,5 @@ +function [a b] = swap(a, b) +% Swap two values +temp = a; +a = b; +b = temp; diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tri_dislz_partials.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tri_dislz_partials.m new file mode 100644 index 0000000..dfc39e1 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tri_dislz_partials.m @@ -0,0 +1,601 @@ +function [uxs, uys, uzs,... + uxd, uyd, uzd,... + uxt, uyt, uzt, normVec] = tri_dislz_partials(x, y, z, sx, sy, sz, pr) +% +% tri_disl.m +% +% Calculates displacements due to slip on a triangular dislocation in an +% elastic half space utilizing the Comninou and Dunders (1975) expressions +% for the displacements due to an angular dislocation in an elastic half +% space. +% +% Arguments +% x : x-coordinates of 3 triangle vertices. +% y : y-coordinates of 3 triangle vertices. +% z : z-coordinates of 3 triangle vertices. +% sx : x-coordinates of observation points +% sy : y-coordinates of observation points +% sz : z-coordinates of observation points +% ss : strike slip displacement +% ds : dip slip displacement +% ts : tensile slip displacement +% pr : Poisson's ratio +% +% Returns +% uij : each uij represents the deformation in the i direction due to +% element slip in the j direction, where i is x, y, z and j is +% s, d, t (corresponding to strike, dip, and tensile slip). + + +% Calculate the slip vector in XYZ coordinates +normVec = cross([x(2);y(2);z(2)]-[x(1);y(1);z(1)], [x(3);y(3);z(3)]-[x(1);y(1);z(1)]); +normVec = normVec./norm(normVec); +% Enforce clockwise circulation +normVec = (sign(normVec(3)) + (normVec(3) == 0))*normVec; +vord = [1 2+(normVec(3) < 0) 3-(normVec(3) < 0)]; +x = x(vord); +y = y(vord); +z = z(vord); +strikeVec = [-sin(atan2(normVec(2),normVec(1))) cos(atan2(normVec(2),normVec(1))) 0]'; +dipVec = cross(normVec, strikeVec); +slipComp = [1 1 1]; +slipVec = [strikeVec(:) dipVec(:) normVec(:)] * slipComp(:); + +% Solution vectors +[uxs, uys, uzs... + uxd, uyd, uzd... + uxt, uyt, uzt] = deal(zeros(size(sx))); + +% Add a copy of the first vertex to the vertex list for indexing +x = [x x(1)]; +y = [y y(1)]; +z = [z z(1)]; + +%%%%%%%%%%%%%%%%%%%%%% +% Leg 1 contribution % +%%%%%%%%%%%%%%%%%%%%%% + +% Calculate strike and dip of leg 1 +strike = 180/pi*(atan2(y(2)-y(1), x(2)-x(1))); +segMapLength = sqrt((x(1)-x(2))^2 + (y(1)-y(2))^2); +[rx ry] = RotateXyVec(x(2)-x(1), y(2)-y(1), -strike); +dip = 180/pi*(atan2(z(2)-z(1), rx)); + +nd = sign(dip) + (dip == 0); +beta = nd*pi/180*(90 - nd*dip); +beta(nd*beta > pi/2) = pi/2 - nd*beta; + +ssVec = [cos(strike/180*pi); sin(strike/180*pi); 0]; +dsVec = [-sin(strike/180*pi); cos(strike/180*pi); 0]; +tsVec = cross(ssVec, dsVec); +lss = dot(slipVec, ssVec); +lds = dot(slipVec, dsVec); +lts = dot(slipVec, tsVec); + +lsss = dot(strikeVec, ssVec); +lssd = dot(strikeVec, dsVec); +lsst = dot(strikeVec, tsVec); + +ldss = dot(dipVec, ssVec); +ldsd = dot(dipVec, dsVec); +ldst = dot(dipVec, tsVec); + +ltss = dot(normVec, ssVec); +ltsd = dot(normVec, dsVec); +ltst = dot(normVec, tsVec); + +ratios = repmat([lsss lssd lsst]./[lss lds lts], length(sx), 1); ratios(isnan(ratios)) = 1; +ratiod = repmat([ldss ldsd ldst]./[lss lds lts], length(sx), 1); ratiod(isnan(ratiod)) = 1; +ratiot = repmat([ltss ltsd ltst]./[lss lds lts], length(sx), 1); ratiot(isnan(ratiot)) = 1; + +% First angular dislocation +[sx1 sy1] = RotateXyVec(sx-x(1), sy-y(1), -strike); +[ux11, uy11, uz11... + ux12, uy12, uz12... + ux13, uy13, uz13] = adv(sx1, sy1, sz-z(1), z(1), beta, pr, lss, lds, lts); + +% Project displacements so that individual slip component partials are returned +uxvec = [ux11 ux12 ux13]; +uyvec = [uy11 uy12 uy13]; +uzvec = [uz11 uz12 uz13]; + +ux1s = dot(uxvec, ratios, 2); +uy1s = dot(uyvec, ratios, 2); +uz1s = dot(uzvec, ratios, 2); + +ux1d = dot(uxvec, ratiod, 2); +uy1d = dot(uyvec, ratiod, 2); +uz1d = dot(uzvec, ratiod, 2); + +ux1t = dot(uxvec, ratiot, 2); +uy1t = dot(uyvec, ratiot, 2); +uz1t = dot(uzvec, ratiot, 2); + +% Second angular dislocation +[sx2 sy2] = RotateXyVec(sx-x(2), sy-y(2), -strike); + [ux21, uy21, uz21... + ux22, uy22, uz22... + ux23, uy23, uz23] = adv(sx2, sy2, sz-z(2), z(2), beta, pr, lss, lds, lts); + +% Project displacements so that individual slip component partials are returned +uxvec = [ux21 ux22 ux23]; +uyvec = [uy21 uy22 uy23]; +uzvec = [uz21 uz22 uz23]; + +ux2s = dot(uxvec, ratios, 2); +uy2s = dot(uyvec, ratios, 2); +uz2s = dot(uzvec, ratios, 2); + +ux2d = dot(uxvec, ratiod, 2); +uy2d = dot(uyvec, ratiod, 2); +uz2d = dot(uzvec, ratiod, 2); + +ux2t = dot(uxvec, ratiot, 2); +uy2t = dot(uyvec, ratiot, 2); +uz2t = dot(uzvec, ratiot, 2); + +% Rotate vectors to correct for strike +[uxns uyns] = RotateXyVec(ux1s-ux2s, uy1s-uy2s, strike); +[uxnd uynd] = RotateXyVec(ux1d-ux2d, uy1d-uy2d, strike); +[uxnt uynt] = RotateXyVec(ux1t-ux2t, uy1t-uy2t, strike); +uzns = uz1s-uz2s; +uznd = uz1d-uz2d; +uznt = uz1t-uz2t; + +% Add the displacements from leg 1 +uxns(isnan(uxns)) = 0; +uyns(isnan(uyns)) = 0; +uzns(isnan(uzns)) = 0; + +uxnd(isnan(uxnd)) = 0; +uynd(isnan(uynd)) = 0; +uznd(isnan(uznd)) = 0; + +uxnt(isnan(uxnt)) = 0; +uynt(isnan(uynt)) = 0; +uznt(isnan(uznt)) = 0; + +uxs = uxs + uxns; +uys = uys + uyns; +uzs = uzs + uzns; + +uxd = uxd + uxnd; +uyd = uyd + uynd; +uzd = uzd + uznd; + +uxt = uxt + uxnt; +uyt = uyt + uynt; +uzt = uzt + uznt; + +%%%%%%%%%%%%%%%%%%%%%% +% Leg 2 contribution % +%%%%%%%%%%%%%%%%%%%%%% + +% Calculate strike and dip of leg 2 +strike = 180/pi*(atan2(y(3)-y(2), x(3)-x(2))); +segMapLength = sqrt((x(2)-x(3))^2 + (y(2)-y(3))^2); +[rx ry] = RotateXyVec(x(3)-x(2), y(3)-y(2), -strike); +dip = 180/pi*(atan2(z(3)-z(2), rx)); + +nd = sign(dip) + (dip == 0); +beta = nd*pi/180*(90 - nd*dip); +beta(nd*beta > pi/2) = pi/2 - nd*beta; + +ssVec = [cos(strike/180*pi); sin(strike/180*pi); 0]; +dsVec = [-sin(strike/180*pi); cos(strike/180*pi); 0]; +tsVec = cross(ssVec, dsVec); +lss = dot(slipVec, ssVec); +lds = dot(slipVec, dsVec); +lts = dot(slipVec, tsVec); + +lsss = dot(strikeVec, ssVec); +lssd = dot(strikeVec, dsVec); +lsst = dot(strikeVec, tsVec); + +ldss = dot(dipVec, ssVec); +ldsd = dot(dipVec, dsVec); +ldst = dot(dipVec, tsVec); + +ltss = dot(normVec, ssVec); +ltsd = dot(normVec, dsVec); +ltst = dot(normVec, tsVec); + +ratios = repmat([lsss lssd lsst]./[lss lds lts], length(sx), 1); ratios(isnan(ratios)) = 1; +ratiod = repmat([ldss ldsd ldst]./[lss lds lts], length(sx), 1); ratiod(isnan(ratiod)) = 1; +ratiot = repmat([ltss ltsd ltst]./[lss lds lts], length(sx), 1); ratiot(isnan(ratiot)) = 1; + +% First angular dislocation +[sx1 sy1] = RotateXyVec(sx-x(2), sy-y(2), -strike); +[ux11, uy11, uz11... + ux12, uy12, uz12... + ux13, uy13, uz13] = adv(sx1, sy1, sz-z(2), z(2), beta, pr, lss, lds, lts); + +% Project displacements so that individual slip component partials are returned +uxvec = [ux11 ux12 ux13]; +uyvec = [uy11 uy12 uy13]; +uzvec = [uz11 uz12 uz13]; + +ux1s = dot(uxvec, ratios, 2); +uy1s = dot(uyvec, ratios, 2); +uz1s = dot(uzvec, ratios, 2); + +ux1d = dot(uxvec, ratiod, 2); +uy1d = dot(uyvec, ratiod, 2); +uz1d = dot(uzvec, ratiod, 2); + +ux1t = dot(uxvec, ratiot, 2); +uy1t = dot(uyvec, ratiot, 2); +uz1t = dot(uzvec, ratiot, 2); + +% Second angular dislocation +[sx2 sy2] = RotateXyVec(sx-x(3), sy-y(3), -strike); + [ux21, uy21, uz21... + ux22, uy22, uz22... + ux23, uy23, uz23] = adv(sx2, sy2, sz-z(3), z(3), beta, pr, lss, lds, lts); + +% Project displacements so that individual slip component partials are returned +uxvec = [ux21 ux22 ux23]; +uyvec = [uy21 uy22 uy23]; +uzvec = [uz21 uz22 uz23]; + +ux2s = dot(uxvec, ratios, 2); +uy2s = dot(uyvec, ratios, 2); +uz2s = dot(uzvec, ratios, 2); + +ux2d = dot(uxvec, ratiod, 2); +uy2d = dot(uyvec, ratiod, 2); +uz2d = dot(uzvec, ratiod, 2); + +ux2t = dot(uxvec, ratiot, 2); +uy2t = dot(uyvec, ratiot, 2); +uz2t = dot(uzvec, ratiot, 2); + +% Rotate vectors to correct for strike +[uxns uyns] = RotateXyVec(ux1s-ux2s, uy1s-uy2s, strike); +[uxnd uynd] = RotateXyVec(ux1d-ux2d, uy1d-uy2d, strike); +[uxnt uynt] = RotateXyVec(ux1t-ux2t, uy1t-uy2t, strike); +uzns = uz1s-uz2s; +uznd = uz1d-uz2d; +uznt = uz1t-uz2t; + +% Add the displacements from leg 2 +uxns(isnan(uxns)) = 0; +uyns(isnan(uyns)) = 0; +uzns(isnan(uzns)) = 0; + +uxnd(isnan(uxnd)) = 0; +uynd(isnan(uynd)) = 0; +uznd(isnan(uznd)) = 0; + +uxnt(isnan(uxnt)) = 0; +uynt(isnan(uynt)) = 0; +uznt(isnan(uznt)) = 0; + +uxs = uxs + uxns; +uys = uys + uyns; +uzs = uzs + uzns; + +uxd = uxd + uxnd; +uyd = uyd + uynd; +uzd = uzd + uznd; + +uxt = uxt + uxnt; +uyt = uyt + uynt; +uzt = uzt + uznt; + +%%%%%%%%%%%%%%%%%%%%%% +% Leg 3 contribution % +%%%%%%%%%%%%%%%%%%%%%% + +% Calculate strike and dip of leg 3 +strike = 180/pi*(atan2(y(4)-y(3), x(4)-x(3))); +segMapLength = sqrt((x(3)-x(4))^2 + (y(3)-y(4))^2); +[rx ry] = RotateXyVec(x(4)-x(3), y(4)-y(3), -strike); +dip = 180/pi*(atan2(z(4)-z(3), rx)); + +nd = sign(dip) + (dip == 0); +beta = nd*pi/180*(90 - nd*dip); +beta(nd*beta > pi/2) = pi/2 - nd*beta; + +ssVec = [cos(strike/180*pi); sin(strike/180*pi); 0]; +dsVec = [-sin(strike/180*pi); cos(strike/180*pi); 0]; +tsVec = cross(ssVec, dsVec); +lss = dot(slipVec, ssVec); +lds = dot(slipVec, dsVec); +lts = dot(slipVec, tsVec); + +lsss = dot(strikeVec, ssVec); +lssd = dot(strikeVec, dsVec); +lsst = dot(strikeVec, tsVec); + +ldss = dot(dipVec, ssVec); +ldsd = dot(dipVec, dsVec); +ldst = dot(dipVec, tsVec); + +ltss = dot(normVec, ssVec); +ltsd = dot(normVec, dsVec); +ltst = dot(normVec, tsVec); + +ratios = repmat([lsss lssd lsst]./[lss lds lts], length(sx), 1); ratios(isnan(ratios)) = 1; +ratiod = repmat([ldss ldsd ldst]./[lss lds lts], length(sx), 1); ratiod(isnan(ratiod)) = 1; +ratiot = repmat([ltss ltsd ltst]./[lss lds lts], length(sx), 1); ratiot(isnan(ratiot)) = 1; + +% First angular dislocation +[sx1 sy1] = RotateXyVec(sx-x(3), sy-y(3), -strike); +[ux11, uy11, uz11... + ux12, uy12, uz12... + ux13, uy13, uz13] = adv(sx1, sy1, sz-z(3), z(3), beta, pr, lss, lds, lts); + +% Project displacements so that individual slip component partials are returned +uxvec = [ux11 ux12 ux13]; +uyvec = [uy11 uy12 uy13]; +uzvec = [uz11 uz12 uz13]; + +ux1s = dot(uxvec, ratios, 2); +uy1s = dot(uyvec, ratios, 2); +uz1s = dot(uzvec, ratios, 2); + +ux1d = dot(uxvec, ratiod, 2); +uy1d = dot(uyvec, ratiod, 2); +uz1d = dot(uzvec, ratiod, 2); + +ux1t = dot(uxvec, ratiot, 2); +uy1t = dot(uyvec, ratiot, 2); +uz1t = dot(uzvec, ratiot, 2); + +% Second angular dislocation +[sx2 sy2] = RotateXyVec(sx-x(4), sy-y(4), -strike); + [ux21, uy21, uz21... + ux22, uy22, uz22... + ux23, uy23, uz23] = adv(sx2, sy2, sz-z(4), z(4), beta, pr, lss, lds, lts); + +% Project displacements so that individual slip component partials are returned +uxvec = [ux21 ux22 ux23]; +uyvec = [uy21 uy22 uy23]; +uzvec = [uz21 uz22 uz23]; + +ux2s = dot(uxvec, ratios, 2); +uy2s = dot(uyvec, ratios, 2); +uz2s = dot(uzvec, ratios, 2); + +ux2d = dot(uxvec, ratiod, 2); +uy2d = dot(uyvec, ratiod, 2); +uz2d = dot(uzvec, ratiod, 2); + +ux2t = dot(uxvec, ratiot, 2); +uy2t = dot(uyvec, ratiot, 2); +uz2t = dot(uzvec, ratiot, 2); + +% Rotate vectors to correct for strike +[uxns uyns] = RotateXyVec(ux1s-ux2s, uy1s-uy2s, strike); +[uxnd uynd] = RotateXyVec(ux1d-ux2d, uy1d-uy2d, strike); +[uxnt uynt] = RotateXyVec(ux1t-ux2t, uy1t-uy2t, strike); +uzns = uz1s-uz2s; +uznd = uz1d-uz2d; +uznt = uz1t-uz2t; + +% Add the displacements from leg 3 +uxns(isnan(uxns)) = 0; +uyns(isnan(uyns)) = 0; +uzns(isnan(uzns)) = 0; + +uxnd(isnan(uxnd)) = 0; +uynd(isnan(uynd)) = 0; +uznd(isnan(uznd)) = 0; + +uxnt(isnan(uxnt)) = 0; +uynt(isnan(uynt)) = 0; +uznt(isnan(uznt)) = 0; + +uxs = uxs + uxns; +uys = uys + uyns; +uzs = uzs + uzns; + +uxd = uxd + uxnd; +uyd = uyd + uynd; +uzd = uzd + uznd; + +uxt = uxt + uxnt; +uyt = uyt + uynt; +uzt = uzt + uznt; + +% Identify indices for stations under current triangle +inPolyIdx = intriangle(sx, sy, x, y, normVec); +t = LinePlaneIntersect(x, y, z, normVec, sx, sy, sz); +underIdx = t > 0 & t < 1 & inPolyIdx; + +% Apply static offset to the points that lie underneath the current triangle +uxs = uxs - underIdx*strikeVec(1); +uys = uys - underIdx*strikeVec(2); +uzs = uzs - underIdx*strikeVec(3); + +uxd = uxd - underIdx*dipVec(1); +uyd = uyd - underIdx*dipVec(2); +uzd = uzd - underIdx*dipVec(3); + +uxt = uxt - underIdx*normVec(1); +uyt = uyt - underIdx*normVec(2); +uzt = uzt - underIdx*normVec(3); + +function [in, on, t] = intriangle(x, y, xv, yv, ~) +% intriangle Tests for points inside a triangle. +% +% From http://paulbourke.net/geometry/insidepoly/ (Solution 3) + +% Make sure the first node has been replicated +xv = [xv(:); xv(1)]; +xv = xv(1:4); +yv = [yv(:); yv(1)]; +yv = yv(1:4); + +t1 = (y(:) - yv(1)).*(xv(2) - xv(1)) - (x(:) - xv(1)).*(yv(2) - yv(1)); +t2 = (y(:) - yv(2)).*(xv(3) - xv(2)) - (x(:) - xv(2)).*(yv(3) - yv(2)); +t3 = (y(:) - yv(3)).*(xv(4) - xv(3)) - (x(:) - xv(3)).*(yv(4) - yv(3)); + +t = [t1 t2 t3]; +on = ((sum(t == 0, 2) > 0) & (sum(t > 0, 2) == 2)); % Must lie on one edge and to the same side of the other edges + +% Alternative determination for the case of vertical triangles: look for points very close to the edges +[di, seg] = pointlinedist([xv, yv], [x, y]); +tol = 1e-11*max([xv([4; 3; 2])-xv([3; 2; 1]); yv([4; 3; 2])-yv([3; 2; 1])]); % Set tolerance +on = on | (max(di, [], 2) < tol & max(seg, [], 2)); % Test for close points +in = (on | (abs(sum(sign(t), 2)) == 3)); % All columns of t must have the same sign, indicating that the point lies tot eh same side of all edge + +function [dist, seg, xi, yi] = pointlinedist(lin, pt) +% pointlinedist Returns the shortest distance between a point a line. +% +% From http://www.paulbourke.net/geometry/pointlineplane + +% Replicate matrices to make dimensions agree +sl = size(lin, 1); +r = sort(repmat(1:sl, 1, 2)); r = r(2:end-1); +x1 = repmat(lin(r(1:2:end), 1)', size(pt, 1), 1); +y1 = repmat(lin(r(1:2:end), 2)', size(pt, 1), 1); +x2 = repmat(lin(r(2:2:end), 1)', size(pt, 1), 1); +y2 = repmat(lin(r(2:2:end), 2)', size(pt, 1), 1); +x3 = repmat(pt(:, 1), 1, size(x1, 2)); +y3 = repmat(pt(:, 2), 1, size(x1, 2)); + +x2m1 = x2 - x1; +y2m1 = y2 - y1; +u = ((x3 - x1).*x2m1 + (y3 - y1).*y2m1)./(x2m1.^2 + y2m1.^2); +seg = (u >= 0 & u <= 1); + +% Intersection coordinates +xi = x1 + u.*x2m1; +yi = y1 + u.*y2m1; + +% Distances +dist = sqrt((x3 - xi).^2 + (y3 - yi).^2); + + +function t = LinePlaneIntersect(x, y, z, normVec, sx, sy, sz) +% Calculate the intersection of a line and a plane using a parametric +% representation of the plane. This is hardcoded for a vertical line. +num = dot(repmat(normVec', size(sx)), repmat([x(1), y(1), z(1)], size(sx))-[sx, sy, sz], 2); +den = dot(repmat(normVec', size(sx)), [sx, sy, 0*sx]-[sx, sy, sz], 2); +den(den == 0) = eps; +t = num./den; % parametric curve parameter +% Special case for vertical elements; set t = 0.5 for points lying below the shallowest depth +t = (normVec(3) ~= 0)*t + (normVec(3) == 0)*0.5*(abs(sz) > abs(min(z))); + +function [xp yp] = RotateXyVec(x, y, alpha) +% Rotate a vector by an angle alpha +x = x(:); +y = y(:); +alpha = pi/180*alpha; +xp = cos(alpha).*x - sin(alpha).*y; +yp = sin(alpha).*x + cos(alpha).*y; + +function [v1B1 v2B1 v3B1 v1B2 v2B2 v3B2 v1B3 v2B3 v3B3] = adv(y1, y2, y3, a, beta, nu, B1, B2, B3) +% These are the displacements in a uniform elastic half space due to slip +% on an angular dislocation (Comninou and Dunders, 1975). Some of the +% equations for the B2 and B3 cases have been corrected following Thomas +% 1993. The equations are coded in way such that they roughly correspond +% to each line in original text. Exceptions have been made where it made +% more sense because of grouping symbols. + +sinbeta = sin(beta); +cosbeta = cos(beta); +cotbeta = 1./tan(beta); +z1 = y1.*cosbeta - y3.*sinbeta; +z3 = y1.*sinbeta + y3.*cosbeta; +R2 = y1.*y1 + y2.*y2 + y3.*y3; +R = sqrt(R2); +y3bar = y3 + 2.*a; +z1bar = y1.*cosbeta + y3bar.*sinbeta; +z3bar = -y1.*sinbeta + y3bar.*cosbeta; +R2bar = y1.*y1 + y2.*y2 + y3bar.*y3bar; +Rbar = sqrt(R2bar); +F = -atan2(y2, y1) + atan2(y2, z1) + atan2(y2.*R.*sinbeta, y1.*z1+(y2.*y2).*cosbeta); +Fbar = -atan2(y2, y1) + atan2(y2, z1bar) + atan2(y2.*Rbar.*sinbeta, y1.*z1bar+(y2.*y2).*cosbeta); + +% Case I: Burgers vector (B1,0,0) +v1InfB1 = 2.*(1-nu).*(F+Fbar) - y1.*y2.*(1./(R.*(R-y3)) + 1./(Rbar.*(Rbar+y3bar))) - ... + y2.*cosbeta.*((R.*sinbeta-y1)./(R.*(R-z3)) + (Rbar.*sinbeta-y1)./(Rbar.*(Rbar+z3bar))); +v2InfB1 = (1-2.*nu).*(log(R-y3)+log(Rbar+y3bar) - cosbeta.*(log(R-z3)+log(Rbar+z3bar))) - ... + y2.*y2.*(1./(R.*(R-y3))+1./(Rbar.*(Rbar+y3bar)) - cosbeta.*(1./(R.*(R-z3))+1./(Rbar.*(Rbar+z3bar)))); +v3InfB1 = y2 .* (1./R - 1./Rbar - cosbeta.*((R.*cosbeta-y3)./(R.*(R-z3)) - (Rbar.*cosbeta+y3bar)./(Rbar.*(Rbar+z3bar)))); +v1InfB1 = v1InfB1 ./ (8.*pi.*(1-nu)); +v2InfB1 = v2InfB1 ./ (8.*pi.*(1-nu)); +v3InfB1 = v3InfB1 ./ (8.*pi.*(1-nu)); + +v1CB1 = -2.*(1-nu).*(1-2.*nu).*Fbar.*(cotbeta.*cotbeta) + (1-2.*nu).*y2./(Rbar+y3bar) .* ((1-2.*nu-a./Rbar).*cotbeta - y1./(Rbar+y3bar).*(nu+a./Rbar)) + ... + (1-2.*nu).*y2.*cosbeta.*cotbeta./(Rbar+z3bar).*(cosbeta+a./Rbar) + a.*y2.*(y3bar-a).*cotbeta./(Rbar.*Rbar.*Rbar) + ... + y2.*(y3bar-a)./(Rbar.*(Rbar+y3bar)).*(-(1-2.*nu).*cotbeta + y1./(Rbar+y3bar) .* (2.*nu+a./Rbar) + a.*y1./(Rbar.*Rbar)) + ... + y2.*(y3bar-a)./(Rbar.*(Rbar+z3bar)).*(cosbeta./(Rbar+z3bar).*((Rbar.*cosbeta+y3bar) .* ((1-2.*nu).*cosbeta-a./Rbar).*cotbeta + 2.*(1-nu).*(Rbar.*sinbeta-y1).*cosbeta) - a.*y3bar.*cosbeta.*cotbeta./(Rbar.*Rbar)); +v2CB1 = (1-2.*nu).*((2.*(1-nu).*(cotbeta.*cotbeta)-nu).*log(Rbar+y3bar) -(2.*(1-nu).*(cotbeta.*cotbeta)+1-2.*nu).*cosbeta.*log(Rbar+z3bar)) - ... + (1-2.*nu)./(Rbar+y3bar).*(y1.*cotbeta.*(1-2.*nu-a./Rbar) + nu.*y3bar - a + (y2.*y2)./(Rbar+y3bar).*(nu+a./Rbar)) - ... + (1-2.*nu).*z1bar.*cotbeta./(Rbar+z3bar).*(cosbeta+a./Rbar) - a.*y1.*(y3bar-a).*cotbeta./(Rbar.*Rbar.*Rbar) + ... + (y3bar-a)./(Rbar+y3bar).*(-2.*nu + 1./Rbar.*((1-2.*nu).*y1.*cotbeta-a) + (y2.*y2)./(Rbar.*(Rbar+y3bar)).*(2.*nu+a./Rbar)+a.*(y2.*y2)./(Rbar.*Rbar.*Rbar)) + ... + (y3bar-a)./(Rbar+z3bar).*((cosbeta.*cosbeta) - 1./Rbar.*((1-2.*nu).*z1bar.*cotbeta+a.*cosbeta) + a.*y3bar.*z1bar.*cotbeta./(Rbar.*Rbar.*Rbar) - 1./(Rbar.*(Rbar+z3bar)) .* ((y2.*y2).*(cosbeta.*cosbeta) - a.*z1bar.*cotbeta./Rbar.*(Rbar.*cosbeta+y3bar))); + +v3CB1 = 2.*(1-nu).*(((1-2.*nu).*Fbar.*cotbeta) + (y2./(Rbar+y3bar).*(2.*nu+a./Rbar)) - (y2.*cosbeta./(Rbar+z3bar).*(cosbeta+a./Rbar))) + ... + y2.*(y3bar-a)./Rbar.*(2.*nu./(Rbar+y3bar)+a./(Rbar.*Rbar)) + ... + y2.*(y3bar-a).*cosbeta./(Rbar.*(Rbar+z3bar)).*(1-2.*nu-(Rbar.*cosbeta+y3bar)./(Rbar+z3bar).*(cosbeta + a./Rbar) - a.*y3bar./(Rbar.*Rbar)); + +v1CB1 = v1CB1 ./ (4.*pi.*(1-nu)); +v2CB1 = v2CB1 ./ (4.*pi.*(1-nu)); +v3CB1 = v3CB1 ./ (4.*pi.*(1-nu)); + +v1B1 = B1.*(v1InfB1 + v1CB1); +v2B1 = B1.*(v2InfB1 + v2CB1); +v3B1 = B1.*(v3InfB1 + v3CB1); + + +% Case II: Burgers vector (0,B2,0) +v1InfB2 = -(1-2.*nu).*(log(R-y3) + log(Rbar+y3bar)-cosbeta.*(log(R-z3)+log(Rbar+z3bar))) + ... + y1.*y1.*(1./(R.*(R-y3))+1./(Rbar.*(Rbar+y3bar))) + z1.*(R.*sinbeta-y1)./(R.*(R-z3)) + z1bar.*(Rbar.*sinbeta-y1)./(Rbar.*(Rbar+z3bar)); +v2InfB2 = 2.*(1-nu).*(F+Fbar) + y1.*y2.*(1./(R.*(R-y3))+1./(Rbar.*(Rbar+y3bar))) - y2.*(z1./(R.*(R-z3))+z1bar./(Rbar.*(Rbar+z3bar))); +v3InfB2 = -(1-2.*nu).*sinbeta.*(log(R-z3)-log(Rbar+z3bar)) - y1.*(1./R-1./Rbar) + z1.*(R.*cosbeta-y3)./(R.*(R-z3)) - z1bar.*(Rbar.*cosbeta+y3bar)./(Rbar.*(Rbar+z3bar)); +v1InfB2 = v1InfB2 ./ (8.*pi.*(1-nu)); +v2InfB2 = v2InfB2 ./ (8.*pi.*(1-nu)); +v3InfB2 = v3InfB2 ./ (8.*pi.*(1-nu)); + +v1CB2 = (1-2.*nu).*((2.*(1-nu).*(cotbeta.*cotbeta)+nu).*log(Rbar+y3bar) - (2.*(1-nu).*(cotbeta.*cotbeta)+1).*cosbeta.*log(Rbar+z3bar)) + ... + (1-2.*nu)./(Rbar+y3bar).* (-(1-2.*nu).*y1.*cotbeta+nu.*y3bar-a+a.*y1.*cotbeta./Rbar + (y1.*y1)./(Rbar+y3bar).*(nu+a./Rbar)) - ... + (1-2.*nu).*cotbeta./(Rbar+z3bar).*(z1bar.*cosbeta - a.*(Rbar.*sinbeta-y1)./(Rbar.*cosbeta)) - a.*y1.*(y3bar-a).*cotbeta./(Rbar.*Rbar.*Rbar) + ... + (y3bar-a)./(Rbar+y3bar).*(2.*nu + 1./Rbar.*((1-2.*nu).*y1.*cotbeta+a) - (y1.*y1)./(Rbar.*(Rbar+y3bar)).*(2.*nu+a./Rbar) - a.*(y1.*y1)./(Rbar.*Rbar.*Rbar)) + ... + (y3bar-a).*cotbeta./(Rbar+z3bar).*(-cosbeta.*sinbeta+a.*y1.*y3bar./(Rbar.*Rbar.*Rbar.*cosbeta) + (Rbar.*sinbeta-y1)./Rbar.*(2.*(1-nu).*cosbeta - (Rbar.*cosbeta+y3bar)./(Rbar+z3bar).*(1+a./(Rbar.*cosbeta)))); +v2CB2 = 2.*(1-nu).*(1-2.*nu).*Fbar.*cotbeta.*cotbeta + (1-2.*nu).*y2./(Rbar+y3bar).*(-(1-2.*nu-a./Rbar).*cotbeta + y1./(Rbar+y3bar).*(nu+a./Rbar)) - ... + (1-2.*nu).*y2.*cotbeta./(Rbar+z3bar).*(1+a./(Rbar.*cosbeta)) - a.*y2.*(y3bar-a).*cotbeta./(Rbar.*Rbar.*Rbar) + ... + y2.*(y3bar-a)./(Rbar.*(Rbar+y3bar)).*((1-2.*nu).*cotbeta - 2.*nu.*y1./(Rbar+y3bar) - a.*y1./Rbar.*(1./Rbar+1./(Rbar+y3bar))) + ... + y2.*(y3bar-a).*cotbeta./(Rbar.*(Rbar+z3bar)).*(-2.*(1-nu).*cosbeta + (Rbar.*cosbeta+y3bar)./(Rbar+z3bar).*(1+a./(Rbar.*cosbeta)) + a.*y3bar./((Rbar.*Rbar).*cosbeta)); +v3CB2 = -2.*(1-nu).*(1-2.*nu).*cotbeta .* (log(Rbar+y3bar)-cosbeta.*log(Rbar+z3bar)) - ... + 2.*(1-nu).*y1./(Rbar+y3bar).*(2.*nu+a./Rbar) + 2.*(1-nu).*z1bar./(Rbar+z3bar).*(cosbeta+a./Rbar) + ... + (y3bar-a)./Rbar.*((1-2.*nu).*cotbeta-2.*nu.*y1./(Rbar+y3bar)-a.*y1./(Rbar.*Rbar)) - ... + (y3bar-a)./(Rbar+z3bar).*(cosbeta.*sinbeta + (Rbar.*cosbeta+y3bar).*cotbeta./Rbar.*(2.*(1-nu).*cosbeta - (Rbar.*cosbeta+y3bar)./(Rbar+z3bar)) + a./Rbar.*(sinbeta - y3bar.*z1bar./(Rbar.*Rbar) - z1bar.*(Rbar.*cosbeta+y3bar)./(Rbar.*(Rbar+z3bar)))); +v1CB2 = v1CB2 ./ (4.*pi.*(1-nu)); +v2CB2 = v2CB2 ./ (4.*pi.*(1-nu)); +v3CB2 = v3CB2 ./ (4.*pi.*(1-nu)); + +v1B2 = B2.*(v1InfB2 + v1CB2); +v2B2 = B2.*(v2InfB2 + v2CB2); +v3B2 = B2.*(v3InfB2 + v3CB2); + + +% Case III: Burgers vector (0,0,B3) +v1InfB3 = y2.*sinbeta.*((R.*sinbeta-y1)./(R.*(R-z3))+(Rbar.*sinbeta-y1)./(Rbar.*(Rbar+z3bar))); +v2InfB3 = (1-2.*nu).*sinbeta.*(log(R-z3)+log(Rbar+z3bar)) - (y2.*y2).*sinbeta.*(1./(R.*(R-z3))+1./(Rbar.*(Rbar+z3bar))); +v3InfB3 = 2.*(1-nu).*(F-Fbar) + y2.*sinbeta.*((R.*cosbeta-y3)./(R.*(R-z3))-(Rbar.*cosbeta+y3bar)./(Rbar.*(Rbar+z3bar))); +v1InfB3 = v1InfB3 ./ (8.*pi.*(1-nu)); +v2InfB3 = v2InfB3 ./ (8.*pi.*(1-nu)); +v3InfB3 = v3InfB3 ./ (8.*pi.*(1-nu)); + +v1CB3 = (1-2.*nu).*(y2./(Rbar+y3bar).*(1+a./Rbar) - y2.*cosbeta./(Rbar+z3bar).*(cosbeta+a./Rbar)) - ... + y2.*(y3bar-a)./Rbar.*(a./(Rbar.*Rbar) + 1./(Rbar+y3bar)) + ... + y2.*(y3bar-a).*cosbeta./(Rbar.*(Rbar+z3bar)).*((Rbar.*cosbeta+y3bar)./(Rbar+z3bar).*(cosbeta+a./Rbar) + a.*y3bar./(Rbar.*Rbar)); +v2CB3 = (1-2.*nu).*(-sinbeta.*log(Rbar+z3bar) - y1./(Rbar+y3bar).*(1+a./Rbar) + z1bar./(Rbar+z3bar).*(cosbeta+a./Rbar)) + ... + y1.*(y3bar-a)./Rbar.*(a./(Rbar.*Rbar) + 1./(Rbar+y3bar)) - ... + (y3bar-a)./(Rbar+z3bar).*(sinbeta.*(cosbeta-a./Rbar) + z1bar./Rbar.*(1+a.*y3bar./(Rbar.*Rbar)) - ... + 1./(Rbar.*(Rbar+z3bar)).*((y2.*y2).*cosbeta.*sinbeta - a.*z1bar./Rbar.*(Rbar.*cosbeta+y3bar))); +v3CB3 = 2.*(1-nu).*Fbar + 2.*(1-nu).*(y2.*sinbeta./(Rbar+z3bar).*(cosbeta + a./Rbar)) + ... + y2.*(y3bar-a).*sinbeta./(Rbar.*(Rbar+z3bar)).*(1 + (Rbar.*cosbeta+y3bar)./(Rbar+z3bar).*(cosbeta+a./Rbar) + a.*y3bar./(Rbar.*Rbar)); +v1CB3 = v1CB3 ./ (4.*pi.*(1-nu)); +v2CB3 = v2CB3 ./ (4.*pi.*(1-nu)); +v3CB3 = v3CB3 ./ (4.*pi.*(1-nu)); + +v1B3 = B3.*(v1InfB3 + v1CB3); +v2B3 = B3.*(v2InfB3 + v2CB3); +v3B3 = B3.*(v3InfB3 + v3CB3); + diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tri_strain_fast_partials.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tri_strain_fast_partials.m new file mode 100644 index 0000000..5864f8d --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tri_strain_fast_partials.m @@ -0,0 +1,790 @@ +function [xxs, yys, zzs, xys, xzs, yzs,... + xxd, yyd, zzd, xyd, xzd, yzd,... + xxt, yyt, zzt, xyt, xzt, yzt, normVec] = tri_strain_fast_partials(x, y, z, sx, sy, sz, pr) +% +% tri_strain.m +% +% Calculates strains due to slip on a triangular dislocation in an +% elastic half space utilizing the symbolically differentiated +% displacement gradient tensor derived from the expressions for +% the displacements due to an angular dislocation in an elastic half +% space (Comninou and Dunders, 1975). +% +% Arguments +% sx : x-coordinates of observation points +% sy : y-coordinates of observation points +% sz : z-coordinates of observation points +% x : x-coordinates of triangle vertices. +% y : y-coordinates of triangle vertices. +% z : z-coordinates of triangle vertices. +% pr : Poisson's ratio +% ss : strike slip displacement +% ts : tensile slip displacement +% ds : dip slip displacement +% +% Returns +% ij : strain components (xx, yy, zz, xy, xz, yz) +% + + +% Calculate the slip vector in XYZ coordinates +normVec = cross([x(2);y(2);z(2)]-[x(1);y(1);z(1)], [x(3);y(3);z(3)]-[x(1);y(1);z(1)]); +normVec = normVec./norm(normVec); +% Enforce clockwise circulation +normVec = (sign(normVec(3)) + (normVec(3) == 0))*normVec; +vord = [1 2+(normVec(3) < 0) 3-(normVec(3) < 0)]; +x = x(vord); +y = y(vord); +z = z(vord); +strikeVec = [-sin(atan2(normVec(2),normVec(1))) cos(atan2(normVec(2),normVec(1))) 0]'; +dipVec = cross(normVec, strikeVec); +slipComp = [1 1 1]; +slipVec = [strikeVec(:) dipVec(:) normVec(:)] * slipComp(:); + +% Solution vectors +xxs = zeros(size(sx)); +yys = xxs; +zzs = xxs; +xys = xxs; +xzs = xxs; +yzs = xxs; + +xxd = xxs; +yyd = xxs; +zzd = xxs; +xyd = xxs; +xzd = xxs; +yzd = xxs; + +xxt = xxs; +yyt = xxs; +zzt = xxs; +xyt = xxs; +xzt = xxs; +yzt = xxs; + +% Add a copy of the first vertex to the vertex list for indexing +x = [x x(1)]; +y = [y y(1)]; +z = [z z(1)]; + +%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% Leg 1 contribution %%% +%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Calculate strike and dip of leg 1 +strike = 180/pi*(atan2(y(2)-y(1), x(2)-x(1))); +segMapLength = sqrt((x(1)-x(2))^2 + (y(1)-y(2))^2); +[rx ry] = RotateXyVec(x(2)-x(1), y(2)-y(1), -strike); +dip = 180/pi*(atan2(z(2)-z(1), rx)); + +nd = sign(dip) + (dip == 0); +beta = nd*pi/180*(90 - nd*dip); +beta(nd*beta > pi/2) = pi/2 - nd*beta; + +ssVec = [cos(strike/180*pi); sin(strike/180*pi); 0]; +dsVec = [-sin(strike/180*pi); cos(strike/180*pi); 0]; +tsVec = cross(ssVec, dsVec); +lss = dot(slipVec, ssVec); +lts = dot(slipVec, tsVec); +lds = dot(slipVec, dsVec); + +lsss = dot(strikeVec, ssVec); +lssd = dot(strikeVec, dsVec); +lsst = dot(strikeVec, tsVec); + +ldss = dot(dipVec, ssVec); +ldsd = dot(dipVec, dsVec); +ldst = dot(dipVec, tsVec); + +ltss = dot(normVec, ssVec); +ltsd = dot(normVec, dsVec); +ltst = dot(normVec, tsVec); + +ratios = repmat([lsss lssd lsst]./[lss lds lts], length(sx), 1); ratios(isnan(ratios)) = 1; +ratiod = repmat([ldss ldsd ldst]./[lss lds lts], length(sx), 1); ratiod(isnan(ratiod)) = 1; +ratiot = repmat([ltss ltsd ltst]./[lss lds lts], length(sx), 1); ratiot(isnan(ratiot)) = 1; + + +% First angular dislocation +[sx1 sy1] = RotateXyVec(sx-x(1), sy-y(1), -strike); +[a111 a221 a331 a121 a131 a231... + a112 a222 a332 a122 a132 a232... + a113 a223 a333 a123 a133 a233] = advs(sx1, sy1, sz-z(1), z(1), beta, pr, lss, lds, lts); + +% Project strains so that individual slip component partials are returned +xxvec = [a111 a112 a113]; +yyvec = [a221 a222 a223]; +zzvec = [a331 a332 a333]; +xyvec = [a121 a122 a123]; +xzvec = [a131 a132 a133]; +yzvec = [a231 a232 a233]; + +a11s = dot(xxvec, ratios, 2); +a22s = dot(yyvec, ratios, 2); +a33s = dot(zzvec, ratios, 2); +a12s = dot(xyvec, ratios, 2); +a13s = dot(xzvec, ratios, 2); +a23s = dot(yzvec, ratios, 2); + +a11d = dot(xxvec, ratiod, 2); +a22d = dot(yyvec, ratiod, 2); +a33d = dot(zzvec, ratiod, 2); +a12d = dot(xyvec, ratiod, 2); +a13d = dot(xzvec, ratiod, 2); +a23d = dot(yzvec, ratiod, 2); + +a11t = dot(xxvec, ratiot, 2); +a22t = dot(yyvec, ratiot, 2); +a33t = dot(zzvec, ratiot, 2); +a12t = dot(xyvec, ratiot, 2); +a13t = dot(xzvec, ratiot, 2); +a23t = dot(yzvec, ratiot, 2); + +% Second angular dislocation +[sx2 sy2] = RotateXyVec(sx-x(2), sy-y(2), -strike); +[b111 b221 b331 b121 b131 b231... + b112 b222 b332 b122 b132 b232... + b113 b223 b333 b123 b133 b233] = advs(sx2, sy2, sz-z(2), z(2), beta, pr, lss, lds, lts); + +% Project strains so that individual slip component partials are returned +xxvec = [b111 b112 b113]; +yyvec = [b221 b222 b223]; +zzvec = [b331 b332 b333]; +xyvec = [b121 b122 b123]; +xzvec = [b131 b132 b133]; +yzvec = [b231 b232 b233]; + +b11s = dot(xxvec, ratios, 2); +b22s = dot(yyvec, ratios, 2); +b33s = dot(zzvec, ratios, 2); +b12s = dot(xyvec, ratios, 2); +b13s = dot(xzvec, ratios, 2); +b23s = dot(yzvec, ratios, 2); + +b11d = dot(xxvec, ratiod, 2); +b22d = dot(yyvec, ratiod, 2); +b33d = dot(zzvec, ratiod, 2); +b12d = dot(xyvec, ratiod, 2); +b13d = dot(xzvec, ratiod, 2); +b23d = dot(yzvec, ratiod, 2); + +b11t = dot(xxvec, ratiot, 2); +b22t = dot(yyvec, ratiot, 2); +b33t = dot(zzvec, ratiot, 2); +b12t = dot(xyvec, ratiot, 2); +b13t = dot(xzvec, ratiot, 2); +b23t = dot(yzvec, ratiot, 2); + +% Rotate tensors to correct for strike +bxxs = a11s-b11s; +byys = a22s-b22s; +bzzs = a33s-b33s; +bxys = a12s-b12s; +bxzs = a13s-b13s; +byzs = a23s-b23s; + +bxxd = a11d-b11d; +byyd = a22d-b22d; +bzzd = a33d-b33d; +bxyd = a12d-b12d; +bxzd = a13d-b13d; +byzd = a23d-b23d; + +bxxt = a11t-b11t; +byyt = a22t-b22t; +bzzt = a33t-b33t; +bxyt = a12t-b12t; +bxzt = a13t-b13t; +byzt = a23t-b23t; + +g = pi/180*strike; +e11ns = (cos(g)*bxxs-sin(g)*bxys)*cos(g)-(cos(g)*bxys-sin(g)*byys)*sin(g); +e12ns = (cos(g)*bxxs-sin(g)*bxys)*sin(g)+(cos(g)*bxys-sin(g)*byys)*cos(g); +e13ns = cos(g)*bxzs-sin(g)*byzs; +e22ns = (sin(g)*bxxs+cos(g)*bxys)*sin(g)+(sin(g)*bxys+cos(g)*byys)*cos(g); +e23ns = sin(g)*bxzs+cos(g)*byzs; +e33ns = bzzs; + +e11nd = (cos(g)*bxxd-sin(g)*bxyd)*cos(g)-(cos(g)*bxyd-sin(g)*byyd)*sin(g); +e12nd = (cos(g)*bxxd-sin(g)*bxyd)*sin(g)+(cos(g)*bxyd-sin(g)*byyd)*cos(g); +e13nd = cos(g)*bxzd-sin(g)*byzd; +e22nd = (sin(g)*bxxd+cos(g)*bxyd)*sin(g)+(sin(g)*bxyd+cos(g)*byyd)*cos(g); +e23nd = sin(g)*bxzd+cos(g)*byzd; +e33nd = bzzd; + +e11nt = (cos(g)*bxxt-sin(g)*bxyt)*cos(g)-(cos(g)*bxyt-sin(g)*byyt)*sin(g); +e12nt = (cos(g)*bxxt-sin(g)*bxyt)*sin(g)+(cos(g)*bxyt-sin(g)*byyt)*cos(g); +e13nt = cos(g)*bxzt-sin(g)*byzt; +e22nt = (sin(g)*bxxt+cos(g)*bxyt)*sin(g)+(sin(g)*bxyt+cos(g)*byyt)*cos(g); +e23nt = sin(g)*bxzt+cos(g)*byzt; +e33nt = bzzt; + +% Add the strains from leg 1 +e11ns(isnan(e11ns)) = 0; +e22ns(isnan(e22ns)) = 0; +e33ns(isnan(e33ns)) = 0; +e12ns(isnan(e12ns)) = 0; +e13ns(isnan(e13ns)) = 0; +e23ns(isnan(e23ns)) = 0; + +e11nd(isnan(e11nd)) = 0; +e22nd(isnan(e22nd)) = 0; +e33nd(isnan(e33nd)) = 0; +e12nd(isnan(e12nd)) = 0; +e13nd(isnan(e13nd)) = 0; +e23nd(isnan(e23nd)) = 0; + +e11nt(isnan(e11nt)) = 0; +e22nt(isnan(e22nt)) = 0; +e33nt(isnan(e33nt)) = 0; +e12nt(isnan(e12nt)) = 0; +e13nt(isnan(e13nt)) = 0; +e23nt(isnan(e23nt)) = 0; + +xxs = xxs + e11ns; +yys = yys + e22ns; +zzs = zzs + e33ns; +xys = xys + e12ns; +xzs = xzs + e13ns; +yzs = yzs + e23ns; + +xxd = xxd + e11nd; +yyd = yyd + e22nd; +zzd = zzd + e33nd; +xyd = xyd + e12nd; +xzd = xzd + e13nd; +yzd = yzd + e23nd; + +xxt = xxt + e11nt; +yyt = yyt + e22nt; +zzt = zzt + e33nt; +xyt = xyt + e12nt; +xzt = xzt + e13nt; +yzt = yzt + e23nt; +%end + +%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% Leg 2 contribution %%% +%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Calculate strike and dip of leg 2 +strike = 180/pi*(atan2(y(3)-y(2), x(3)-x(2))); +segMapLength = sqrt((x(2)-x(3))^2 + (y(2)-y(3))^2); +[rx ry] = RotateXyVec(x(3)-x(2), y(3)-y(2), -strike); +dip = 180/pi*(atan2(z(3)-z(2), rx)); + +nd = sign(dip) + (dip == 0); +beta = nd*pi/180*(90 - nd*dip); +beta(nd*beta > pi/2) = pi/2 - nd*beta; + +ssVec = [cos(strike/180*pi); sin(strike/180*pi); 0]; +dsVec = [-sin(strike/180*pi); cos(strike/180*pi); 0]; +tsVec = cross(ssVec, dsVec); +lss = dot(slipVec, ssVec); +lts = dot(slipVec, tsVec); +lds = dot(slipVec, dsVec); + +lsss = dot(strikeVec, ssVec); +lssd = dot(strikeVec, dsVec); +lsst = dot(strikeVec, tsVec); + +ldss = dot(dipVec, ssVec); +ldsd = dot(dipVec, dsVec); +ldst = dot(dipVec, tsVec); + +ltss = dot(normVec, ssVec); +ltsd = dot(normVec, dsVec); +ltst = dot(normVec, tsVec); + +ratios = repmat([lsss lssd lsst]./[lss lds lts], length(sx), 1); ratios(isnan(ratios)) = 1; +ratiod = repmat([ldss ldsd ldst]./[lss lds lts], length(sx), 1); ratiod(isnan(ratiod)) = 1; +ratiot = repmat([ltss ltsd ltst]./[lss lds lts], length(sx), 1); ratiot(isnan(ratiot)) = 1; + +% First angular dislocation +[sx1 sy1] = RotateXyVec(sx-x(2), sy-y(2), -strike); +[a111 a221 a331 a121 a131 a231... + a112 a222 a332 a122 a132 a232... + a113 a223 a333 a123 a133 a233] = advs(sx1, sy1, sz-z(2), z(2), beta, pr, lss, lds, lts); + +% Project strains so that individual slip component partials are returned +xxvec = [a111 a112 a113]; +yyvec = [a221 a222 a223]; +zzvec = [a331 a332 a333]; +xyvec = [a121 a122 a123]; +xzvec = [a131 a132 a133]; +yzvec = [a231 a232 a233]; + +a11s = dot(xxvec, ratios, 2); +a22s = dot(yyvec, ratios, 2); +a33s = dot(zzvec, ratios, 2); +a12s = dot(xyvec, ratios, 2); +a13s = dot(xzvec, ratios, 2); +a23s = dot(yzvec, ratios, 2); + +a11d = dot(xxvec, ratiod, 2); +a22d = dot(yyvec, ratiod, 2); +a33d = dot(zzvec, ratiod, 2); +a12d = dot(xyvec, ratiod, 2); +a13d = dot(xzvec, ratiod, 2); +a23d = dot(yzvec, ratiod, 2); + +a11t = dot(xxvec, ratiot, 2); +a22t = dot(yyvec, ratiot, 2); +a33t = dot(zzvec, ratiot, 2); +a12t = dot(xyvec, ratiot, 2); +a13t = dot(xzvec, ratiot, 2); +a23t = dot(yzvec, ratiot, 2); + +% Second angular dislocation +[sx2 sy2] = RotateXyVec(sx-x(3), sy-y(3), -strike); +[b111 b221 b331 b121 b131 b231... + b112 b222 b332 b122 b132 b232... + b113 b223 b333 b123 b133 b233] = advs(sx2, sy2, sz-z(3), z(3), beta, pr, lss, lds, lts); + +% Project strains so that individual slip component partials are returned +xxvec = [b111 b112 b113]; +yyvec = [b221 b222 b223]; +zzvec = [b331 b332 b333]; +xyvec = [b121 b122 b123]; +xzvec = [b131 b132 b133]; +yzvec = [b231 b232 b233]; + +b11s = dot(xxvec, ratios, 2); +b22s = dot(yyvec, ratios, 2); +b33s = dot(zzvec, ratios, 2); +b12s = dot(xyvec, ratios, 2); +b13s = dot(xzvec, ratios, 2); +b23s = dot(yzvec, ratios, 2); + +b11d = dot(xxvec, ratiod, 2); +b22d = dot(yyvec, ratiod, 2); +b33d = dot(zzvec, ratiod, 2); +b12d = dot(xyvec, ratiod, 2); +b13d = dot(xzvec, ratiod, 2); +b23d = dot(yzvec, ratiod, 2); + +b11t = dot(xxvec, ratiot, 2); +b22t = dot(yyvec, ratiot, 2); +b33t = dot(zzvec, ratiot, 2); +b12t = dot(xyvec, ratiot, 2); +b13t = dot(xzvec, ratiot, 2); +b23t = dot(yzvec, ratiot, 2); + +% Rotate tensors to correct for strike +bxxs = a11s-b11s; +byys = a22s-b22s; +bzzs = a33s-b33s; +bxys = a12s-b12s; +bxzs = a13s-b13s; +byzs = a23s-b23s; + +bxxd = a11d-b11d; +byyd = a22d-b22d; +bzzd = a33d-b33d; +bxyd = a12d-b12d; +bxzd = a13d-b13d; +byzd = a23d-b23d; + +bxxt = a11t-b11t; +byyt = a22t-b22t; +bzzt = a33t-b33t; +bxyt = a12t-b12t; +bxzt = a13t-b13t; +byzt = a23t-b23t; + +g = pi/180*strike; +e11ns = (cos(g)*bxxs-sin(g)*bxys)*cos(g)-(cos(g)*bxys-sin(g)*byys)*sin(g); +e12ns = (cos(g)*bxxs-sin(g)*bxys)*sin(g)+(cos(g)*bxys-sin(g)*byys)*cos(g); +e13ns = cos(g)*bxzs-sin(g)*byzs; +e22ns = (sin(g)*bxxs+cos(g)*bxys)*sin(g)+(sin(g)*bxys+cos(g)*byys)*cos(g); +e23ns = sin(g)*bxzs+cos(g)*byzs; +e33ns = bzzs; + +e11nd = (cos(g)*bxxd-sin(g)*bxyd)*cos(g)-(cos(g)*bxyd-sin(g)*byyd)*sin(g); +e12nd = (cos(g)*bxxd-sin(g)*bxyd)*sin(g)+(cos(g)*bxyd-sin(g)*byyd)*cos(g); +e13nd = cos(g)*bxzd-sin(g)*byzd; +e22nd = (sin(g)*bxxd+cos(g)*bxyd)*sin(g)+(sin(g)*bxyd+cos(g)*byyd)*cos(g); +e23nd = sin(g)*bxzd+cos(g)*byzd; +e33nd = bzzd; + +e11nt = (cos(g)*bxxt-sin(g)*bxyt)*cos(g)-(cos(g)*bxyt-sin(g)*byyt)*sin(g); +e12nt = (cos(g)*bxxt-sin(g)*bxyt)*sin(g)+(cos(g)*bxyt-sin(g)*byyt)*cos(g); +e13nt = cos(g)*bxzt-sin(g)*byzt; +e22nt = (sin(g)*bxxt+cos(g)*bxyt)*sin(g)+(sin(g)*bxyt+cos(g)*byyt)*cos(g); +e23nt = sin(g)*bxzt+cos(g)*byzt; +e33nt = bzzt; + +% Add the strains from leg 2 +e11ns(isnan(e11ns)) = 0; +e22ns(isnan(e22ns)) = 0; +e33ns(isnan(e33ns)) = 0; +e12ns(isnan(e12ns)) = 0; +e13ns(isnan(e13ns)) = 0; +e23ns(isnan(e23ns)) = 0; + +e11nd(isnan(e11nd)) = 0; +e22nd(isnan(e22nd)) = 0; +e33nd(isnan(e33nd)) = 0; +e12nd(isnan(e12nd)) = 0; +e13nd(isnan(e13nd)) = 0; +e23nd(isnan(e23nd)) = 0; + +e11nt(isnan(e11nt)) = 0; +e22nt(isnan(e22nt)) = 0; +e33nt(isnan(e33nt)) = 0; +e12nt(isnan(e12nt)) = 0; +e13nt(isnan(e13nt)) = 0; +e23nt(isnan(e23nt)) = 0; + +xxs = xxs + e11ns; +yys = yys + e22ns; +zzs = zzs + e33ns; +xys = xys + e12ns; +xzs = xzs + e13ns; +yzs = yzs + e23ns; + +xxd = xxd + e11nd; +yyd = yyd + e22nd; +zzd = zzd + e33nd; +xyd = xyd + e12nd; +xzd = xzd + e13nd; +yzd = yzd + e23nd; + +xxt = xxt + e11nt; +yyt = yyt + e22nt; +zzt = zzt + e33nt; +xyt = xyt + e12nt; +xzt = xzt + e13nt; +yzt = yzt + e23nt; + +%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% Leg 3 contribution %%% +%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Calculate strike and dip of leg 1 +strike = 180/pi*(atan2(y(4)-y(3), x(4)-x(3))); +segMapLength = sqrt((x(3)-x(4))^2 + (y(3)-y(4))^2); +[rx ry] = RotateXyVec(x(4)-x(3), y(4)-y(3), -strike); +dip = 180/pi*(atan2(z(4)-z(3), rx)); + +nd = sign(dip) + (dip == 0); +beta = nd*pi/180*(90 - nd*dip); +beta(nd*beta > pi/2) = pi/2 - nd*beta; + +ssVec = [cos(strike/180*pi); sin(strike/180*pi); 0]; +dsVec = [-sin(strike/180*pi); cos(strike/180*pi); 0]; +tsVec = cross(ssVec, dsVec); +lss = dot(slipVec, ssVec); +lts = dot(slipVec, tsVec); +lds = dot(slipVec, dsVec); + +lsss = dot(strikeVec, ssVec); +lssd = dot(strikeVec, dsVec); +lsst = dot(strikeVec, tsVec); + +ldss = dot(dipVec, ssVec); +ldsd = dot(dipVec, dsVec); +ldst = dot(dipVec, tsVec); + +ltss = dot(normVec, ssVec); +ltsd = dot(normVec, dsVec); +ltst = dot(normVec, tsVec); + +ratios = repmat([lsss lssd lsst]./[lss lds lts], length(sx), 1); ratios(isnan(ratios)) = 1; +ratiod = repmat([ldss ldsd ldst]./[lss lds lts], length(sx), 1); ratiod(isnan(ratiod)) = 1; +ratiot = repmat([ltss ltsd ltst]./[lss lds lts], length(sx), 1); ratiot(isnan(ratiot)) = 1; + +% First angular dislocation +[sx1 sy1] = RotateXyVec(sx-x(3), sy-y(3), -strike); +[a111 a221 a331 a121 a131 a231... + a112 a222 a332 a122 a132 a232... + a113 a223 a333 a123 a133 a233] = advs(sx1, sy1, sz-z(3), z(3), beta, pr, lss, lds, lts); + +% Project strains so that individual slip component partials are returned +xxvec = [a111 a112 a113]; +yyvec = [a221 a222 a223]; +zzvec = [a331 a332 a333]; +xyvec = [a121 a122 a123]; +xzvec = [a131 a132 a133]; +yzvec = [a231 a232 a233]; + +a11s = dot(xxvec, ratios, 2); +a22s = dot(yyvec, ratios, 2); +a33s = dot(zzvec, ratios, 2); +a12s = dot(xyvec, ratios, 2); +a13s = dot(xzvec, ratios, 2); +a23s = dot(yzvec, ratios, 2); + +a11d = dot(xxvec, ratiod, 2); +a22d = dot(yyvec, ratiod, 2); +a33d = dot(zzvec, ratiod, 2); +a12d = dot(xyvec, ratiod, 2); +a13d = dot(xzvec, ratiod, 2); +a23d = dot(yzvec, ratiod, 2); + +a11t = dot(xxvec, ratiot, 2); +a22t = dot(yyvec, ratiot, 2); +a33t = dot(zzvec, ratiot, 2); +a12t = dot(xyvec, ratiot, 2); +a13t = dot(xzvec, ratiot, 2); +a23t = dot(yzvec, ratiot, 2); + +% Second angular dislocation +[sx2 sy2] = RotateXyVec(sx-x(4), sy-y(4), -strike); +[b111 b221 b331 b121 b131 b231... + b112 b222 b332 b122 b132 b232... + b113 b223 b333 b123 b133 b233] = advs(sx2, sy2, sz-z(4), z(4), beta, pr, lss, lds, lts); + +% Project strains so that individual slip component partials are returned +xxvec = [b111 b112 b113]; +yyvec = [b221 b222 b223]; +zzvec = [b331 b332 b333]; +xyvec = [b121 b122 b123]; +xzvec = [b131 b132 b133]; +yzvec = [b231 b232 b233]; + +b11s = dot(xxvec, ratios, 2); +b22s = dot(yyvec, ratios, 2); +b33s = dot(zzvec, ratios, 2); +b12s = dot(xyvec, ratios, 2); +b13s = dot(xzvec, ratios, 2); +b23s = dot(yzvec, ratios, 2); + +b11d = dot(xxvec, ratiod, 2); +b22d = dot(yyvec, ratiod, 2); +b33d = dot(zzvec, ratiod, 2); +b12d = dot(xyvec, ratiod, 2); +b13d = dot(xzvec, ratiod, 2); +b23d = dot(yzvec, ratiod, 2); + +b11t = dot(xxvec, ratiot, 2); +b22t = dot(yyvec, ratiot, 2); +b33t = dot(zzvec, ratiot, 2); +b12t = dot(xyvec, ratiot, 2); +b13t = dot(xzvec, ratiot, 2); +b23t = dot(yzvec, ratiot, 2); + +% Rotate tensors to correct for strike +bxxs = a11s-b11s; +byys = a22s-b22s; +bzzs = a33s-b33s; +bxys = a12s-b12s; +bxzs = a13s-b13s; +byzs = a23s-b23s; + +bxxd = a11d-b11d; +byyd = a22d-b22d; +bzzd = a33d-b33d; +bxyd = a12d-b12d; +bxzd = a13d-b13d; +byzd = a23d-b23d; + +bxxt = a11t-b11t; +byyt = a22t-b22t; +bzzt = a33t-b33t; +bxyt = a12t-b12t; +bxzt = a13t-b13t; +byzt = a23t-b23t; + +g = pi/180*strike; +e11ns = (cos(g)*bxxs-sin(g)*bxys)*cos(g)-(cos(g)*bxys-sin(g)*byys)*sin(g); +e12ns = (cos(g)*bxxs-sin(g)*bxys)*sin(g)+(cos(g)*bxys-sin(g)*byys)*cos(g); +e13ns = cos(g)*bxzs-sin(g)*byzs; +e22ns = (sin(g)*bxxs+cos(g)*bxys)*sin(g)+(sin(g)*bxys+cos(g)*byys)*cos(g); +e23ns = sin(g)*bxzs+cos(g)*byzs; +e33ns = bzzs; + +e11nd = (cos(g)*bxxd-sin(g)*bxyd)*cos(g)-(cos(g)*bxyd-sin(g)*byyd)*sin(g); +e12nd = (cos(g)*bxxd-sin(g)*bxyd)*sin(g)+(cos(g)*bxyd-sin(g)*byyd)*cos(g); +e13nd = cos(g)*bxzd-sin(g)*byzd; +e22nd = (sin(g)*bxxd+cos(g)*bxyd)*sin(g)+(sin(g)*bxyd+cos(g)*byyd)*cos(g); +e23nd = sin(g)*bxzd+cos(g)*byzd; +e33nd = bzzd; + +e11nt = (cos(g)*bxxt-sin(g)*bxyt)*cos(g)-(cos(g)*bxyt-sin(g)*byyt)*sin(g); +e12nt = (cos(g)*bxxt-sin(g)*bxyt)*sin(g)+(cos(g)*bxyt-sin(g)*byyt)*cos(g); +e13nt = cos(g)*bxzt-sin(g)*byzt; +e22nt = (sin(g)*bxxt+cos(g)*bxyt)*sin(g)+(sin(g)*bxyt+cos(g)*byyt)*cos(g); +e23nt = sin(g)*bxzt+cos(g)*byzt; +e33nt = bzzt; + +% Add the strains from leg 3 +e11ns(isnan(e11ns)) = 0; +e22ns(isnan(e22ns)) = 0; +e33ns(isnan(e33ns)) = 0; +e12ns(isnan(e12ns)) = 0; +e13ns(isnan(e13ns)) = 0; +e23ns(isnan(e23ns)) = 0; + +e11nd(isnan(e11nd)) = 0; +e22nd(isnan(e22nd)) = 0; +e33nd(isnan(e33nd)) = 0; +e12nd(isnan(e12nd)) = 0; +e13nd(isnan(e13nd)) = 0; +e23nd(isnan(e23nd)) = 0; + +e11nt(isnan(e11nt)) = 0; +e22nt(isnan(e22nt)) = 0; +e33nt(isnan(e33nt)) = 0; +e12nt(isnan(e12nt)) = 0; +e13nt(isnan(e13nt)) = 0; +e23nt(isnan(e23nt)) = 0; + +xxs = xxs + e11ns; +yys = yys + e22ns; +zzs = zzs + e33ns; +xys = xys + e12ns; +xzs = xzs + e13ns; +yzs = yzs + e23ns; + +xxd = xxd + e11nd; +yyd = yyd + e22nd; +zzd = zzd + e33nd; +xyd = xyd + e12nd; +xzd = xzd + e13nd; +yzd = yzd + e23nd; + +xxt = xxt + e11nt; +yyt = yyt + e22nt; +zzt = zzt + e33nt; +xyt = xyt + e12nt; +xzt = xzt + e13nt; +yzt = yzt + e23nt; + +function [a b] = swap(a, b) +% Swap two values +temp = a; +a = b; +b = temp; + + +function [xp yp] = RotateXyVec(x, y, alpha) +% Rotate a vector by an angle alpha +x = x(:); +y = y(:); +alpha = pi/180*alpha; +xp = cos(alpha).*x - sin(alpha).*y; +yp = sin(alpha).*x + cos(alpha).*y; + + +function [e11s e22s e33s e12s e13s e23s... + e11d e22d e33d e12d e13d e23d... + e11t e22t e33t e12t e13t e23t] = advs(y1, y2, y3, a, b, nu, B1, B2, B3) +% These are the strains in a uniform elastic half space due to slip +% on an angular dislocation. They were calculated by symbolically +% differentiating the expressions for the displacements (Comninou and +% Dunders, 1975, with typos noted by Thomas 1993) then combining the +% elements of the displacement gradient tensor to form the strain tensor. + +sinb = sin(b); +sinb2 = sinb.^2; +cosb = cos(b); +cosb2 = cosb.^2; +cotb = 1./tan(b); +cotb2 = cotb.^2; + +y12 = y1.^2; +y22 = y2.^2; +y32 = y3.^2; +y122 = y1.^2 + y2.^2; +y13 = y1.^3; +y23 = y2.^3; + +y1cb = y1.*cosb; +y1sb = y1.*sinb; +y3sb = y3.*sinb; +y3cb = y3.*cosb; +y22cb2 = y22.*cosb2; +y22cb = y22.*cosb; +y22cbp2 = y22cb.^2; %%%%%%%%%% +ycys2 = (y1cb-y3sb).^2; + +oh = 1./2; +th = 3./2; +fh = 5./2; +oe = 1./8; + +sys = y12+y22+y32; +systh = sys.^th; +sysq = sys.^(oh); +isysq = 1./sysq; + +nunu = 2.*nu; +omnunu = 1-nunu; +tmnunu = 2-nunu; +aa = 2.*a; +y3aa = y3+2.*a; +y3aa2 = (y3+2.*a).^2; +yy2 = y122+y3aa2; +iyy2 = 1./yy2; +yy22 = yy2.^2; +y1y22 = y1./yy22; +yy2q = yy2.^oh; +iyy2q = 1./yy2q; +yy2th = yy2.^th; +yy2fh = yy2.^fh; + +yya = (yy2q+y3+aa); +yyas = yya.^2; +yysb = (y1cb+y3aa.*sinb); +yysb2 = yysb.^2; +yyysby = (y1.*yysb+y22cb); +yyysby2 = yyysby.^2; +yyycb = (yy2q-y1sb+y3aa.*cosb); +yyycb2 = yyycb.^2; +smymy = (sysq-y1sb-y3cb); +syy2 = smymy.^2; +yyyy = (y1.*(y1cb-y3sb)+y22cb); +yyyy2 = yyyy.^2; +sy2 = (sysq-y3).^2; +ysby = (yy2q.*sinb-y1); +ssby = (sysq.*sinb-y1); +ty3fa = (2.*y3+4.*a); +ycbya = (yy2q.*cosb+y3+aa); +hytcb = oh./yy2q.*ty3fa+cosb; +cbay = cosb+a./yy2q; +iyysb = iyy2q.*y1-sinb; +hyto = oh./yy2q.*ty3fa+1; +nay = nunu+a./yy2q; +oay = 1+a./yy2q; +scby = sysq.*cosb-y3; +sby7 = sinb-y3aa.*yysb./yy2-yysb.*ycbya./yy2q./yyycb; +oyysby = 1+y22.*yy2.*sinb2./yyysby2; +piomn = pi./(1-nu); +yCyY2 = ycbya./yyycb2; +yCyY = ycbya./yyycb; +ythycb = yy2th./yyycb; + +e11s = B1.*(oe.*((tmnunu).*(2.*y2./y12./(1+y22./y12)-y2./ycys2.*cosb./(1+y22./ycys2)+(y2./sysq.*sinb./yyyy.*y1-y2.*sysq.*sinb./yyyy2.*(2.*y1cb-y3sb))./(1+y22.*(sys).*sinb2./yyyy2)-y2./yysb2.*cosb./(1+y22./yysb2)+(y2./yy2q.*sinb./yyysby.*y1-y2.*yy2q.*sinb./yyysby2.*(2.*y1cb+y3aa.*sinb))./oyysby)-y2.*(isysq./(sysq-y3)+iyy2q./yya)-y1.*y2.*(-1./systh./(sysq-y3).*y1-1./(sys)./sy2.*y1-1./yy2th./yya.*y1-iyy2./yyas.*y1)-y2.*cosb.*((isysq.*sinb.*y1-1)./sysq./smymy-ssby./systh./smymy.*y1-ssby./sysq./syy2.*(isysq.*y1-sinb)+(iyy2q.*sinb.*y1-1)./yy2q./yyycb-ysby./yy2th./yyycb.*y1-ysby./yy2q./yyycb2.*iyysb))./pi./(1-nu)+1./4.*((-2+nunu).*(omnunu).*(y2./y12./(1+y22./y12)-y2./yysb2.*cosb./(1+y22./yysb2)+(y2./yy2q.*sinb./yyysby.*y1-y2.*yy2q.*sinb./yyysby2.*(2.*y1cb+y3aa.*sinb))./oyysby).*cotb2-(omnunu).*y2./yyas.*((omnunu-a./yy2q).*cotb-y1./yya.*(nu+a./yy2q))./yy2q.*y1+(omnunu).*y2./yya.*(a./yy2th.*y1.*cotb-1./yya.*(nu+a./yy2q)+y12./yyas.*(nu+a./yy2q)./yy2q+y12./yya.*a./yy2th)-(omnunu).*y2.*cosb.*cotb./yyycb2.*cbay.*iyysb-(omnunu).*y2.*cosb.*cotb./yyycb.*a./yy2th.*y1-3.*a.*y2.*(y3+a).*cotb./yy2fh.*y1-y2.*(y3+a)./yy2th./yya.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2).*y1-y2.*(y3+a)./yy2./yyas.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2).*y1+y2.*(y3+a)./yy2q./yya.*(1./yya.*nay-y12./yyas.*nay./yy2q-y12./yya.*a./yy2th+a./yy2-aa.*y12./yy22)-y2.*(y3+a)./yy2th./yyycb.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2).*y1-y2.*(y3+a)./yy2q./yyycb2.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2).*iyysb+y2.*(y3+a)./yy2q./yyycb.*(-cosb./yyycb2.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb).*iyysb+cosb./yyycb.*(iyy2q.*cosb.*y1.*((omnunu).*cosb-a./yy2q).*cotb+ycbya.*a./yy2th.*y1.*cotb+(tmnunu).*(iyy2q.*sinb.*y1-1).*cosb)+aa.*y3aa.*cosb.*cotb./yy22.*y1))./pi./(1-nu)); +e11d = B2.*(oe.*((-1+nunu).*(isysq.*y1./(sysq-y3)+iyy2q.*y1./yya-cosb.*((isysq.*y1-sinb)./smymy+iyysb./yyycb))+2.*y1.*(isysq./(sysq-y3)+iyy2q./yya)+y12.*(-1./systh./(sysq-y3).*y1-1./(sys)./sy2.*y1-1./yy2th./yya.*y1-iyy2./yyas.*y1)+cosb.*ssby./sysq./smymy+(y1cb-y3sb).*(isysq.*sinb.*y1-1)./sysq./smymy-(y1cb-y3sb).*ssby./systh./smymy.*y1-(y1cb-y3sb).*ssby./sysq./syy2.*(isysq.*y1-sinb)+cosb.*ysby./yy2q./yyycb+yysb.*(iyy2q.*sinb.*y1-1)./yy2q./yyycb-yysb.*ysby./yy2th./yyycb.*y1-yysb.*ysby./yy2q./yyycb2.*iyysb)./pi./(1-nu)+1./4.*((omnunu).*(((tmnunu).*cotb2+nu)./yy2q.*y1./yya-((tmnunu).*cotb2+1).*cosb.*iyysb./yyycb)-(omnunu)./yyas.*((-1+nunu).*y1.*cotb+nu.*y3aa-a+a.*y1.*cotb./yy2q+y12./yya.*(nu+a./yy2q))./yy2q.*y1+(omnunu)./yya.*((-1+nunu).*cotb+a.*cotb./yy2q-a.*y12.*cotb./yy2th+2.*y1./yya.*(nu+a./yy2q)-y13./yyas.*(nu+a./yy2q)./yy2q-y13./yya.*a./yy2th)+(omnunu).*cotb./yyycb2.*(yysb.*cosb-a.*ysby./yy2q./cosb).*iyysb-(omnunu).*cotb./yyycb.*(cosb2-a.*(iyy2q.*sinb.*y1-1)./yy2q./cosb+a.*ysby./yy2th./cosb.*y1)-a.*(y3+a).*cotb./yy2th+3.*a.*y12.*(y3+a).*cotb./yy2fh-(y3+a)./yyas.*(nunu+iyy2q.*((omnunu).*y1.*cotb+a)-y12./yy2q./yya.*nay-a.*y12./yy2th)./yy2q.*y1+(y3+a)./yya.*(-1./yy2th.*((omnunu).*y1.*cotb+a).*y1+iyy2q.*(omnunu).*cotb-2.*y1./yy2q./yya.*nay+y13./yy2th./yya.*nay+y13./yy2./yyas.*nay+y13./yy22./yya.*a-aa./yy2th.*y1+3.*a.*y13./yy2fh)-(y3+a).*cotb./yyycb2.*(-cosb.*sinb+a.*y1.*y3aa./yy2th./cosb+ysby./yy2q.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb))).*iyysb+(y3+a).*cotb./yyycb.*(a.*y3aa./yy2th./cosb-3.*a.*y12.*y3aa./yy2fh./cosb+(iyy2q.*sinb.*y1-1)./yy2q.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb))-ysby./yy2th.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb)).*y1+ysby./yy2q.*(-iyy2q.*cosb.*y1./yyycb.*(1+a./yy2q./cosb)+yCyY2.*(1+a./yy2q./cosb).*iyysb+yCyY.*a./yy2th./cosb.*y1)))./pi./(1-nu)); +e11t = B3.*(oe.*y2.*sinb.*((isysq.*sinb.*y1-1)./sysq./smymy-ssby./systh./smymy.*y1-ssby./sysq./syy2.*(isysq.*y1-sinb)+(iyy2q.*sinb.*y1-1)./yy2q./yyycb-ysby./yy2th./yyycb.*y1-ysby./yy2q./yyycb2.*iyysb)./pi./(1-nu)+1./4.*((omnunu).*(-y2./yyas.*oay./yy2q.*y1-y2./yya.*a./yy2th.*y1+y2.*cosb./yyycb2.*cbay.*iyysb+y2.*cosb./yyycb.*a./yy2th.*y1)+y2.*(y3+a)./yy2th.*(a./yy2+1./yya).*y1-y2.*(y3+a)./yy2q.*(-aa./yy22.*y1-1./yyas./yy2q.*y1)-y2.*(y3+a).*cosb./yy2th./yyycb.*(yCyY.*cbay+a.*y3aa./yy2).*y1-y2.*(y3+a).*cosb./yy2q./yyycb2.*(yCyY.*cbay+a.*y3aa./yy2).*iyysb+y2.*(y3+a).*cosb./yy2q./yyycb.*(iyy2q.*cosb.*y1./yyycb.*cbay-yCyY2.*cbay.*iyysb-yCyY.*a./yy2th.*y1-aa.*y3aa./yy22.*y1))./pi./(1-nu)); + +e22s = B1.*(oe.*((omnunu).*(isysq.*y2./(sysq-y3)+iyy2q.*y2./yya-cosb.*(isysq.*y2./smymy+iyy2q.*y2./yyycb))-2.*y2.*(isysq./(sysq-y3)+iyy2q./yya-cosb.*(isysq./smymy+iyy2q./yyycb))-y22.*(-1./systh./(sysq-y3).*y2-1./(sys)./sy2.*y2-1./yy2th./yya.*y2-iyy2./yyas.*y2-cosb.*(-1./systh./smymy.*y2-1./(sys)./syy2.*y2-1./yy2th./yyycb.*y2-iyy2./yyycb2.*y2)))./pi./(1-nu)+1./4.*((omnunu).*(((tmnunu).*cotb2-nu)./yy2q.*y2./yya-((tmnunu).*cotb2+omnunu).*cosb./yy2q.*y2./yyycb)+(omnunu)./yyas.*(y1.*cotb.*(omnunu-a./yy2q)+nu.*y3aa-a+y22./yya.*(nu+a./yy2q))./yy2q.*y2-(omnunu)./yya.*(a.*y1.*cotb./yy2th.*y2+2.*y2./yya.*(nu+a./yy2q)-y23./yyas.*(nu+a./yy2q)./yy2q-y23./yya.*a./yy2th)+(omnunu).*yysb.*cotb./yyycb2.*cbay./yy2q.*y2+(omnunu).*yysb.*cotb./yyycb.*a./yy2th.*y2+3.*a.*y2.*(y3+a).*cotb./yy2fh.*y1-(y3+a)./yyas.*(-nunu+iyy2q.*((omnunu).*y1.*cotb-a)+y22./yy2q./yya.*nay+a.*y22./yy2th)./yy2q.*y2+(y3+a)./yya.*(-1./yy2th.*((omnunu).*y1.*cotb-a).*y2+2.*y2./yy2q./yya.*nay-y23./yy2th./yya.*nay-y23./yy2./yyas.*nay-y23./yy22./yya.*a+aa./yy2th.*y2-3.*a.*y23./yy2fh)-(y3+a)./yyycb2.*(cosb2-iyy2q.*((omnunu).*yysb.*cotb+a.*cosb)+a.*y3aa.*yysb.*cotb./yy2th-iyy2q./yyycb.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya))./yy2q.*y2+(y3+a)./yyycb.*(1./yy2th.*((omnunu).*yysb.*cotb+a.*cosb).*y2-3.*a.*y3aa.*yysb.*cotb./yy2fh.*y2+1./yy2th./yyycb.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya).*y2+iyy2./yyycb2.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya).*y2-iyy2q./yyycb.*(2.*y2.*cosb2+a.*yysb.*cotb./yy2th.*ycbya.*y2-a.*yysb.*cotb./yy2.*cosb.*y2)))./pi./(1-nu)); +e22d = B2.*(oe.*((tmnunu).*(-2./y1./(1+y22./y12)+1./(y1cb-y3sb)./(1+y22./ycys2)+(sysq.*sinb./yyyy+y22./sysq.*sinb./yyyy-2.*y22.*sysq.*sinb./yyyy2.*cosb)./(1+y22.*(sys).*sinb2./yyyy2)+1./yysb./(1+y22./yysb2)+(yy2q.*sinb./yyysby+y22./yy2q.*sinb./yyysby-2.*y22.*yy2q.*sinb./yyysby2.*cosb)./oyysby)+y1.*(isysq./(sysq-y3)+iyy2q./yya)+y1.*y2.*(-1./systh./(sysq-y3).*y2-1./(sys)./sy2.*y2-1./yy2th./yya.*y2-iyy2./yyas.*y2)-(y1cb-y3sb)./sysq./smymy-yysb./yy2q./yyycb-y2.*(-(y1cb-y3sb)./systh./smymy.*y2-(y1cb-y3sb)./(sys)./syy2.*y2-yysb./yy2th./yyycb.*y2-yysb./yy2./yyycb2.*y2))./pi./(1-nu)+1./4.*((tmnunu).*(omnunu).*(-1./y1./(1+y22./y12)+1./yysb./(1+y22./yysb2)+(yy2q.*sinb./yyysby+y22./yy2q.*sinb./yyysby-2.*y22.*yy2q.*sinb./yyysby2.*cosb)./oyysby).*cotb2+(omnunu)./yya.*((-1+nunu+a./yy2q).*cotb+y1./yya.*(nu+a./yy2q))-(omnunu).*y22./yyas.*((-1+nunu+a./yy2q).*cotb+y1./yya.*(nu+a./yy2q))./yy2q+(omnunu).*y2./yya.*(-a./yy2th.*y2.*cotb-y1./yyas.*(nu+a./yy2q)./yy2q.*y2-y2./yya.*a./yy2th.*y1)-(omnunu).*cotb./yyycb.*(1+a./yy2q./cosb)+(omnunu).*y22.*cotb./yyycb2.*(1+a./yy2q./cosb)./yy2q+(omnunu).*y22.*cotb./yyycb.*a./yy2th./cosb-a.*(y3+a).*cotb./yy2th+3.*a.*y22.*(y3+a).*cotb./yy2fh+(y3+a)./yy2q./yya.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya))-y22.*(y3+a)./yy2th./yya.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya))-y22.*(y3+a)./yy2./yyas.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya))+y2.*(y3+a)./yy2q./yya.*(nunu.*y1./yyas./yy2q.*y2+a.*y1./yy2th.*(iyy2q+1./yya).*y2-a.*y1./yy2q.*(-1./yy2th.*y2-1./yyas./yy2q.*y2))+(y3+a).*cotb./yy2q./yyycb.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb)-y22.*(y3+a).*cotb./yy2th./yyycb.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb)-y22.*(y3+a).*cotb./yy2./yyycb2.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb)+y2.*(y3+a).*cotb./yy2q./yyycb.*(iyy2q.*cosb.*y2./yyycb.*(1+a./yy2q./cosb)-yCyY2.*(1+a./yy2q./cosb)./yy2q.*y2-yCyY.*a./yy2th./cosb.*y2-aa.*y3aa./yy22./cosb.*y2))./pi./(1-nu)); +e22t = B3.*(oe.*((omnunu).*sinb.*(isysq.*y2./smymy+iyy2q.*y2./yyycb)-2.*y2.*sinb.*(isysq./smymy+iyy2q./yyycb)-y22.*sinb.*(-1./systh./smymy.*y2-1./(sys)./syy2.*y2-1./yy2th./yyycb.*y2-iyy2./yyycb2.*y2))./pi./(1-nu)+1./4.*((omnunu).*(-sinb./yy2q.*y2./yyycb+y2./yyas.*oay./yy2q.*y1+y2./yya.*a./yy2th.*y1-yysb./yyycb2.*cbay./yy2q.*y2-yysb./yyycb.*a./yy2th.*y2)-y2.*(y3+a)./yy2th.*(a./yy2+1./yya).*y1+y1.*(y3+a)./yy2q.*(-aa./yy22.*y2-1./yyas./yy2q.*y2)+(y3+a)./yyycb2.*(sinb.*(cosb-a./yy2q)+yysb./yy2q.*(1+a.*y3aa./yy2)-iyy2q./yyycb.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya))./yy2q.*y2-(y3+a)./yyycb.*(sinb.*a./yy2th.*y2-yysb./yy2th.*(1+a.*y3aa./yy2).*y2-2.*yysb./yy2fh.*a.*y3aa.*y2+1./yy2th./yyycb.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya).*y2+iyy2./yyycb2.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya).*y2-iyy2q./yyycb.*(2.*y2.*cosb.*sinb+a.*yysb./yy2th.*ycbya.*y2-a.*yysb./yy2.*cosb.*y2)))./pi./(1-nu)); + +e33s = B1.*(oe.*y2.*(-1./systh.*y3+oh./yy2th.*ty3fa-cosb.*((isysq.*cosb.*y3-1)./sysq./smymy-scby./systh./smymy.*y3-scby./sysq./syy2.*(isysq.*y3-cosb)-(oh./yy2q.*cosb.*ty3fa+1)./yy2q./yyycb+oh.*ycbya./yy2th./yyycb.*ty3fa+ycbya./yy2q./yyycb2.*(hytcb)))./pi./(1-nu)+1./4.*((tmnunu).*((omnunu).*(-y2./yysb2.*sinb./(1+y22./yysb2)+(oh.*y2./yy2q.*sinb./yyysby.*ty3fa-y2.*yy2q.*sinb2./yyysby2.*y1)./oyysby).*cotb-y2./yyas.*nay.*hyto-oh.*y2./yya.*a./yy2th.*ty3fa+y2.*cosb./yyycb2.*cbay.*(hytcb)+oh.*y2.*cosb./yyycb.*a./yy2th.*ty3fa)+y2./yy2q.*(nunu./yya+a./yy2)-oh.*y2.*(y3+a)./yy2th.*(nunu./yya+a./yy2).*ty3fa+y2.*(y3+a)./yy2q.*(-nunu./yyas.*hyto-a./yy22.*ty3fa)+y2.*cosb./yy2q./yyycb.*(omnunu-yCyY.*cbay-a.*y3aa./yy2)-oh.*y2.*(y3+a).*cosb./yy2th./yyycb.*(omnunu-yCyY.*cbay-a.*y3aa./yy2).*ty3fa-y2.*(y3+a).*cosb./yy2q./yyycb2.*(omnunu-yCyY.*cbay-a.*y3aa./yy2).*(hytcb)+y2.*(y3+a).*cosb./yy2q./yyycb.*(-(oh./yy2q.*cosb.*ty3fa+1)./yyycb.*cbay+yCyY2.*cbay.*(hytcb)+oh.*yCyY.*a./yy2th.*ty3fa-a./yy2+a.*y3aa./yy22.*ty3fa))./pi./(1-nu)); +e33d = B2.*(oe.*((-1+nunu).*sinb.*((isysq.*y3-cosb)./smymy-(hytcb)./yyycb)-y1.*(-1./systh.*y3+oh./yy2th.*ty3fa)-sinb.*scby./sysq./smymy+(y1cb-y3sb).*(isysq.*cosb.*y3-1)./sysq./smymy-(y1cb-y3sb).*scby./systh./smymy.*y3-(y1cb-y3sb).*scby./sysq./syy2.*(isysq.*y3-cosb)-sinb.*ycbya./yy2q./yyycb-yysb.*(oh./yy2q.*cosb.*ty3fa+1)./yy2q./yyycb+oh.*yysb.*ycbya./yy2th./yyycb.*ty3fa+yysb.*ycbya./yy2q./yyycb2.*(hytcb))./pi./(1-nu)+1./4.*((-2+nunu).*(omnunu).*cotb.*(hyto./yya-cosb.*(hytcb)./yyycb)+(tmnunu).*y1./yyas.*nay.*hyto+oh.*(tmnunu).*y1./yya.*a./yy2th.*ty3fa+(tmnunu).*sinb./yyycb.*cbay-(tmnunu).*yysb./yyycb2.*cbay.*(hytcb)-oh.*(tmnunu).*yysb./yyycb.*a./yy2th.*ty3fa+iyy2q.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2)-oh.*(y3+a)./yy2th.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2).*ty3fa+(y3+a)./yy2q.*(nunu.*y1./yyas.*hyto+a.*y1y22.*ty3fa)-1./yyycb.*(cosb.*sinb+ycbya.*cotb./yy2q.*((tmnunu).*cosb-yCyY)+a./yy2q.*sby7)+(y3+a)./yyycb2.*(cosb.*sinb+ycbya.*cotb./yy2q.*((tmnunu).*cosb-yCyY)+a./yy2q.*sby7).*(hytcb)-(y3+a)./yyycb.*((oh./yy2q.*cosb.*ty3fa+1).*cotb./yy2q.*((tmnunu).*cosb-yCyY)-oh.*ycbya.*cotb./yy2th.*((tmnunu).*cosb-yCyY).*ty3fa+ycbya.*cotb./yy2q.*(-(oh./yy2q.*cosb.*ty3fa+1)./yyycb+yCyY2.*(hytcb))-oh.*a./yy2th.*sby7.*ty3fa+a./yy2q.*(-yysb./yy2-y3aa.*sinb./yy2+y3aa.*yysb./yy22.*ty3fa-sinb.*ycbya./yy2q./yyycb-yysb.*(oh./yy2q.*cosb.*ty3fa+1)./yy2q./yyycb+oh.*yysb.*ycbya./yy2th./yyycb.*ty3fa+yysb.*ycbya./yy2q./yyycb2.*(hytcb))))./pi./(1-nu)); +e33t = B3.*(oe.*((tmnunu).*(y2./ycys2.*sinb./(1+y22./ycys2)+(y2./sysq.*sinb./yyyy.*y3+y2.*sysq.*sinb2./yyyy2.*y1)./(1+y22.*(sys).*sinb2./yyyy2)+y2./yysb2.*sinb./(1+y22./yysb2)-(oh.*y2./yy2q.*sinb./yyysby.*ty3fa-y2.*yy2q.*sinb2./yyysby2.*y1)./oyysby)+y2.*sinb.*((isysq.*cosb.*y3-1)./sysq./smymy-scby./systh./smymy.*y3-scby./sysq./syy2.*(isysq.*y3-cosb)-(oh./yy2q.*cosb.*ty3fa+1)./yy2q./yyycb+oh.*ycbya./yy2th./yyycb.*ty3fa+ycbya./yy2q./yyycb2.*(hytcb)))./pi./(1-nu)+1./4.*((tmnunu).*(-y2./yysb2.*sinb./(1+y22./yysb2)+(oh.*y2./yy2q.*sinb./yyysby.*ty3fa-y2.*yy2q.*sinb2./yyysby2.*y1)./oyysby)-(tmnunu).*y2.*sinb./yyycb2.*cbay.*(hytcb)-oh.*(tmnunu).*y2.*sinb./yyycb.*a./yy2th.*ty3fa+y2.*sinb./yy2q./yyycb.*(1+yCyY.*cbay+a.*y3aa./yy2)-oh.*y2.*(y3+a).*sinb./yy2th./yyycb.*(1+yCyY.*cbay+a.*y3aa./yy2).*ty3fa-y2.*(y3+a).*sinb./yy2q./yyycb2.*(1+yCyY.*cbay+a.*y3aa./yy2).*(hytcb)+y2.*(y3+a).*sinb./yy2q./yyycb.*((oh./yy2q.*cosb.*ty3fa+1)./yyycb.*cbay-yCyY2.*cbay.*(hytcb)-oh.*yCyY.*a./yy2th.*ty3fa+a./yy2-a.*y3aa./yy22.*ty3fa))./pi./(1-nu)); + +e12s = oh.*B1.*(oe.*((tmnunu).*(-2./y1./(1+y22./y12)+1./(y1cb-y3sb)./(1+y22./ycys2)+(sysq.*sinb./yyyy+y22./sysq.*sinb./yyyy-2.*y22.*sysq.*sinb./yyyy2.*cosb)./(1+y22.*(sys).*sinb2./yyyy2)+1./yysb./(1+y22./yysb2)+(yy2q.*sinb./yyysby+y22./yy2q.*sinb./yyysby-2.*y22.*yy2q.*sinb./yyysby2.*cosb)./oyysby)-y1.*(isysq./(sysq-y3)+iyy2q./yya)-y1.*y2.*(-1./systh./(sysq-y3).*y2-1./(sys)./sy2.*y2-1./yy2th./yya.*y2-iyy2./yyas.*y2)-cosb.*(ssby./sysq./smymy+ysby./yy2q./yyycb)-y2.*cosb.*(1./(sys).*sinb.*y2./smymy-ssby./systh./smymy.*y2-ssby./(sys)./syy2.*y2+iyy2.*sinb.*y2./yyycb-ysby./yy2th./yyycb.*y2-ysby./yy2./yyycb2.*y2))./pi./(1-nu)+1./4.*((-2+nunu).*(omnunu).*(-1./y1./(1+y22./y12)+1./yysb./(1+y22./yysb2)+(yy2q.*sinb./yyysby+y22./yy2q.*sinb./yyysby-2.*y22.*yy2q.*sinb./yyysby2.*cosb)./oyysby).*cotb2+(omnunu)./yya.*((omnunu-a./yy2q).*cotb-y1./yya.*(nu+a./yy2q))-(omnunu).*y22./yyas.*((omnunu-a./yy2q).*cotb-y1./yya.*(nu+a./yy2q))./yy2q+(omnunu).*y2./yya.*(a./yy2th.*y2.*cotb+y1./yyas.*(nu+a./yy2q)./yy2q.*y2+y2./yya.*a./yy2th.*y1)+(omnunu).*cosb.*cotb./yyycb.*cbay-(omnunu).*y22cb.*cotb./yyycb2.*cbay./yy2q-(omnunu).*y22cb.*cotb./yyycb.*a./yy2th+a.*(y3+a).*cotb./yy2th-3.*a.*y22.*(y3+a).*cotb./yy2fh+(y3+a)./yy2q./yya.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2)-y22.*(y3+a)./yy2th./yya.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2)-y22.*(y3+a)./yy2./yyas.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2)+y2.*(y3+a)./yy2q./yya.*(-y1./yyas.*nay./yy2q.*y2-y2./yya.*a./yy2th.*y1-aa.*y1y22.*y2)+(y3+a)./yy2q./yyycb.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2)-y22.*(y3+a)./yy2th./yyycb.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2)-y22.*(y3+a)./yy2./yyycb2.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2)+y2.*(y3+a)./yy2q./yyycb.*(-cosb./yyycb2.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)./yy2q.*y2+cosb./yyycb.*(iyy2q.*cosb.*y2.*((omnunu).*cosb-a./yy2q).*cotb+ycbya.*a./yy2th.*y2.*cotb+(tmnunu)./yy2q.*sinb.*y2.*cosb)+aa.*y3aa.*cosb.*cotb./yy22.*y2))./pi./(1-nu)); +e12s = e12s + oh.*B1.*(oe.*((omnunu).*(isysq.*y1./(sysq-y3)+iyy2q.*y1./yya-cosb.*((isysq.*y1-sinb)./smymy+iyysb./yyycb))-y22.*(-1./systh./(sysq-y3).*y1-1./(sys)./sy2.*y1-1./yy2th./yya.*y1-iyy2./yyas.*y1-cosb.*(-1./systh./smymy.*y1-isysq./syy2.*(isysq.*y1-sinb)-1./yy2th./yyycb.*y1-iyy2q./yyycb2.*iyysb)))./pi./(1-nu)+1./4.*((omnunu).*(((tmnunu).*cotb2-nu)./yy2q.*y1./yya-((tmnunu).*cotb2+omnunu).*cosb.*iyysb./yyycb)+(omnunu)./yyas.*(y1.*cotb.*(omnunu-a./yy2q)+nu.*y3aa-a+y22./yya.*(nu+a./yy2q))./yy2q.*y1-(omnunu)./yya.*((omnunu-a./yy2q).*cotb+a.*y12.*cotb./yy2th-y22./yyas.*(nu+a./yy2q)./yy2q.*y1-y22./yya.*a./yy2th.*y1)-(omnunu).*cosb.*cotb./yyycb.*cbay+(omnunu).*yysb.*cotb./yyycb2.*cbay.*iyysb+(omnunu).*yysb.*cotb./yyycb.*a./yy2th.*y1-a.*(y3+a).*cotb./yy2th+3.*a.*y12.*(y3+a).*cotb./yy2fh-(y3+a)./yyas.*(-nunu+iyy2q.*((omnunu).*y1.*cotb-a)+y22./yy2q./yya.*nay+a.*y22./yy2th)./yy2q.*y1+(y3+a)./yya.*(-1./yy2th.*((omnunu).*y1.*cotb-a).*y1+iyy2q.*(omnunu).*cotb-y22./yy2th./yya.*nay.*y1-y22./yy2./yyas.*nay.*y1-y22./yy22./yya.*a.*y1-3.*a.*y22./yy2fh.*y1)-(y3+a)./yyycb2.*(cosb2-iyy2q.*((omnunu).*yysb.*cotb+a.*cosb)+a.*y3aa.*yysb.*cotb./yy2th-iyy2q./yyycb.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya)).*iyysb+(y3+a)./yyycb.*(1./yy2th.*((omnunu).*yysb.*cotb+a.*cosb).*y1-iyy2q.*(omnunu).*cosb.*cotb+a.*y3aa.*cosb.*cotb./yy2th-3.*a.*y3aa.*yysb.*cotb./yy2fh.*y1+1./yy2th./yyycb.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya).*y1+iyy2q./yyycb2.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya).*iyysb-iyy2q./yyycb.*(-a.*cosb.*cotb./yy2q.*ycbya+a.*yysb.*cotb./yy2th.*ycbya.*y1-a.*yysb.*cotb./yy2.*cosb.*y1)))./pi./(1-nu)); +e12d = oh.*B2.*(oe.*((-1+nunu).*(isysq.*y2./(sysq-y3)+iyy2q.*y2./yya-cosb.*(isysq.*y2./smymy+iyy2q.*y2./yyycb))+y12.*(-1./systh./(sysq-y3).*y2-1./(sys)./sy2.*y2-1./yy2th./yya.*y2-iyy2./yyas.*y2)+(y1cb-y3sb)./(sys).*sinb.*y2./smymy-(y1cb-y3sb).*ssby./systh./smymy.*y2-(y1cb-y3sb).*ssby./(sys)./syy2.*y2+yysb./yy2.*sinb.*y2./yyycb-yysb.*ysby./yy2th./yyycb.*y2-yysb.*ysby./yy2./yyycb2.*y2)./pi./(1-nu)+1./4.*((omnunu).*(((tmnunu).*cotb2+nu)./yy2q.*y2./yya-((tmnunu).*cotb2+1).*cosb./yy2q.*y2./yyycb)-(omnunu)./yyas.*((-1+nunu).*y1.*cotb+nu.*y3aa-a+a.*y1.*cotb./yy2q+y12./yya.*(nu+a./yy2q))./yy2q.*y2+(omnunu)./yya.*(-a.*y1.*cotb./yy2th.*y2-y12./yyas.*(nu+a./yy2q)./yy2q.*y2-y12./yya.*a./yy2th.*y2)+(omnunu).*cotb./yyycb2.*(yysb.*cosb-a.*ysby./yy2q./cosb)./yy2q.*y2-(omnunu).*cotb./yyycb.*(-a./yy2.*sinb.*y2./cosb+a.*ysby./yy2th./cosb.*y2)+3.*a.*y2.*(y3+a).*cotb./yy2fh.*y1-(y3+a)./yyas.*(nunu+iyy2q.*((omnunu).*y1.*cotb+a)-y12./yy2q./yya.*nay-a.*y12./yy2th)./yy2q.*y2+(y3+a)./yya.*(-1./yy2th.*((omnunu).*y1.*cotb+a).*y2+y12./yy2th./yya.*nay.*y2+y12./yy2./yyas.*nay.*y2+y12./yy22./yya.*a.*y2+3.*a.*y12./yy2fh.*y2)-(y3+a).*cotb./yyycb2.*(-cosb.*sinb+a.*y1.*y3aa./yy2th./cosb+ysby./yy2q.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb)))./yy2q.*y2+(y3+a).*cotb./yyycb.*(-3.*a.*y1.*y3aa./yy2fh./cosb.*y2+iyy2.*sinb.*y2.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb))-ysby./yy2th.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb)).*y2+ysby./yy2q.*(-iyy2q.*cosb.*y2./yyycb.*(1+a./yy2q./cosb)+yCyY2.*(1+a./yy2q./cosb)./yy2q.*y2+yCyY.*a./yy2th./cosb.*y2)))./pi./(1-nu)); +e12d = e12d + oh.*B2.*(oe.*((tmnunu).*(2.*y2./y12./(1+y22./y12)-y2./ycys2.*cosb./(1+y22./ycys2)+(y2./sysq.*sinb./yyyy.*y1-y2.*sysq.*sinb./yyyy2.*(2.*y1cb-y3sb))./(1+y22.*(sys).*sinb2./yyyy2)-y2./yysb2.*cosb./(1+y22./yysb2)+(y2./yy2q.*sinb./yyysby.*y1-y2.*yy2q.*sinb./yyysby2.*(2.*y1cb+y3aa.*sinb))./oyysby)+y2.*(isysq./(sysq-y3)+iyy2q./yya)+y1.*y2.*(-1./systh./(sysq-y3).*y1-1./(sys)./sy2.*y1-1./yy2th./yya.*y1-iyy2./yyas.*y1)-y2.*(cosb./sysq./smymy-(y1cb-y3sb)./systh./smymy.*y1-(y1cb-y3sb)./sysq./syy2.*(isysq.*y1-sinb)+cosb./yy2q./yyycb-yysb./yy2th./yyycb.*y1-yysb./yy2q./yyycb2.*iyysb))./pi./(1-nu)+1./4.*((tmnunu).*(omnunu).*(y2./y12./(1+y22./y12)-y2./yysb2.*cosb./(1+y22./yysb2)+(y2./yy2q.*sinb./yyysby.*y1-y2.*yy2q.*sinb./yyysby2.*(2.*y1cb+y3aa.*sinb))./oyysby).*cotb2-(omnunu).*y2./yyas.*((-1+nunu+a./yy2q).*cotb+y1./yya.*(nu+a./yy2q))./yy2q.*y1+(omnunu).*y2./yya.*(-a./yy2th.*y1.*cotb+1./yya.*(nu+a./yy2q)-y12./yyas.*(nu+a./yy2q)./yy2q-y12./yya.*a./yy2th)+(omnunu).*y2.*cotb./yyycb2.*(1+a./yy2q./cosb).*iyysb+(omnunu).*y2.*cotb./yyycb.*a./yy2th./cosb.*y1+3.*a.*y2.*(y3+a).*cotb./yy2fh.*y1-y2.*(y3+a)./yy2th./yya.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya)).*y1-y2.*(y3+a)./yy2./yyas.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya)).*y1+y2.*(y3+a)./yy2q./yya.*(-nunu./yya+nunu.*y12./yyas./yy2q-a./yy2q.*(iyy2q+1./yya)+a.*y12./yy2th.*(iyy2q+1./yya)-a.*y1./yy2q.*(-1./yy2th.*y1-1./yyas./yy2q.*y1))-y2.*(y3+a).*cotb./yy2th./yyycb.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb).*y1-y2.*(y3+a).*cotb./yy2q./yyycb2.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb).*iyysb+y2.*(y3+a).*cotb./yy2q./yyycb.*(iyy2q.*cosb.*y1./yyycb.*(1+a./yy2q./cosb)-yCyY2.*(1+a./yy2q./cosb).*iyysb-yCyY.*a./yy2th./cosb.*y1-aa.*y3aa./yy22./cosb.*y1))./pi./(1-nu)); +e12t = oh.*B3.*(oe.*sinb.*(ssby./sysq./smymy+ysby./yy2q./yyycb)./pi./(1-nu)+oe.*y2.*sinb.*(1./(sys).*sinb.*y2./smymy-ssby./systh./smymy.*y2-ssby./(sys)./syy2.*y2+iyy2.*sinb.*y2./yyycb-ysby./yy2th./yyycb.*y2-ysby./yy2./yyycb2.*y2)./pi./(1-nu)+1./4.*((omnunu).*(1./yya.*oay-y22./yyas.*oay./yy2q-y22./yya.*a./yy2th-cosb./yyycb.*cbay+y22cb./yyycb2.*cbay./yy2q+y22cb./yyycb.*a./yy2th)-(y3+a)./yy2q.*(a./yy2+1./yya)+y22.*(y3+a)./yy2th.*(a./yy2+1./yya)-y2.*(y3+a)./yy2q.*(-aa./yy22.*y2-1./yyas./yy2q.*y2)+(y3+a).*cosb./yy2q./yyycb.*(yCyY.*cbay+a.*y3aa./yy2)-y22.*(y3+a).*cosb./yy2th./yyycb.*(yCyY.*cbay+a.*y3aa./yy2)-y22.*(y3+a).*cosb./yy2./yyycb2.*(yCyY.*cbay+a.*y3aa./yy2)+y2.*(y3+a).*cosb./yy2q./yyycb.*(iyy2q.*cosb.*y2./yyycb.*cbay-yCyY2.*cbay./yy2q.*y2-yCyY.*a./yy2th.*y2-aa.*y3aa./yy22.*y2))./pi./(1-nu)); +e12t = e12t + oh.*B3.*(oe.*((omnunu).*sinb.*((isysq.*y1-sinb)./smymy+iyysb./yyycb)-y22.*sinb.*(-1./systh./smymy.*y1-isysq./syy2.*(isysq.*y1-sinb)-1./yy2th./yyycb.*y1-iyy2q./yyycb2.*iyysb))./pi./(1-nu)+1./4.*((omnunu).*(-sinb.*iyysb./yyycb-1./yya.*oay+y12./yyas.*oay./yy2q+y12./yya.*a./yy2th+cosb./yyycb.*cbay-yysb./yyycb2.*cbay.*iyysb-yysb./yyycb.*a./yy2th.*y1)+(y3+a)./yy2q.*(a./yy2+1./yya)-y12.*(y3+a)./yy2th.*(a./yy2+1./yya)+y1.*(y3+a)./yy2q.*(-aa./yy22.*y1-1./yyas./yy2q.*y1)+(y3+a)./yyycb2.*(sinb.*(cosb-a./yy2q)+yysb./yy2q.*(1+a.*y3aa./yy2)-iyy2q./yyycb.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya)).*iyysb-(y3+a)./yyycb.*(sinb.*a./yy2th.*y1+cosb./yy2q.*(1+a.*y3aa./yy2)-yysb./yy2th.*(1+a.*y3aa./yy2).*y1-2.*yysb./yy2fh.*a.*y3aa.*y1+1./yy2th./yyycb.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya).*y1+iyy2q./yyycb2.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya).*iyysb-iyy2q./yyycb.*(-a.*cosb./yy2q.*ycbya+a.*yysb./yy2th.*ycbya.*y1-a.*yysb./yy2.*cosb.*y1)))./pi./(1-nu)); + +e13s = oh.*B1.*(oe.*((tmnunu).*(y2./ycys2.*sinb./(1+y22./ycys2)+(y2./sysq.*sinb./yyyy.*y3+y2.*sysq.*sinb2./yyyy2.*y1)./(1+y22.*(sys).*sinb2./yyyy2)-y2./yysb2.*sinb./(1+y22./yysb2)+(oh.*y2./yy2q.*sinb./yyysby.*ty3fa-y2.*yy2q.*sinb2./yyysby2.*y1)./oyysby)-y1.*y2.*(-1./systh./(sysq-y3).*y3-isysq./sy2.*(isysq.*y3-1)-oh./yy2th./yya.*ty3fa-iyy2q./yyas.*hyto)-y2.*cosb.*(1./(sys).*sinb.*y3./smymy-ssby./systh./smymy.*y3-ssby./sysq./syy2.*(isysq.*y3-cosb)+oh./yy2.*sinb.*ty3fa./yyycb-oh.*ysby./yy2th./yyycb.*ty3fa-ysby./yy2q./yyycb2.*(hytcb)))./pi./(1-nu)+1./4.*((-2+nunu).*(omnunu).*(-y2./yysb2.*sinb./(1+y22./yysb2)+(oh.*y2./yy2q.*sinb./yyysby.*ty3fa-y2.*yy2q.*sinb2./yyysby2.*y1)./oyysby).*cotb2-(omnunu).*y2./yyas.*((omnunu-a./yy2q).*cotb-y1./yya.*(nu+a./yy2q)).*hyto+(omnunu).*y2./yya.*(oh.*a./yy2th.*ty3fa.*cotb+y1./yyas.*(nu+a./yy2q).*hyto+oh.*y1./yya.*a./yy2th.*ty3fa)-(omnunu).*y2.*cosb.*cotb./yyycb2.*cbay.*(hytcb)-oh.*(omnunu).*y2.*cosb.*cotb./yyycb.*a./yy2th.*ty3fa+a./yy2th.*y2.*cotb-th.*a.*y2.*(y3+a).*cotb./yy2fh.*ty3fa+y2./yy2q./yya.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2)-oh.*y2.*(y3+a)./yy2th./yya.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2).*ty3fa-y2.*(y3+a)./yy2q./yyas.*((-1+nunu).*cotb+y1./yya.*nay+a.*y1./yy2).*hyto+y2.*(y3+a)./yy2q./yya.*(-y1./yyas.*nay.*hyto-oh.*y1./yya.*a./yy2th.*ty3fa-a.*y1y22.*ty3fa)+y2./yy2q./yyycb.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2)-oh.*y2.*(y3+a)./yy2th./yyycb.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2).*ty3fa-y2.*(y3+a)./yy2q./yyycb2.*(cosb./yyycb.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb)-a.*y3aa.*cosb.*cotb./yy2).*(hytcb)+y2.*(y3+a)./yy2q./yyycb.*(-cosb./yyycb2.*(ycbya.*((omnunu).*cosb-a./yy2q).*cotb+(tmnunu).*ysby.*cosb).*(hytcb)+cosb./yyycb.*((oh./yy2q.*cosb.*ty3fa+1).*((omnunu).*cosb-a./yy2q).*cotb+oh.*ycbya.*a./yy2th.*ty3fa.*cotb+oh.*(tmnunu)./yy2q.*sinb.*ty3fa.*cosb)-a.*cosb.*cotb./yy2+a.*y3aa.*cosb.*cotb./yy22.*ty3fa))./pi./(1-nu)); +e13s = e13s + oh.*B1.*(oe.*y2.*(-1./systh.*y1+1./yy2th.*y1-cosb.*(1./(sys).*cosb.*y1./smymy-scby./systh./smymy.*y1-scby./sysq./syy2.*(isysq.*y1-sinb)-iyy2.*cosb.*y1./yyycb+ycbya./yy2th./yyycb.*y1+ycbya./yy2q./yyycb2.*iyysb))./pi./(1-nu)+1./4.*((tmnunu).*((omnunu).*(y2./y12./(1+y22./y12)-y2./yysb2.*cosb./(1+y22./yysb2)+(y2./yy2q.*sinb./yyysby.*y1-y2.*yy2q.*sinb./yyysby2.*(2.*y1cb+y3aa.*sinb))./oyysby).*cotb-y1./yyas.*nay./yy2q.*y2-y2./yya.*a./yy2th.*y1+y2.*cosb./yyycb2.*cbay.*iyysb+y2.*cosb./yyycb.*a./yy2th.*y1)-y2.*(y3+a)./yy2th.*(nunu./yya+a./yy2).*y1+y2.*(y3+a)./yy2q.*(-nunu./yyas./yy2q.*y1-aa./yy22.*y1)-y2.*(y3+a).*cosb./yy2th./yyycb.*(omnunu-yCyY.*cbay-a.*y3aa./yy2).*y1-y2.*(y3+a).*cosb./yy2q./yyycb2.*(omnunu-yCyY.*cbay-a.*y3aa./yy2).*iyysb+y2.*(y3+a).*cosb./yy2q./yyycb.*(-iyy2q.*cosb.*y1./yyycb.*cbay+yCyY2.*cbay.*iyysb+yCyY.*a./yy2th.*y1+aa.*y3aa./yy22.*y1))./pi./(1-nu)); +e13d = oh.*B2.*(oe.*((-1+nunu).*((isysq.*y3-1)./(sysq-y3)+hyto./yya-cosb.*((isysq.*y3-cosb)./smymy+(hytcb)./yyycb))+y12.*(-1./systh./(sysq-y3).*y3-isysq./sy2.*(isysq.*y3-1)-oh./yy2th./yya.*ty3fa-iyy2q./yyas.*hyto)-sinb.*ssby./sysq./smymy+(y1cb-y3sb)./(sys).*sinb.*y3./smymy-(y1cb-y3sb).*ssby./systh./smymy.*y3-(y1cb-y3sb).*ssby./sysq./syy2.*(isysq.*y3-cosb)+sinb.*ysby./yy2q./yyycb+oh.*yysb./yy2.*sinb.*ty3fa./yyycb-oh.*yysb.*ysby./yy2th./yyycb.*ty3fa-yysb.*ysby./yy2q./yyycb2.*(hytcb))./pi./(1-nu)+1./4.*((omnunu).*(((tmnunu).*cotb2+nu).*hyto./yya-((tmnunu).*cotb2+1).*cosb.*(hytcb)./yyycb)-(omnunu)./yyas.*((-1+nunu).*y1.*cotb+nu.*y3aa-a+a.*y1.*cotb./yy2q+y12./yya.*(nu+a./yy2q)).*hyto+(omnunu)./yya.*(nu-oh.*a.*y1.*cotb./yy2th.*ty3fa-y12./yyas.*(nu+a./yy2q).*hyto-oh.*y12./yya.*a./yy2th.*ty3fa)+(omnunu).*cotb./yyycb2.*(yysb.*cosb-a.*ysby./yy2q./cosb).*(hytcb)-(omnunu).*cotb./yyycb.*(cosb.*sinb-oh.*a./yy2.*sinb.*ty3fa./cosb+oh.*a.*ysby./yy2th./cosb.*ty3fa)-a./yy2th.*y1.*cotb+th.*a.*y1.*(y3+a).*cotb./yy2fh.*ty3fa+1./yya.*(nunu+iyy2q.*((omnunu).*y1.*cotb+a)-y12./yy2q./yya.*nay-a.*y12./yy2th)-(y3+a)./yyas.*(nunu+iyy2q.*((omnunu).*y1.*cotb+a)-y12./yy2q./yya.*nay-a.*y12./yy2th).*hyto+(y3+a)./yya.*(-oh./yy2th.*((omnunu).*y1.*cotb+a).*ty3fa+oh.*y12./yy2th./yya.*nay.*ty3fa+y12./yy2q./yyas.*nay.*hyto+oh.*y12./yy22./yya.*a.*ty3fa+th.*a.*y12./yy2fh.*ty3fa)+cotb./yyycb.*(-cosb.*sinb+a.*y1.*y3aa./yy2th./cosb+ysby./yy2q.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb)))-(y3+a).*cotb./yyycb2.*(-cosb.*sinb+a.*y1.*y3aa./yy2th./cosb+ysby./yy2q.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb))).*(hytcb)+(y3+a).*cotb./yyycb.*(a./yy2th./cosb.*y1-th.*a.*y1.*y3aa./yy2fh./cosb.*ty3fa+oh./yy2.*sinb.*ty3fa.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb))-oh.*ysby./yy2th.*((tmnunu).*cosb-yCyY.*(1+a./yy2q./cosb)).*ty3fa+ysby./yy2q.*(-(oh./yy2q.*cosb.*ty3fa+1)./yyycb.*(1+a./yy2q./cosb)+yCyY2.*(1+a./yy2q./cosb).*(hytcb)+oh.*yCyY.*a./yy2th./cosb.*ty3fa)))./pi./(1-nu)); +e13d = e13d + oh.*B2.*(oe.*((-1+nunu).*sinb.*((isysq.*y1-sinb)./smymy-iyysb./yyycb)-isysq+iyy2q-y1.*(-1./systh.*y1+1./yy2th.*y1)+cosb.*scby./sysq./smymy+(y1cb-y3sb)./(sys).*cosb.*y1./smymy-(y1cb-y3sb).*scby./systh./smymy.*y1-(y1cb-y3sb).*scby./sysq./syy2.*(isysq.*y1-sinb)-cosb.*ycbya./yy2q./yyycb-yysb./yy2.*cosb.*y1./yyycb+yysb.*ycbya./yy2th./yyycb.*y1+yysb.*ycbya./yy2q./yyycb2.*iyysb)./pi./(1-nu)+1./4.*((-2+nunu).*(omnunu).*cotb.*(iyy2q.*y1./yya-cosb.*iyysb./yyycb)-(tmnunu)./yya.*nay+(tmnunu).*y12./yyas.*nay./yy2q+(tmnunu).*y12./yya.*a./yy2th+(tmnunu).*cosb./yyycb.*cbay-(tmnunu).*yysb./yyycb2.*cbay.*iyysb-(tmnunu).*yysb./yyycb.*a./yy2th.*y1-(y3+a)./yy2th.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2).*y1+(y3+a)./yy2q.*(-nunu./yya+nunu.*y12./yyas./yy2q-a./yy2+aa.*y12./yy22)+(y3+a)./yyycb2.*(cosb.*sinb+ycbya.*cotb./yy2q.*((tmnunu).*cosb-yCyY)+a./yy2q.*sby7).*iyysb-(y3+a)./yyycb.*(iyy2.*cosb.*y1.*cotb.*((tmnunu).*cosb-yCyY)-ycbya.*cotb./yy2th.*((tmnunu).*cosb-yCyY).*y1+ycbya.*cotb./yy2q.*(-iyy2q.*cosb.*y1./yyycb+yCyY2.*iyysb)-a./yy2th.*sby7.*y1+a./yy2q.*(-y3aa.*cosb./yy2+2.*y3aa.*yysb./yy22.*y1-cosb.*ycbya./yy2q./yyycb-yysb./yy2.*cosb.*y1./yyycb+yysb.*ycbya./yy2th./yyycb.*y1+yysb.*ycbya./yy2q./yyycb2.*iyysb)))./pi./(1-nu)); +e13t = oh.*B3.*(oe.*y2.*sinb.*(1./(sys).*sinb.*y3./smymy-ssby./systh./smymy.*y3-ssby./sysq./syy2.*(isysq.*y3-cosb)+oh./yy2.*sinb.*ty3fa./yyycb-oh.*ysby./yy2th./yyycb.*ty3fa-ysby./yy2q./yyycb2.*(hytcb))./pi./(1-nu)+1./4.*((omnunu).*(-y2./yyas.*oay.*hyto-oh.*y2./yya.*a./yy2th.*ty3fa+y2.*cosb./yyycb2.*cbay.*(hytcb)+oh.*y2.*cosb./yyycb.*a./yy2th.*ty3fa)-y2./yy2q.*(a./yy2+1./yya)+oh.*y2.*(y3+a)./yy2th.*(a./yy2+1./yya).*ty3fa-y2.*(y3+a)./yy2q.*(-a./yy22.*ty3fa-1./yyas.*hyto)+y2.*cosb./yy2q./yyycb.*(yCyY.*cbay+a.*y3aa./yy2)-oh.*y2.*(y3+a).*cosb./yy2th./yyycb.*(yCyY.*cbay+a.*y3aa./yy2).*ty3fa-y2.*(y3+a).*cosb./yy2q./yyycb2.*(yCyY.*cbay+a.*y3aa./yy2).*(hytcb)+y2.*(y3+a).*cosb./yy2q./yyycb.*((oh./yy2q.*cosb.*ty3fa+1)./yyycb.*cbay-yCyY2.*cbay.*(hytcb)-oh.*yCyY.*a./yy2th.*ty3fa+a./yy2-a.*y3aa./yy22.*ty3fa))./pi./(1-nu)); +e13t = e13t + oh.*B3.*(oe.*((tmnunu).*(-y2./ycys2.*cosb./(1+y22./ycys2)+(y2./sysq.*sinb./yyyy.*y1-y2.*sysq.*sinb./yyyy2.*(2.*y1cb-y3sb))./(1+y22.*(sys).*sinb2./yyyy2)+y2./yysb2.*cosb./(1+y22./yysb2)-(y2./yy2q.*sinb./yyysby.*y1-y2.*yy2q.*sinb./yyysby2.*(2.*y1cb+y3aa.*sinb))./oyysby)+y2.*sinb.*(1./(sys).*cosb.*y1./smymy-scby./systh./smymy.*y1-scby./sysq./syy2.*(isysq.*y1-sinb)-iyy2.*cosb.*y1./yyycb+ycbya./yy2th./yyycb.*y1+ycbya./yy2q./yyycb2.*iyysb))./pi./(1-nu)+1./4.*((tmnunu).*(y2./y12./(1+y22./y12)-y2./yysb2.*cosb./(1+y22./yysb2)+(y2./yy2q.*sinb./yyysby.*y1-y2.*yy2q.*sinb./yyysby2.*(2.*y1cb+y3aa.*sinb))./oyysby)-(tmnunu).*y2.*sinb./yyycb2.*cbay.*iyysb-(tmnunu).*y2.*sinb./yyycb.*a./yy2th.*y1-y2.*(y3+a).*sinb./yy2th./yyycb.*(1+yCyY.*cbay+a.*y3aa./yy2).*y1-y2.*(y3+a).*sinb./yy2q./yyycb2.*(1+yCyY.*cbay+a.*y3aa./yy2).*iyysb+y2.*(y3+a).*sinb./yy2q./yyycb.*(iyy2q.*cosb.*y1./yyycb.*cbay-yCyY2.*cbay.*iyysb-yCyY.*a./yy2th.*y1-aa.*y3aa./yy22.*y1))./pi./(1-nu)); + +e23s = oh.*B1.*(oe.*((omnunu).*((isysq.*y3-1)./(sysq-y3)+hyto./yya-cosb.*((isysq.*y3-cosb)./smymy+(hytcb)./yyycb))-y22.*(-1./systh./(sysq-y3).*y3-isysq./sy2.*(isysq.*y3-1)-oh./yy2th./yya.*ty3fa-iyy2q./yyas.*hyto-cosb.*(-1./systh./smymy.*y3-isysq./syy2.*(isysq.*y3-cosb)-oh./yy2th./yyycb.*ty3fa-iyy2q./yyycb2.*(hytcb))))./pi./(1-nu)+1./4.*((omnunu).*(((tmnunu).*cotb2-nu).*hyto./yya-((tmnunu).*cotb2+omnunu).*cosb.*(hytcb)./yyycb)+(omnunu)./yyas.*(y1.*cotb.*(omnunu-a./yy2q)+nu.*y3aa-a+y22./yya.*(nu+a./yy2q)).*hyto-(omnunu)./yya.*(oh.*a.*y1.*cotb./yy2th.*ty3fa+nu-y22./yyas.*(nu+a./yy2q).*hyto-oh.*y22./yya.*a./yy2th.*ty3fa)-(omnunu).*sinb.*cotb./yyycb.*cbay+(omnunu).*yysb.*cotb./yyycb2.*cbay.*(hytcb)+oh.*(omnunu).*yysb.*cotb./yyycb.*a./yy2th.*ty3fa-a./yy2th.*y1.*cotb+th.*a.*y1.*(y3+a).*cotb./yy2fh.*ty3fa+1./yya.*(-nunu+iyy2q.*((omnunu).*y1.*cotb-a)+y22./yy2q./yya.*nay+a.*y22./yy2th)-(y3+a)./yyas.*(-nunu+iyy2q.*((omnunu).*y1.*cotb-a)+y22./yy2q./yya.*nay+a.*y22./yy2th).*hyto+(y3+a)./yya.*(-oh./yy2th.*((omnunu).*y1.*cotb-a).*ty3fa-oh.*y22./yy2th./yya.*nay.*ty3fa-y22./yy2q./yyas.*nay.*hyto-oh.*y22./yy22./yya.*a.*ty3fa-th.*a.*y22./yy2fh.*ty3fa)+1./yyycb.*(cosb2-iyy2q.*((omnunu).*yysb.*cotb+a.*cosb)+a.*y3aa.*yysb.*cotb./yy2th-iyy2q./yyycb.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya))-(y3+a)./yyycb2.*(cosb2-iyy2q.*((omnunu).*yysb.*cotb+a.*cosb)+a.*y3aa.*yysb.*cotb./yy2th-iyy2q./yyycb.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya)).*(hytcb)+(y3+a)./yyycb.*(oh./yy2th.*((omnunu).*yysb.*cotb+a.*cosb).*ty3fa-iyy2q.*(omnunu).*sinb.*cotb+a.*yysb.*cotb./yy2th+a.*y3aa.*sinb.*cotb./yy2th-th.*a.*y3aa.*yysb.*cotb./yy2fh.*ty3fa+oh./yy2th./yyycb.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya).*ty3fa+iyy2q./yyycb2.*(y22cb2-a.*yysb.*cotb./yy2q.*ycbya).*(hytcb)-iyy2q./yyycb.*(-a.*sinb.*cotb./yy2q.*ycbya+oh.*a.*yysb.*cotb./yy2th.*ycbya.*ty3fa-a.*yysb.*cotb./yy2q.*(oh./yy2q.*cosb.*ty3fa+1))))./pi./(1-nu)); +e23s = e23s + oh.*B1.*(oe.*(isysq-iyy2q-cosb.*(scby./sysq./smymy-ycbya./yy2q./yyycb))./pi./(1-nu)+oe.*y2.*(-1./systh.*y2+1./yy2th.*y2-cosb.*(1./(sys).*cosb.*y2./smymy-scby./systh./smymy.*y2-scby./(sys)./syy2.*y2-iyy2.*cosb.*y2./yyycb+ycbya./yy2th./yyycb.*y2+ycbya./yy2./yyycb2.*y2))./pi./(1-nu)+1./4.*((tmnunu).*((omnunu).*(-1./y1./(1+y22./y12)+1./yysb./(1+y22./yysb2)+(yy2q.*sinb./yyysby+y22./yy2q.*sinb./yyysby-2.*y22.*yy2q.*sinb./yyysby2.*cosb)./oyysby).*cotb+1./yya.*nay-y22./yyas.*nay./yy2q-y22./yya.*a./yy2th-cosb./yyycb.*cbay+y22cb./yyycb2.*cbay./yy2q+y22cb./yyycb.*a./yy2th)+(y3+a)./yy2q.*(nunu./yya+a./yy2)-y22.*(y3+a)./yy2th.*(nunu./yya+a./yy2)+y2.*(y3+a)./yy2q.*(-nunu./yyas./yy2q.*y2-aa./yy22.*y2)+(y3+a).*cosb./yy2q./yyycb.*(omnunu-yCyY.*cbay-a.*y3aa./yy2)-y22.*(y3+a).*cosb./yy2th./yyycb.*(omnunu-yCyY.*cbay-a.*y3aa./yy2)-y22.*(y3+a).*cosb./yy2./yyycb2.*(omnunu-yCyY.*cbay-a.*y3aa./yy2)+y2.*(y3+a).*cosb./yy2q./yyycb.*(-iyy2q.*cosb.*y2./yyycb.*cbay+yCyY2.*cbay./yy2q.*y2+yCyY.*a./yy2th.*y2+aa.*y3aa./yy22.*y2))./pi./(1-nu)); +e23d = oh.*B2.*(oe.*((tmnunu).*(y2./ycys2.*sinb./(1+y22./ycys2)+(y2./sysq.*sinb./yyyy.*y3+y2.*sysq.*sinb2./yyyy2.*y1)./(1+y22.*(sys).*sinb2./yyyy2)-y2./yysb2.*sinb./(1+y22./yysb2)+(oh.*y2./yy2q.*sinb./yyysby.*ty3fa-y2.*yy2q.*sinb2./yyysby2.*y1)./oyysby)+y1.*y2.*(-1./systh./(sysq-y3).*y3-isysq./sy2.*(isysq.*y3-1)-oh./yy2th./yya.*ty3fa-iyy2q./yyas.*hyto)-y2.*(-sinb./sysq./smymy-(y1cb-y3sb)./systh./smymy.*y3-(y1cb-y3sb)./sysq./syy2.*(isysq.*y3-cosb)+sinb./yy2q./yyycb-oh.*yysb./yy2th./yyycb.*ty3fa-yysb./yy2q./yyycb2.*(hytcb)))./pi./(1-nu)+1./4.*((tmnunu).*(omnunu).*(-y2./yysb2.*sinb./(1+y22./yysb2)+(oh.*y2./yy2q.*sinb./yyysby.*ty3fa-y2.*yy2q.*sinb2./yyysby2.*y1)./oyysby).*cotb2-(omnunu).*y2./yyas.*((-1+nunu+a./yy2q).*cotb+y1./yya.*(nu+a./yy2q)).*hyto+(omnunu).*y2./yya.*(-oh.*a./yy2th.*ty3fa.*cotb-y1./yyas.*(nu+a./yy2q).*hyto-oh.*y1./yya.*a./yy2th.*ty3fa)+(omnunu).*y2.*cotb./yyycb2.*(1+a./yy2q./cosb).*(hytcb)+oh.*(omnunu).*y2.*cotb./yyycb.*a./yy2th./cosb.*ty3fa-a./yy2th.*y2.*cotb+th.*a.*y2.*(y3+a).*cotb./yy2fh.*ty3fa+y2./yy2q./yya.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya))-oh.*y2.*(y3+a)./yy2th./yya.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya)).*ty3fa-y2.*(y3+a)./yy2q./yyas.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2q.*(iyy2q+1./yya)).*hyto+y2.*(y3+a)./yy2q./yya.*(nunu.*y1./yyas.*hyto+oh.*a.*y1./yy2th.*(iyy2q+1./yya).*ty3fa-a.*y1./yy2q.*(-oh./yy2th.*ty3fa-1./yyas.*hyto))+y2.*cotb./yy2q./yyycb.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb)-oh.*y2.*(y3+a).*cotb./yy2th./yyycb.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb).*ty3fa-y2.*(y3+a).*cotb./yy2q./yyycb2.*((-2+nunu).*cosb+yCyY.*(1+a./yy2q./cosb)+a.*y3aa./yy2./cosb).*(hytcb)+y2.*(y3+a).*cotb./yy2q./yyycb.*((oh./yy2q.*cosb.*ty3fa+1)./yyycb.*(1+a./yy2q./cosb)-yCyY2.*(1+a./yy2q./cosb).*(hytcb)-oh.*yCyY.*a./yy2th./cosb.*ty3fa+a./yy2./cosb-a.*y3aa./yy22./cosb.*ty3fa))./pi./(1-nu)); +e23d = e23d + oh.*B2.*(oe.*((-1+nunu).*sinb.*(isysq.*y2./smymy-iyy2q.*y2./yyycb)-y1.*(-1./systh.*y2+1./yy2th.*y2)+(y1cb-y3sb)./(sys).*cosb.*y2./smymy-(y1cb-y3sb).*scby./systh./smymy.*y2-(y1cb-y3sb).*scby./(sys)./syy2.*y2-yysb./yy2.*cosb.*y2./yyycb+yysb.*ycbya./yy2th./yyycb.*y2+yysb.*ycbya./yy2./yyycb2.*y2)./pi./(1-nu)+1./4.*((-2+nunu).*(omnunu).*cotb.*(iyy2q.*y2./yya-cosb./yy2q.*y2./yyycb)+(tmnunu).*y1./yyas.*nay./yy2q.*y2+(tmnunu).*y1./yya.*a./yy2th.*y2-(tmnunu).*yysb./yyycb2.*cbay./yy2q.*y2-(tmnunu).*yysb./yyycb.*a./yy2th.*y2-(y3+a)./yy2th.*((omnunu).*cotb-nunu.*y1./yya-a.*y1./yy2).*y2+(y3+a)./yy2q.*(nunu.*y1./yyas./yy2q.*y2+aa.*y1y22.*y2)+(y3+a)./yyycb2.*(cosb.*sinb+ycbya.*cotb./yy2q.*((tmnunu).*cosb-yCyY)+a./yy2q.*sby7)./yy2q.*y2-(y3+a)./yyycb.*(iyy2.*cosb.*y2.*cotb.*((tmnunu).*cosb-yCyY)-ycbya.*cotb./yy2th.*((tmnunu).*cosb-yCyY).*y2+ycbya.*cotb./yy2q.*(-cosb./yy2q.*y2./yyycb+yCyY2./yy2q.*y2)-a./yy2th.*sby7.*y2+a./yy2q.*(2.*y3aa.*yysb./yy22.*y2-yysb./yy2.*cosb.*y2./yyycb+yysb.*ycbya./yy2th./yyycb.*y2+yysb.*ycbya./yy2./yyycb2.*y2)))./pi./(1-nu)); +e23t = oh.*B3.*(oe.*((omnunu).*sinb.*((isysq.*y3-cosb)./smymy+(hytcb)./yyycb)-y22.*sinb.*(-1./systh./smymy.*y3-isysq./syy2.*(isysq.*y3-cosb)-oh./yy2th./yyycb.*ty3fa-iyy2q./yyycb2.*(hytcb)))./pi./(1-nu)+1./4.*((omnunu).*(-sinb.*(hytcb)./yyycb+y1./yyas.*oay.*hyto+oh.*y1./yya.*a./yy2th.*ty3fa+sinb./yyycb.*cbay-yysb./yyycb2.*cbay.*(hytcb)-oh.*yysb./yyycb.*a./yy2th.*ty3fa)+y1./yy2q.*(a./yy2+1./yya)-oh.*y1.*(y3+a)./yy2th.*(a./yy2+1./yya).*ty3fa+y1.*(y3+a)./yy2q.*(-a./yy22.*ty3fa-1./yyas.*hyto)-1./yyycb.*(sinb.*(cosb-a./yy2q)+yysb./yy2q.*(1+a.*y3aa./yy2)-iyy2q./yyycb.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya))+(y3+a)./yyycb2.*(sinb.*(cosb-a./yy2q)+yysb./yy2q.*(1+a.*y3aa./yy2)-iyy2q./yyycb.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya)).*(hytcb)-(y3+a)./yyycb.*(oh.*sinb.*a./yy2th.*ty3fa+sinb./yy2q.*(1+a.*y3aa./yy2)-oh.*yysb./yy2th.*(1+a.*y3aa./yy2).*ty3fa+yysb./yy2q.*(a./yy2-a.*y3aa./yy22.*ty3fa)+oh./yy2th./yyycb.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya).*ty3fa+iyy2q./yyycb2.*(y22cb.*sinb-a.*yysb./yy2q.*ycbya).*(hytcb)-iyy2q./yyycb.*(-a.*sinb./yy2q.*ycbya+oh.*a.*yysb./yy2th.*ycbya.*ty3fa-a.*yysb./yy2q.*(oh./yy2q.*cosb.*ty3fa+1))))./pi./(1-nu)); +e23t = e23t + oh.*B3.*(oe.*((tmnunu).*(1./(y1cb-y3sb)./(1+y22./ycys2)+(sysq.*sinb./yyyy+y22./sysq.*sinb./yyyy-2.*y22.*sysq.*sinb./yyyy2.*cosb)./(1+y22.*(sys).*sinb2./yyyy2)-1./yysb./(1+y22./yysb2)-(yy2q.*sinb./yyysby+y22./yy2q.*sinb./yyysby-2.*y22.*yy2q.*sinb./yyysby2.*cosb)./oyysby)+sinb.*(scby./sysq./smymy-ycbya./yy2q./yyycb)+y2.*sinb.*(1./(sys).*cosb.*y2./smymy-scby./systh./smymy.*y2-scby./(sys)./syy2.*y2-iyy2.*cosb.*y2./yyycb+ycbya./yy2th./yyycb.*y2+ycbya./yy2./yyycb2.*y2))./pi./(1-nu)+1./4.*((tmnunu).*(-1./y1./(1+y22./y12)+1./yysb./(1+y22./yysb2)+(yy2q.*sinb./yyysby+y22./yy2q.*sinb./yyysby-2.*y22.*yy2q.*sinb./yyysby2.*cosb)./oyysby)+(tmnunu).*sinb./yyycb.*cbay-(tmnunu).*y22.*sinb./yyycb2.*cbay./yy2q-(tmnunu).*y22.*sinb./yyycb.*a./yy2th+(y3+a).*sinb./yy2q./yyycb.*(1+yCyY.*cbay+a.*y3aa./yy2)-y22.*(y3+a).*sinb./yy2th./yyycb.*(1+yCyY.*cbay+a.*y3aa./yy2)-y22.*(y3+a).*sinb./yy2./yyycb2.*(1+yCyY.*cbay+a.*y3aa./yy2)+y2.*(y3+a).*sinb./yy2q./yyycb.*(iyy2q.*cosb.*y2./yyycb.*cbay-yCyY2.*cbay./yy2q.*y2-yCyY.*a./yy2th.*y2-aa.*y3aa./yy22.*y2))./pi./(1-nu)); \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tristrikedip.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tristrikedip.m new file mode 100644 index 0000000..5105a0a --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/tristrikedip.m @@ -0,0 +1,19 @@ +function [s, d, nv] = tristrikedip(p,t) + +% TRISTRIKEDIP: Strike and dip of triangles assuming counter-clockwise +% (CCW) node ordering. +% +% P : Nx3 array of XYZ node co-ordinates +% T : Mx3 array of triangles as indices into P +% S : Mx1 array of triangle strikes +% D : Mx1 array of triangle dips + +d12 = p(t(:,2),:)-p(t(:,1),:); +d13 = p(t(:,3),:)-p(t(:,1),:); +nv = cross(d12, d13, 2); +nv = nv./repmat(mag(nv, 2), 1, 3); +[s, d] = cart2sph(nv(:, 1), nv(:, 2), nv(:, 3)); +s = wrapTo360(-rad2deg(s)); +d = 90 - rad2deg(d); + +end % tristrikedip() \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/xyz2enumat_strain.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/xyz2enumat_strain.m new file mode 100644 index 0000000..db3d168 --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/tribem-master/tridisl/xyz2enumat_strain.m @@ -0,0 +1,47 @@ +function Gp = xyz2enumat_strain(G, az) +% xyz2enumat_strain Rotates a strain matrix of x, y, z vectors to E, N, U +% GP = xyz2enumat_strain(G, AZ) rotates the x, y, z values of matrix G +% to E, N, U by rotating about AZ, returning the rotated values +% to matrix GP. AZ can be a scalar, a vector of values equal +% to the number of columns of G, or a vector of values equal to +% the number of columns of G divided by 2 or 3 (reflecting columns +% containing displacements due to slip components). G is assumed +% to be structured so that rows contain [EXX; EYY; EZZ; EXY; EXZ; EYZ] +% values for each point and GP is returned as [EEE; ENN; EUU; EEN; EEU; ENZ]. +% + +% Check inputs +sa = numel(az); +sG = size(G); + +if sa == 1 + az = repmat(az, sG(1)/6, sG(2)); +elseif sa == sG(2) + az = repmat(az(:)', sG(1)/6, 1); +elseif sa == sG(2)/3 + az = repmat(reshape(repmat(az(:)', 3, 1), sG(2), 1)', sG(1)/6, 1); +elseif sa == sG(2)/2 + az = repmat(reshape(repmat(az(:)', 2, 1), sG(2), 1)', sG(1)/6, 1); +end + +% Copy matrix +Gp = G; + +% Extract tensor components +uxx = G(1:6:end, :); +uyy = G(2:6:end, :); +uzz = G(3:6:end, :); +uxy = G(4:6:end, :); +uxz = G(5:6:end, :); +uyz = G(6:6:end, :); + +% Do rotation +caz = cosd(az); +saz = sind(az); +Gp(1:6:end, :) = caz.*(uxx.*caz - uxy.*saz) - saz.*(uxy.*caz - uyy.*saz); +Gp(4:6:end, :) = caz.*(uxy.*caz - uyy.*saz) + saz.*(uxx.*caz - uxy.*saz); +Gp(5:6:end, :) = uxz.*caz - uyz.*saz; +Gp(2:6:end, :) = caz.*(uyy.*caz + uxy.*saz) + saz.*(uxy.*caz + uxx.*saz); +Gp(6:6:end, :) = uyz.*caz + uxz.*saz; + + \ No newline at end of file diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/utmconv.m b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/utmconv.m new file mode 100644 index 0000000..c5cd18c --- /dev/null +++ b/Pearson_and_Loveless_Tectonics_2021_Inputs/Supporting Functions/utmconv.m @@ -0,0 +1,28 @@ +function [b, uz] = utmconv(a, fi, uz) +% UTMCONV General UTM conversion function. +% B = UTMCONV(A, TYPE, UZ) converts the n-by-2 array A from geographic +% to Cartesian coordinates, or vice versa, using the UTM projection. +% TYPE specifies the conversion from (long., lat.) to UTM (type = 0) or +% from UTM to (long., lat.) (type = 1). UZ specifies the UTM zone, which +% should be set as the returned string from UTMZONE for a TYPE = 1 +% conversion and can be either specified or omitted for a TYPE = 0 conversion. +% If omitted, the zone is determined from the input coordinates. +% + +mstruct = defaultm('utm'); +if fi == 0 % Lon., lat. to x, y + if ~exist('uz', 'var'); + mstruct.zone = utmzone(a(:, 2), a(:, 1)); + else + mstruct.zone = uz; + end + mstruct = defaultm(mstruct); + [x, y] = mfwdtran(mstruct, a(:, 2), a(:, 1)); + b = [x(:) y(:)]; + uz = mstruct.zone; +else + mstruct.zone = uz; + mstruct = defaultm(mstruct); + [lat, lon] = minvtran(mstruct, a(:, 1), a(:, 2)); + b = [lon(:) lat(:)]; +end \ No newline at end of file diff --git "a/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/Icon\r" "b/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/Icon\r" new file mode 100644 index 0000000..e69de29 diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/comparisondata.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/comparisondata.mat new file mode 100644 index 0000000..5007b27 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/comparisondata.mat differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/modelinputs.mat b/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/modelinputs.mat new file mode 100644 index 0000000..a86eb34 Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/matfiles/modelinputs.mat differ diff --git a/Pearson_and_Loveless_Tectonics_2021_Inputs/methodology.mlx b/Pearson_and_Loveless_Tectonics_2021_Inputs/methodology.mlx new file mode 100644 index 0000000..0b049ab Binary files /dev/null and b/Pearson_and_Loveless_Tectonics_2021_Inputs/methodology.mlx differ diff --git a/findremotestress.m b/findremotestress.m new file mode 100644 index 0000000..b33cf34 --- /dev/null +++ b/findremotestress.m @@ -0,0 +1,331 @@ +function [slip, trac, varargout] = tribemx(patch, d, bc, varargin) +% TRIBEMX Triangular element boundary element solver. +% [SLIP, TRAC] = TRIBEMX(PATCH, D, BC) estimates slip or traction on triangular +% elements given a mesh in structure PATCH, a set of slip and traction +% boundary conditions D and a boundary condition identifer matrix, BC. +% +% PATCH can either be a string giving the full patch to a Gmsh .msh file +% or a structure given as PATCH = READPATCHES(PATCHFILE). Given NEL +% triangular elements, D should be an NEL-by-3 array of boundary conditions, +% giving either the slip or traction conditions on each element. For elements +% with slip prescribed, the corresponding line of D should be: +% +% [strike slip, dip slip, tensile slip] +% +% and for elements whose traction conditions are specified, D should read: +% +% [shear stress (strike), shear stress (dip), normal stress]. +% +% The NEL-by-3 array BC specifies the type of boundary conditions for each +% element, given as 0 for slip conditions and 1 for traction conditions. +% +% [SLIP, TRAC, O] = TRIBEMX(PATCH, D, BC, OBS) will also calculate values at a set of +% observation coordinates defined by input argument OBS. OBS can be a structure +% containing fields x, y, z, and v, where x, y, and z are N-by-1 arrays giving +% the coordinates of N observation points, and v is a character specifying what +% will be calculated at these points: +% u: Calculate displacement (returned to O.u as a 3N-by-1 vector) +% s: Calculate stress (returned to O.s as a 6N-by-1 vector) +% e: Calculate strain (returned to O.e as 6N-by-1 vector) +% +% [SLIP, TRAC, G] = TRIBEMX(PATCH, D, BC) will output the structure G containing +% fields of Green's functions relating slip to displacement and/or traction. This +% structure can be reused as an input argument, speeding computation when only the +% boundary conditions and not the problem geometry have changed. +% +% [SLIP, TRAC, O, G] = TRIBEMX(PATCH, D, BC, OBS) will output both O and G, when OBS +% is specified as an input argument. +% +% [...] = TRIBEMX(PATCH, D, BC, REMS) allows specification of a remote stress tensor, +% REMS. The tensor components, assuming Cartesian coordinates, should be given as +% +% REMS = [sigma_xx, sigma_yy, 0, sigma_xy, 0, 0]'; % 0 values for components involving z +% +% [...] = TRIBEMX(PATCH, D, BC, RHO) allows specification of a density (assumed kg/m^3) +% that will be used to apply lithostatic stress to the problem. RHO must be greater than +% 1; if you wish to ignore lithostatic stress, don't prescribe a density. +% +% [...] = TRIBEMX(PATCH, D, BC, G) uses a structure G of already-calculated +% traction (G.sp) and displacement partials (G.u). No checking is done to assure +% that the sizes of G fields are appropriate for the problem; this must be done +% externally. Therefore, this option is best used when only the boundary conditions +% change from one model run to the next, i.e., all of the problem geometry remains +% consistent. +% +% [...] = TRIBEMX(PATCH, D, BC, CHOP) accepts CHOP as a flag to indicate whether +% or not the components of slip should be chopped according to element geometry. If +% CHOP = 1, only strike-slip and dip-slip will be considered for dipping faults, and +% only strike-slip and tensile motion will be considered for vertical faults. +% +% [...] = TRIBEMX(PATCH, D, BC, G, CHOP) accepts both G and CHOP as input arguments. +% If the input G fields are already chopped, no additional trimming will be done. +% +% +% SIGN CONVENTIONS: +%------------------ +% +% SLIP: +% + | - +% ------------------------------- +% 1. Strike: Sinistral | Dextral +% 2. Dip: Reverse | Normal +% 3. Tensile: Opening | Closing +% +% TRACTION: +% + | - +% ---------------------------------------- +% 1. Strike shear: Strike | Strike + 180 +% 2. Dip shear: Updip | Downdip +% 3. Normal: Tensile | Compressional +% +% For comparison, Poly3D's sign conventions are: +% +% SLIP: +% + | - +% ------------------------------- +% 1. Dip: Normal | Reverse +% 2. Strike: Sinistral | Dextral +% 3. Tensile: Opening | Closing +% +% TRACTION: +% + | - +% ---------------------------------------- +% 1. Dip shear: Downdip | Updip +% 2. Strike shear: Strike | Strike + 180 +% 3. Normal: Tensile | Compressional +% + +chop = 0; + +% Parse optional inputs +noa = length(varargin); +if noa > 0 + for i = 1:noa % Loop through optional arguments + if isstruct(varargin{i}) % If it's a structure, it's either observations or partials + if isfield(varargin{i}, 'x') % If field x exists, it's observations + obs = varargin{i}; + else % If not, + G = varargin{i}; % It's partials + end + else + if length(varargin{i}) == 1 % If a single value was entered, it's either chop flag or Poisson's ratio + if varargin{i} <= 0.5 % If it's less than or equal to 0.5, it's PR + pr = varargin{i}; + elseif double(varargin{i}) == 1 + chop = varargin{i}; % If it's a 1 or true, it's chop flag + elseif varargin{i} > 1 + lith = varargin{i}; % If it's greater than one, it's a density for lithostatic stress + end + elseif length(varargin{i}) == 2 % If a 2-element vector was specified, + lame = varargin{i}; % Lame parameters were specified + elseif length(varargin{i}) >= 4 + rems = varargin{i}; % Remote stress tensor + end + end + end +end + +% Read patch file, if necessary +if ischar(patch) + patch = ReadPatches(patch); + patch = PatchCoordsx(patch); +end + +% Calculate patch coordinates, if necessary +if ~isfield(patch, 'xc') + patch = PatchCoordsx(patch); +end + +% Total number of elements +tne = sum(patch.nEl); + +% Project remote stress tensor onto elements +if exist('rems', 'var') + rems([5 6]) = 0; % Make sure traction-free surface of half space condition is met + remsp = ProjectStrainPartialsMats(repmat(rems(:), sum(patch.nEl), 1), patch.strike, patch.dip); +end + +% Add lithostatic stress, if requested +if exist('lith', 'var') + lstress = -abs(lith.*9.8*patch.zc); % Magnitude of lithostatic load; assumes meters and compression + lstress = stack6([lstress, lstress, lstress, zeros(sum(patch.nEl), 3)]); % Full stress tensor + ltrac = ProjectStrainPartialsMats(lstress, patch.strike, patch.dip); % Lithostatic tractions + if exist('remsp', 'var') + remsp = remsp + ltrac; % Add lithostatic to existing remote stress + else + remsp = ltrac; % Or consider lithostatic as the only remote stress + end +end + +% Check for existence of specified Lame parameters +if ~exist('lame', 'var') + mu = 3e10; lambda = 3e10; % Defaults +else + mu = lame(2); lambda = lame(1); +end + +% (Re)calculate Poisson's ratio from Lame parameters +pr = lambda./(2*(lambda + mu)); + +% Make a structure containing perturbed element centroid coordinates +% Centroids are perturbed toward the half-space surface along the normal vector +psc = 1e-5; % Centroid perturbation scaling factor +[cent.x, cent.y, cent.z] = deal(patch.xc+psc.*patch.nv(:, 1), patch.yc+psc.*patch.nv(:, 2), patch.zc+psc.*patch.nv(:, 3)); + +% Augment this structure with any observation coordinates +if exist('obs', 'var') + obs.x = obs.x(:); + obs.y = obs.y(:); + obs.z = obs.z(:); + if ~isfield(obs, 'v') % Default behavior is to calculate displacements only at observation coordinates + obs.v = 'd'; + end + opt = zeros(length(obs.x), 2); % Initialize observation coordinate calculation option array + if contains(obs.v, 'd') % Calculate displacements at observation coordinates + opt(:, 1) = 1; + end + if contains(obs.v, 's') | contains(obs.v, 'e') % Calculate stresses/strains at observation coordinates + opt(:, 2) = 1; + end +else + [obs.x, obs.y, obs.z] = deal([]); + obs.v = 'x'; + opt = zeros(0, 2); +end + +% Augmented calculation coordinates +cc.x = [cent.x; obs.x]; +cc.y = [cent.y; obs.y]; +cc.z = [cent.z; obs.z]; +% Set partials calculation option; this will be adjusted if need be when observations are considered +opt = logical([repmat([0 1], tne, 1); opt]); + +% Call GetTriCombinedPartials for elements and coordinates +if ~exist('G', 'var') + % Check for existence of specified Poisson's ratio + if ~exist('pr', 'var') + pr = 0.25; + end + [G.u, G.e, G.tz] = GetTriCombinedPartialsx(patch, cc, opt, pr); + G.s = StrainToStressComp(G.e', mu, lambda)'; + G.sp = ProjectStrainPartialsMats(G.s(1:6*tne, :), patch.strike, patch.dip); +end + +% Trim arrays for slip components, if requested and if not already done +if chop > 0 + triD = find(G.tz == 2); + triT = find(G.tz == 3); + colkeep = setdiff(1:3*tne, [3*triD-0; 3*triT-1]); % Define columns to keep + if size(G.sp, 2) == numel(patch.v) % If the columns have not already been trimmed... + G.s = G.s(:, colkeep); % ...trim them + G.e = G.e(:, colkeep); + G.sp = G.sp(:, colkeep); + if size(G.u, 2) > size(G.e, 2) + G.u = G.u(:, colkeep); + end + end +else + colkeep = 1:3*tne; % All columns retained if no chopping is requested +end + +% Determine which elements need slip estimated, and which have slip prescribed +c3 = 0; % Flag to indicate that the arrays came in as 3 column arrays +if max([size(bc, 2), size(d, 2)]) == 3 + c3 = 1; + d = reshape(d', numel(d), 1); + bc = reshape(bc', numel(bc), 1); +end +bc = logical(bc(:)); +islip = find(~bc(colkeep)); % Indices of prescribed slips +pslip = d(colkeep); pslip = pslip(islip); % Actual prescribed slips +itrac = find(bc); % Indices of prescibed tractions +ptrac = d(itrac); % Actual prescribed tractions +esidx = find(bc(colkeep)); % Indices of the slip components that will be estimated + +% Determine traction induced by any input displacement boundary conditions +dstress = G.sp(:, islip)*pslip; + +if ~exist('remsp', 'var') % If there is no remote stress + % Corrected traction is prescribed traction minus contribution from displacement b.c. + elstress = ptrac - dstress(itrac); + % Estimate slips that produce corrected traction + m = G.sp(itrac, esidx)\elstress; + % Assemble full slip vector (prescribed and estimated) + slip = zeros(3*tne, 1); + slip(islip) = pslip; + slip(itrac) = m; + % Assemble full traction vector (prescribed and estimated) + trac = zeros(3*tne, 1); + trac(islip) = dstress(islip); % Traction from prescribed slip + trac(itrac) = ptrac; % Prescribed traction +else + elstress = 0*d; % Full element stress vector + elstress(itrac) = ptrac; % Corrected traction is prescribed traction minus contribution from displacement b.c. + elstress = elstress - dstress - remsp; % Also corrected for remote stress projected onto elements + g = G.sp; seye = eye(size(G.sp, 1)); % Set up design matrix + g(:, islip) = seye(:, islip); % Substitute identity matrix for prescribed slip columns + m = g\elstress; + % Assemble full slip vector (prescribed and estimated) + slip = m; + slip(islip) = pslip; + % Assemble full traction vector (prescribed and estimated) + trac = -elstress; +end + +% Forward calculation for observations +if contains(obs.v, 'd') + o.u = G.u*slip(:); + if c3 == 1 % Check to see if output should be multicolumn + o.u = unstack3(o.u); + end +else + o.u = []; +end +if contains(obs.v, 'e') + if exist('rems', 'var') + oreme = StressToStrainComp(rems, mu, lambda); + else + oreme = 0; + end + o.e = G.e(6*tne+1:end, :)*slip(:) + repmat(oreme(:), length(obs.x), 1); + if c3 == 1 % Check to see if output should be multicolumn + o.e = unstack6(o.e); + end +else + o.e = []; +end +if contains(obs.v, 's') + if exist('rems', 'var') + orems = repmat(rems(:), length(obs.x), 1); + else + orems = 0; + end + o.s = G.s(6*tne+1:end, :)*slip(:) + orems; + if c3 == 1 % Check to see if output should be multicolumn + o.s = unstack6(o.s); + end +else + o.s = []; +end + + +% Reshape if original boundary condition array was n-by-3 +if c3 == 1 + slip = reshape(slip, 3, tne)'; + trac = reshape(trac, 3, tne)'; +end + +% Process optional output arguments +if nargout == 3 % 3rd argument could be o or G + if contains(obs.v, 'x') % If no observation points are specified, it must be G + varargout{:} = G; + else + varargout{:} = o; + end +end + +if nargout == 4 + varargout{1} = o; + varargout{2} = G; +end +