基于卡尔曼滤波检测GNSS 数据中的智能手机位移附matlab代码

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#智能手机 #matlab #开发语言

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此博客聚焦Matlab应用，涵盖智能优化算法改进、机器学习与深度学习预测、图像处理、路径规划等多领域。还介绍斯图加特大学项目，评估智能手机在海啸预警系统的可用性，通过模拟地震位移、测量GNSS数据并经卡尔曼滤波检测位移。

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智能优化算法神经网络预测雷达通信无线传感器电力系统

信号处理图像处理路径规划元胞自动机无人机

物理应用机器学习

🔥 内容介绍

斯图加特大学大地测量学和地理信息学硕士项目

该项目的核心思想是评估智能手机在海啸预警系统中的可用性。模拟了震级为 7 的地震的位移，并在数据中检测到了位移。

步骤 1：使用 Okada 程序模拟震级为 7 的地震的位移

步骤 2：根据模拟动作测量智能手机数据的动态运动的 GNSS 数据

步骤 3：通过卡尔曼滤波处理数据，检测 GNSS 数据中的智能手机位移

📣 部分代码

function varargout=okada85(varargin)%OKADA85 Surface deformation due to a finite rectangular source.%  [uE,uN,uZ,uZE,uZN,uNN,uNE,uEN,uEE] = OKADA85(...%     E,N,DEPTH,STRIKE,DIP,LENGTH,WIDTH,RAKE,SLIP,OPEN)%  computes displacements, tilts and strains at the surface of an elastic%  half-space, due to a dislocation defined by RAKE, SLIP, and OPEN on a %  rectangular fault defined by orientation STRIKE and DIP, and size LENGTH and%  WIDTH. The fault centroid is located (0,0,-DEPTH).%%     E,N    : coordinates of observation points in a geographic referential %              (East,North,Up) relative to fault centroid (units are described below)%     DEPTH  : depth of the fault centroid (DEPTH > 0)%     STRIKE : fault trace direction (0 to 360 relative to North), defined so %              that the fault dips to the right side of the trace%     DIP    : angle between the fault and a horizontal plane (0 to 90)%     LENGTH : fault length in the STRIKE direction (LENGTH > 0)%     WIDTH  : fault width in the DIP direction (WIDTH > 0)%     RAKE   : direction the hanging wall moves during rupture, measured relative%              to the fault STRIKE (-180 to 180).%     SLIP   : dislocation in RAKE direction (length unit)%     OPEN   : dislocation in tensile component (same unit as SLIP)%%  returns the following variables (same matrix size as E and N):%     uN,uE,uZ        : displacements (unit of SLIP and OPEN)%     uZE,uZN         : tilts (in rad * FACTOR)%     uNN,uNE,uEN,uEE : horizontal strains POSITIVE = COMPRESSION (unit of FACTOR)%%  Length unit consistency: E, N, DEPTH, LENGTH, and WIDTH must have the same %  unit (e.g. km) which can be different from that of SLIP and OPEN (e.g. m) but%  with a possible FACTOR on tilt and strain results (in this case, an %  amplification of km/m = 1000). To have FACTOR = 1 (tilt in radians and %  correct strain unit), use the same length unit for all aforesaid variables.%%  [...] = OKADA85(...,NU) specifies Poisson's ratio NU (default is 0.25 for%  an isotropic medium).%%  Formulas and notations from Okada [1985] solution excepted for strain %  convention (here positive strain means compression), and for the fault %  parameters after Aki & Richards [1980], e.g.:%        DIP=90, RAKE=0   : left lateral (senestral) strike slip%        DIP=90, RAKE=180 : right lateral (dextral) strike slip%        DIP=70, RAKE=90  : reverse fault%        DIP=70, RAKE=-90 : normal fault%%  It is also possible to produce partial outputs, with following syntax:%     [uE,uN,uZ] = OKADA85(...) for displacements only;%     [uE,uN,uZ,uZE,uZN] = OKADA85(...) for displacements and tilts;%     [uE,uN,uZ,uNN,uNE,uEN,uEE] = OKADA85(...) for displacements and strains;%     [uZE,uZN] = OKADA85(...) for tilts only;%     [uZE,uZN,uNN,uNE,uEN,uEE] = OKADA85(...) for tilts and strains;%     [uNN,uNE,uEN,uEE] = OKADA85(...) for strains only.%%  Note that vertical strain components can be obtained with following equations:%     uNZ = -uZN;%     uEZ = -uZE;%     uZZ = -(uEE + uNN)*NU/(1-NU);%%  [...] = OKADA85(...,'plot') or OKADA85(...) without output argument %  produces a 3-D figure with fault geometry and dislocation at scale (if%  all of the fault parameters are scalar).%%  Equations are all vectorized excepted for argument DIP which must be%  a scalar (beacause of a singularity in Okada's equations); all other%  arguments can be scalar or matrix of the same size.%%  Example:%%     [E,N] = meshgrid(linspace(-10,10,50));%     [uE,uN,uZ] = okada85(E,N,2,30,70,5,3,-45,1,1,'plot');%     figure, surf(E,N,uN)%%  considers a 5x3 fault at depth 2, N30-strike, 70-dip, and unit dislocation%  in all directions (reverse, senestral and open). Displacements are computed%  on a regular grid from -10 to 10, and North displacements are plotted as a%  surface.%%%  Author: Franois Beauducel <beauducel@ipgp.fr>%     Institut de Physique du Globe de Paris%  Created: 1997%  Updated: 2014-05-24%%  References:%     Aki K., and P. G. Richards, Quantitative seismology, Freemann & Co,%        New York, 1980.%     Okada Y., Surface deformation due to shear and tensile faults in a%        half-space, Bull. Seismol. Soc. Am., 75:4, 1135-1154, 1985.%%  Acknowledgments: Dmitry Nicolsky, Qian Yao, Halldor Geirsson%  Development history:%     [2014-05-24]: fixes a bug for tilt calculation (K1) when DIP=90.%        Detected by Halldor Geirsson.%     [2012-11-08]: solves partially mathematical singularities in %        specific cases like DIP=90, STRIKE=0, and fault reaching surface.%        Detected by Qian Yao.%     [2012-08-29]: allows vectorization of RAKE, SLIP and OPEN.%     [2011-03-08]: help review.%     [2011-03-06]: new optional argument to plot fault geometry with%        output arguments, and bug correction for the fault centroid position%        (in calculation and plot).%     [2010-11-29]: change coordinates and depth to fault centroid %        (instead of middle top edge).%     [2010-09-24]: bugs correction in the syntax of I1, K2 and uyy_tf%        functions, affecting some components. Detected by Dmitry Nicolsky.%%  Copyright (c) 1997-2012, Franois Beauducel, covered by BSD License.%  All rights reserved.%%  Redistribution and use in source and binary forms, with or without %  modification, are permitted provided that the following conditions are %  met:%%     * Redistributions of source code must retain the above copyright %       notice, this list of conditions and the following disclaimer.%     * Redistributions in binary form must reproduce the above copyright %       notice, this list of conditions and the following disclaimer in %       the documentation and/or other materials provided with the distribution%                             %  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" %  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE %  IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE %  ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE %  LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR %  CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF %  SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS %  INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN %  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) %  ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE %  POSSIBILITY OF SUCH DAMAGE.if nargin < 10  error('Not enough input arguments.')endif nargin > 12  error('Too many input arguments.')endif any(~cellfun(@isnumeric,varargin(1:10)))  error('Input arguments E,N,DEPTH,STRIKE,DIP,LENGTH,WIDTH,RAKE,SLIP,OPEN must be numeric.')endif ~isscalar(varargin{5})  error('DIP argument must be scalar.')end% Default values for optional input argumentsplotflag = 0;  % no plotnu = 0.25;  % isotropic Poisson's ratio% Assigns input argumentse = varargin{1};n = varargin{2};depth = varargin{3};strike = varargin{4}*pi/180;  % converting STRIKE in radiandip = varargin{5}*pi/180;  % converting DIP in radian ('delta' in Okada's equations)L = varargin{6};W = varargin{7};rake = varargin{8}*pi/180;  % converting RAKE in radianslip = varargin{9};U3 = varargin{10};switch nargincase 11  if isnumeric(varargin{11})    nu = varargin{11};  else    makeplot = varargin{11};  endcase 12  makeplot = varargin{12};endif exist('makeplot','var')  if strcmp(makeplot,'plot')    plotflag = 1;  else    error('Unknown last argument.')  endendif plotflag & any([numel(depth),numel(strike),numel(L),numel(W),numel(rake),numel(slip),numel(U3)]>1)  warning('Cannot make plot with fault geometry parameters other than scalars.')  plotflag = 0;end% Defines dislocation in the fault plane systemU1 = cos(rake).*slip;U2 = sin(rake).*slip;% Converts fault coordinates (E,N,DEPTH) relative to centroid% into Okada's reference system (X,Y,D)d = depth + sin(dip).*W/2;  % d is fault's top edgeec = e + cos(strike).*cos(dip).*W/2;nc = n - sin(strike).*cos(dip).*W/2;x = cos(strike).*nc + sin(strike).*ec + L/2;y = sin(strike).*nc - cos(strike).*ec + cos(dip).*W;% Variable substitution (independent from xi and eta)p = y.*cos(dip) + d.*sin(dip);q = y.*sin(dip) - d.*cos(dip);% Displacementsif any(nargout==[3, 5, 7, 9])  ux = -U1/(2*pi) .* chinnery(@ux_ss,x,p,L,W,q,dip,nu) ... % strike-slip    - U2/(2*pi) .* chinnery(@ux_ds,x,p,L,W,q,dip,nu) ... % dip-slip    + U3/(2*pi) .* chinnery(@ux_tf,x,p,L,W,q,dip,nu); ... % tensile fault  uy = -U1/(2*pi) .* chinnery(@uy_ss,x,p,L,W,q,dip,nu) ... % strike-slip    - U2/(2*pi) .* chinnery(@uy_ds,x,p,L,W,q,dip,nu) ... % dip-slip    + U3/(2*pi) .* chinnery(@uy_tf,x,p,L,W,q,dip,nu); ... % tensile fault  uz = -U1/(2*pi) .* chinnery(@uz_ss,x,p,L,W,q,dip,nu) ... % strike-slip    - U2/(2*pi) .* chinnery(@uz_ds,x,p,L,W,q,dip,nu) ... % dip-slip    + U3/(2*pi) .* chinnery(@uz_tf,x,p,L,W,q,dip,nu); ... % tensile fault  % Rotation from Okada's axes to geographic  ue = sin(strike).*ux - cos(strike).*uy;  un = cos(strike).*ux + sin(strike).*uy;end% Tiltif any(nargout==[2, 5, 6, 9])  uzx = -U1/(2*pi) .* chinnery(@uzx_ss,x,p,L,W,q,dip,nu) ... % strike-slip     - U2/(2*pi) .* chinnery(@uzx_ds,x,p,L,W,q,dip,nu) ... % dip-slip     + U3/(2*pi) .* chinnery(@uzx_tf,x,p,L,W,q,dip,nu); ... % tensile fault  uzy = -U1/(2*pi) .* chinnery(@uzy_ss,x,p,L,W,q,dip,nu) ... % strike-slip     - U2/(2*pi) .* chinnery(@uzy_ds,x,p,L,W,q,dip,nu) ... % dip-slip     + U3/(2*pi) .* chinnery(@uzy_tf,x,p,L,W,q,dip,nu); ... % tensile fault  % Rotation from Okada's axes to geographic  uze = -sin(strike).*uzx + cos(strike).*uzy;  uzn = -cos(strike).*uzx - sin(strike).*uzy;end% Strainif any(nargout==[4, 6, 7, 9])  uxx = -U1/(2*pi) .* chinnery(@uxx_ss,x,p,L,W,q,dip,nu) ... % strike-slip     - U2/(2*pi) .* chinnery(@uxx_ds,x,p,L,W,q,dip,nu) ... % dip-slip     + U3/(2*pi) .* chinnery(@uxx_tf,x,p,L,W,q,dip,nu); ... % tensile fault  uxy = -U1/(2*pi) .* chinnery(@uxy_ss,x,p,L,W,q,dip,nu) ... % strike-slip     - U2/(2*pi) .* chinnery(@uxy_ds,x,p,L,W,q,dip,nu) ... % dip-slip     + U3/(2*pi) .* chinnery(@uxy_tf,x,p,L,W,q,dip,nu); ... % tensile fault  uyx = -U1/(2*pi) .* chinnery(@uyx_ss,x,p,L,W,q,dip,nu) ... % strike-slip     - U2/(2*pi) .* chinnery(@uyx_ds,x,p,L,W,q,dip,nu) ... % dip-slip    + U3/(2*pi) .* chinnery(@uyx_tf,x,p,L,W,q,dip,nu); ... % tensile fault  uyy = -U1/(2*pi) .* chinnery(@uyy_ss,x,p,L,W,q,dip,nu) ... % strike-slip     - U2/(2*pi) .* chinnery(@uyy_ds,x,p,L,W,q,dip,nu) ... % dip-slip     + U3/(2*pi) .* chinnery(@uyy_tf,x,p,L,W,q,dip,nu); ... % tensile fault  % Rotation from Okada's axes to geographic  unn = cos(strike).^2*uxx + sin(2*strike).*(uxy + uyx)/2 + sin(strike).^2.*uyy;  une = sin(2*strike).*(uxx - uyy)/2 + sin(strike).^2.*uyx - cos(strike).^2.*uxy;  uen = sin(2*strike).*(uxx - uyy)/2 - cos(strike).^2.*uyx + sin(strike).^2.*uxy;  uee = sin(strike).^2*uxx - sin(2*strike).*(uyx + uxy)/2 + cos(strike).^2.*uyy;end% Assigns output argumentsswitch nargout  case 2    varargout = {uze, uzn};  case 3    varargout = {ue, un, uz};  case 4    varargout = {unn, une, uen, uee};  case 5    varargout = {ue, un, uz, uze, uzn};  case 6    varargout = {uze, ezn, unn, une, uen, uee};  case 7    varargout = {ue, un, uz, unn, une, uen, uee};  case 9    varargout = {ue, un, uz, uze, uzn, unn, une, uen, uee};  case 0    plotflag = 1;  otherwise    disp('Unvalid number of output arguments.')end% no output argument: plots geometry of the fault and dislocationif plotflag  figure  plot(e,n,'.r','MarkerSize',.1)  alpha = pi/2 - strike;  x_fault = L/2*cos(alpha)*[-1,1,1,-1] + sin(alpha)*cos(dip)*W/2*[-1,-1,1,1];  y_fault = L/2*sin(alpha)*[-1,1,1,-1] + cos(alpha)*cos(dip)*W/2*[1,1,-1,-1];  z_fault = -d + sin(dip)*W*[1,1,0,0];  ddx = U1*cos(alpha) - U2*sin(alpha)*cos(dip) + U3*sin(alpha)*sin(dip);  ddy = U1*sin(alpha) + U2*cos(alpha)*cos(dip) - U3*cos(alpha)*sin(dip);  ddz = U2*sin(dip) + U3*cos(dip);  patch(x_fault,y_fault,z_fault,.3*[1,1,1],'EdgeColor','k','LineWidth',2)  patch(x_fault+ddx/2,y_fault+ddy/2,z_fault+ddz/2,.6*[1,1,1], ...    'EdgeColor','k','LineWidth',1,'FaceAlpha',.5)  patch(x_fault-ddx/2,y_fault-ddy/2,z_fault-ddz/2,.6*[1,1,1], ...    'EdgeColor','k','LineWidth',1,'FaceAlpha',.5)  xlabel('East'); ylabel('North'); zlabel('Vertical')  view(3); grid on; axis equal; rotate3dend%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Notes for I... and K... subfunctions:%%  1. original formulas use Lame's parameters as mu/(mu+lambda) which%     depends only on the Poisson's ratio = 1 - 2*nu%  2. tests for cos(dip) == 0 are made with "cos(dip) > eps" %     because cos(90*pi/180) is not zero but = 6.1232e-17 (!)%     NOTE: don't use cosd and sind because of incompatibility%     with Matlab v6 and earlier...% =================================================================% Chinnery's notation [equation (24) p. 1143]% -----------------------------------------------------------------function u=chinnery(f,x,p,L,W,q,dip,nu)u = feval(f,x,p,q,dip,nu) ...  - feval(f,x,p-W,q,dip,nu) ...  - feval(f,x-L,p,q,dip,nu) ...  + feval(f,x-L,p-W,q,dip,nu);% =================================================================% Displacement subfunctions% strike-slip displacement subfunctions [equation (25) p. 1144]% -----------------------------------------------------------------function u=ux_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = xi.*q./(R.*(R + eta)) ...  + I1(xi,eta,q,dip,nu,R).*sin(dip);k = find(q~=0);u(k) = u(k) + atan(xi(k).*eta(k)./(q(k).*R(k)));% -----------------------------------------------------------------function u=uy_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = (eta.*cos(dip) + q.*sin(dip)).*q./(R.*(R + eta)) ...  + q.*cos(dip)./(R + eta) ...  + I2(eta,q,dip,nu,R).*sin(dip);% -----------------------------------------------------------------function u=uz_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);u = (eta.*sin(dip) - q.*cos(dip)).*q./(R.*(R + eta)) ...  + q.*sin(dip)./(R + eta) ...  + I4(db,eta,q,dip,nu,R).*sin(dip);% dip-slip displacement subfunctions [equation (26) p. 1144]% -----------------------------------------------------------------function u=ux_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = q./R ...  - I3(eta,q,dip,nu,R).*sin(dip).*cos(dip);% -----------------------------------------------------------------function u=uy_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = (eta.*cos(dip) + q.*sin(dip)).*q./(R.*(R + xi)) ...  - I1(xi,eta,q,dip,nu,R).*sin(dip).*cos(dip);k = find(q~=0);u(k) = u(k) + cos(dip).*atan(xi(k).*eta(k)./(q(k).*R(k)));% -----------------------------------------------------------------function u=uz_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);u = db.*q./(R.*(R + xi)) ...  - I5(xi,eta,q,dip,nu,R,db).*sin(dip).*cos(dip);k = find(q~=0);u(k) = u(k) + sin(dip).*atan(xi(k).*eta(k)./(q(k).*R(k)));% tensile fault displacement subfunctions [equation (27) p. 1144]% -----------------------------------------------------------------function u=ux_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = q.^2 ./(R.*(R + eta)) ...  - I3(eta,q,dip,nu,R).*sin(dip).^2;% -----------------------------------------------------------------function u=uy_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = -(eta.*sin(dip) - q.*cos(dip)).*q./(R.*(R + xi)) ...  - sin(dip).*xi.*q./(R.*(R + eta)) ...  - I1(xi,eta,q,dip,nu,R).*sin(dip).^2;k = find(q~=0);u(k) = u(k) + sin(dip).*atan(xi(k).*eta(k)./(q(k).*R(k)));% -----------------------------------------------------------------function u=uz_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);u = (eta.*cos(dip) + q.*sin(dip)).*q./(R.*(R + xi)) ...  + cos(dip).*xi.*q./(R.*(R + eta)) ...  - I5(xi,eta,q,dip,nu,R,db).*sin(dip).^2;k = find(q~=0);u(k) = u(k) - cos(dip).*atan(xi(k).*eta(k)./(q(k).*R(k)));% I... displacement subfunctions [equations (28) (29) p. 1144-1145]% -----------------------------------------------------------------function I=I1(xi,eta,q,dip,nu,R)db = eta.*sin(dip) - q.*cos(dip);if cos(dip) > eps  I = (1 - 2*nu) * (-xi./(cos(dip).*(R + db))) ...    - sin(dip)./cos(dip).*I5(xi,eta,q,dip,nu,R,db);else  I = -(1 - 2*nu)/2 * xi.*q./(R + db).^2;end% -----------------------------------------------------------------function I=I2(eta,q,dip,nu,R)I = (1 - 2*nu) * (-log(R + eta)) - I3(eta,q,dip,nu,R);% -----------------------------------------------------------------function I=I3(eta,q,dip,nu,R)yb = eta.*cos(dip) + q.*sin(dip);db = eta.*sin(dip) - q.*cos(dip);if cos(dip) > eps  I = (1 - 2*nu) * (yb./(cos(dip)*(R + db)) - log(R + eta)) ...    + sin(dip)./cos(dip) * I4(db,eta,q,dip,nu,R);else  I = (1 - 2*nu)/2 * (eta./(R + db) + yb.*q./(R + db).^2 - log(R + eta));end% -----------------------------------------------------------------function I=I4(db,eta,q,dip,nu,R)if cos(dip) > eps  I = (1 - 2*nu) * 1./cos(dip) * (log(R + db) - sin(dip).*log(R + eta));else  I = -(1 - 2*nu) * q./(R + db);end% -----------------------------------------------------------------function I=I5(xi,eta,q,dip,nu,R,db)X = sqrt(xi.^2 + q.^2);if cos(dip) > eps  I = (1 - 2*nu) * 2./cos(dip) ...    .* atan((eta.*(X + q.*cos(dip)) + X.*(R + X).*sin(dip)) ...      ./(xi.*(R + X).*cos(dip)));  I(xi==0) = 0;else  I = -(1 - 2*nu) * xi.*sin(dip)./(R + db);end% =================================================================% Tilt subfunctions% strike-slip tilt subfunctions [equation (37) p. 1147]% -----------------------------------------------------------------function u=uzx_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = -xi.*q.^2.*A(eta,R).*cos(dip) ...  + ((xi.*q)./R.^3 - K1(xi,eta,q,dip,nu,R)).*sin(dip);% -----------------------------------------------------------------function u=uzy_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);yb = eta.*cos(dip) + q.*sin(dip);u = (db.*q./R.^3).*cos(dip) ...  + (xi.^2.*q.*A(eta,R).*cos(dip) - sin(dip)./R + yb.*q./R.^3 ...    - K2(xi,eta,q,dip,nu,R)).*sin(dip);% dip-slip tilt subfunctions [equation (38) p. 1147]% -----------------------------------------------------------------function u=uzx_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);u = db.*q./R.^3 ...  + q.*sin(dip)./(R.*(R + eta)) ...  + K3(xi,eta,q,dip,nu,R).*sin(dip).*cos(dip);% -----------------------------------------------------------------function u=uzy_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);yb = eta.*cos(dip) + q.*sin(dip);u = yb.*db.*q.*A(xi,R) ...  - (2*db./(R.*(R + xi)) + xi.*sin(dip)./(R.*(R + eta))).*sin(dip) ...  + K1(xi,eta,q,dip,nu,R).*sin(dip).*cos(dip);% tensile fault tilt subfunctions [equation (39) p. 1147]% -----------------------------------------------------------------function u=uzx_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = q.^2./R.^3.*sin(dip) ...  - q.^3.*A(eta,R).*cos(dip) ...  + K3(xi,eta,q,dip,nu,R).*sin(dip).^2;% -----------------------------------------------------------------function u=uzy_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);yb = eta.*cos(dip) + q.*sin(dip);u = (yb.*sin(dip) + db.*cos(dip)).*q.^2.*A(xi,R) ...  + xi.*q.^2.*A(eta,R).*sin(dip).*cos(dip) ...  - (2*q./(R.*(R + xi)) - K1(xi,eta,q,dip,nu,R)).*sin(dip).^2;% -----------------------------------------------------------------function a=A(x,R)a = (2*R + x)./(R.^3.*(R + x).^2);% K... tilt subfunctions [equations (40) (41) p. 1148]% -----------------------------------------------------------------function K=K1(xi,eta,q,dip,nu,R)db = eta.*sin(dip) - q.*cos(dip);if cos(dip) > eps  K = (1 - 2*nu) * xi./cos(dip) .* (1./(R.*(R + db)) - sin(dip)./(R.*(R + eta)));else  K = (1 - 2*nu) * xi.*q./(R.*(R + db).^2);end% -----------------------------------------------------------------function K=K2(xi,eta,q,dip,nu,R)K = (1 - 2*nu) * (-sin(dip)./R + q.*cos(dip)./(R.*(R + eta))) ...  - K3(xi,eta,q,dip,nu,R);% -----------------------------------------------------------------function K=K3(xi,eta,q,dip,nu,R)db = eta.*sin(dip) - q.*cos(dip);yb = eta.*cos(dip) + q.*sin(dip);if cos(dip) > eps  K = (1 - 2*nu) * 1./cos(dip) .* (q./(R.*(R + eta)) - yb./(R.*(R + db)));else  K = (1 - 2*nu) * sin(dip)./(R + db) .* (xi.^2./(R.*(R + db)) - 1);end% =================================================================% Strain subfunctions% strike-slip strain subfunctions [equation (31) p. 1145]% -----------------------------------------------------------------function u=uxx_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = xi.^2.*q.*A(eta,R) ...  - J1(xi,eta,q,dip,nu,R).*sin(dip);% -----------------------------------------------------------------function u=uxy_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);u = xi.^3.*db./(R.^3.*(eta.^2 + q.^2)) ...  - (xi.^3.*A(eta,R) + J2(xi,eta,q,dip,nu,R)).*sin(dip);% -----------------------------------------------------------------function u=uyx_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = xi.*q./R.^3.*cos(dip) ...  + (xi.*q.^2.*A(eta,R) - J2(xi,eta,q,dip,nu,R)).*sin(dip);% -----------------------------------------------------------------function u=uyy_ss(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);yb = eta.*cos(dip) + q.*sin(dip);u = yb.*q./R.^3.*cos(dip) ...  + (q.^3.*A(eta,R).*sin(dip) - 2*q.*sin(dip)./(R.*(R + eta)) ...    - (xi.^2 + eta.^2)./R.^3.*cos(dip) - J4(xi,eta,q,dip,nu,R)).*sin(dip);  % dip-slip strain subfunctions [equation (32) p. 1146]% -----------------------------------------------------------------function u=uxx_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = xi.*q./R.^3 ...  + J3(xi,eta,q,dip,nu,R).*sin(dip).*cos(dip);% -----------------------------------------------------------------function u=uxy_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);yb = eta.*cos(dip) + q.*sin(dip);u = yb.*q./R.^3 ...  - sin(dip)./R ...  + J1(xi,eta,q,dip,nu,R).*sin(dip).*cos(dip);% -----------------------------------------------------------------function u=uyx_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);yb = eta.*cos(dip) + q.*sin(dip);u = yb.*q./R.^3 ...  + q.*cos(dip)./(R.*(R + eta)) ...  + J1(xi,eta,q,dip,nu,R).*sin(dip).*cos(dip);% -----------------------------------------------------------------function u=uyy_ds(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);yb = eta.*cos(dip) + q.*sin(dip);u = yb.^2.*q.*A(xi,R) ...  - (2*yb./(R.*(R + xi)) + xi.*cos(dip)./(R.*(R + eta))).*sin(dip) ...  + J2(xi,eta,q,dip,nu,R).*sin(dip).*cos(dip);% tensile fault strain subfunctions [equation (33) p. 1146]% -----------------------------------------------------------------function u=uxx_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = xi.*q.^2.*A(eta,R) ...  + J3(xi,eta,q,dip,nu,R).*sin(dip).^2;% -----------------------------------------------------------------function u=uxy_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);u = -db.*q./R.^3 ...  - xi.^2.*q.*A(eta,R).*sin(dip) ...  + J1(xi,eta,q,dip,nu,R).*sin(dip).^2;% -----------------------------------------------------------------function u=uyx_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);u = q.^2./R.^3.*cos(dip) ...  + q.^3.*A(eta,R).*sin(dip) ...  + J1(xi,eta,q,dip,nu,R).*sin(dip).^2;% -----------------------------------------------------------------function u=uyy_tf(xi,eta,q,dip,nu)R = sqrt(xi.^2 + eta.^2 + q.^2);db = eta.*sin(dip) - q.*cos(dip);yb = eta.*cos(dip) + q.*sin(dip);u = (yb.*cos(dip) - db.*sin(dip)).*q.^2.*A(xi,R) ...  - q.*sin(2*dip)./(R.*(R + xi)) ...  - (xi.*q.^2.*A(eta,R) - J2(xi,eta,q,dip,nu,R)).*sin(dip).^2;% J... tensile fault subfunctions [equations (34) (35) p. 1146-1147]% -----------------------------------------------------------------function J=J1(xi,eta,q,dip,nu,R)db = eta.*sin(dip) - q.*cos(dip);if cos(dip) > eps  J = (1 - 2*nu) * 1./cos(dip) * (xi.^2./(R.*(R + db).^2) - 1./(R + db)) ...    - sin(dip)./cos(dip)*K3(xi,eta,q,dip,nu,R);else  J = (1 - 2*nu)/2 * q./(R + db).^2 .* (2*xi.^2./(R.*(R + db)) - 1);end% -----------------------------------------------------------------function J=J2(xi,eta,q,dip,nu,R)db = eta.*sin(dip) - q.*cos(dip);yb = eta.*cos(dip) + q.*sin(dip);if cos(dip) > eps  J = (1 - 2*nu) * 1./cos(dip) * xi.*yb./(R.*(R + db).^2) ...    - sin(dip)./cos(dip)*K1(xi,eta,q,dip,nu,R);else  J = (1 - 2*nu)/2 * xi.*sin(dip)./(R + db).^2 .* (2*q.^2./(R.*(R + db)) - 1);end% -----------------------------------------------------------------function J=J3(xi,eta,q,dip,nu,R)J = (1 - 2*nu) * -xi./(R.*(R + eta)) ...  - J2(xi,eta,q,dip,nu,R);% -----------------------------------------------------------------function J=J4(xi,eta,q,dip,nu,R)J = (1 - 2*nu) * (-cos(dip)./R - q.*sin(dip)./(R.*(R + eta))) ...  - J1(xi,eta,q,dip,nu,R);