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3Dseismic_pml.m
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%PML based on the paper 弹性波正演模拟中pml吸收边界条件的改进（秦臻 et al., 2009）
clear;
close all;
clc;
%***********************************************************************
% fundamental parameters 基本参数
%***********************************************************************
rho_0=1000; % density=1000 kg/m^3
Vc_0=1000; Vs_0=1000; % Scaling factor, compressional velocity Vp=1000 m/s, shear velocity Vs=1000 m/s
freq=200; % (central frequency in Hz) 中心频率Hz
npml=10; % Number of pml layers
dt=1.0*1.0e-5;
time_window=0.02;
nt=round(time_window/dt); %计算时间迭代次数
%uniform surrounding rock
param=[ 4 4 4 4 4 %density rho_r
0 0 0 0 0 %电导率sigma or pi/(Q*eta) 都设为0.
3.4 3.4 3.4 3.4 3.4 %Vc_r
2 2 2 2 2]; %Vs_r
m=3; R=1.0*1.0e-5; %pml parameters
%***********************************************************************
% mesh parameters 网格参数
%***********************************************************************
domain_x=100; %网格的总尺寸in m
domain_y=100;
domain_z=100;
dx=0.5;
dy=dx;dz=dx;
nx=round(domain_x/dx); %横向的网格数目
ny=round(domain_y/dx); %竖向的网格数目
nz=round(domain_z/dz); %纵向的网格数目
nx=nx+2*npml;
ny=ny+2*npml;
nz=nz+2*npml;
fsx=nx/2; fsy=ny/2; fsz=nz/2; %发射点位置 按nx*ny*nz矩阵定义
%***********************************************************************
%激励源
%***********************************************************************
source=zeros(1,nt); %雷克子波
for i=1:nt
A=1;t=i*dt-1/freq;
source(i)=A*(1-2*(pi*freq*t)^2)*exp(-(pi*freq*t)^2);
end
% figure(1);
% plot(source);
% getframe(gca);
% ***********************************************************************
% 介质参数
% ***********************************************************************
index=ones(nx,ny,nz);
param1=reshape(param(1,index),size(index));
param2=reshape(param(2,index),size(index));
param3=reshape(param(3,index),size(index));
param4=reshape(param(4,index),size(index));
%***********************************************************************
%初始化
%***********************************************************************
Vx =zeros(nx+1,ny,nz); Vy =zeros(nx,ny+1,nz); Vz =zeros(nx,ny,nz+1);
Txy =zeros(nx+1,ny+1,nz); Tyz =zeros(nx,ny+1,nz+1); Txz =zeros(nx+1,ny,nz+1);
Txx =zeros(nx,ny,nz); Tyy =zeros(nx,ny,nz); Tzz =zeros(nx,ny,nz);
% PML-related Paremeters and Variables
MP_Vx_xa=zeros(2*npml,ny,nz); MP_Vx_xb=zeros(2*npml,ny,nz);
MP_Vx_ya=zeros(nx+1,2*npml,nz); MP_Vx_yb=zeros(nx+1,2*npml,nz);
MP_Vx_za=zeros(nx+1,ny,2*npml); MP_Vx_zb=zeros(nx+1,ny,2*npml);
MP_Vy_xa=zeros(2*npml,ny+1,nz); MP_Vy_xb=zeros(2*npml,ny+1,nz);
MP_Vy_ya=zeros(nx,2*npml,nz); MP_Vy_yb=zeros(nx,2*npml,nz);
MP_Vy_za=zeros(nx,ny+1,2*npml); MP_Vy_zb=zeros(nx,ny+1,2*npml);
MP_Vz_xa=zeros(2*npml,ny,nz+1); MP_Vz_xb=zeros(2*npml,ny,nz+1);
MP_Vz_ya=zeros(nx,2*npml,nz+1); MP_Vz_yb=zeros(nx,2*npml,nz+1);
MP_Vz_za=zeros(nx,ny,2*npml); MP_Vz_zb=zeros(nx,ny,2*npml);
MP_Txy_xa=zeros(2*npml,ny+1,nz); MP_Txy_xb=zeros(2*npml,ny+1,nz);
MP_Txy_ya=zeros(nx+1,2*npml,nz); MP_Txy_yb=zeros(nx+1,2*npml,nz);
MP_Txy_za=zeros(nx+1,ny+1,2*npml); MP_Txy_zb=zeros(nx+1,ny+1,2*npml);
MP_Tyz_xa=zeros(2*npml,ny+1,nz+1); MP_Tyz_xb=zeros(2*npml,ny+1,nz+1);
MP_Tyz_ya=zeros(nx,2*npml,nz+1); MP_Tyz_yb=zeros(nx,2*npml,nz+1);
MP_Tyz_za=zeros(nx,ny+1,2*npml); MP_Tyz_zb=zeros(nx,ny+1,2*npml);
MP_Txz_xa=zeros(2*npml,ny,nz+1); MP_Txz_xb=zeros(2*npml,ny,nz+1);
MP_Txz_ya=zeros(nx+1,2*npml,nz+1); MP_Txz_yb=zeros(nx+1,2*npml,nz+1);
MP_Trz_za=zeros(nx+1,ny,2*npml); MP_Trz_zb=zeros(nx+1,ny,2*npml);
MP_Txx_xa=zeros(2*npml,ny,nz); MP_Txx_xb=zeros(2*npml,ny,nz);
MP_Txx_ya=zeros(nx,2*npml,nz); MP_Txx_yb=zeros(nx,2*npml,nz);
MP_Txx_za=zeros(nx,ny,2*npml); MP_Txx_zb=zeros(nx,ny,2*npml);
MP_Tyy_xa=zeros(2*npml,ny,nz); MP_Tyy_xb=zeros(2*npml,ny,nz);
MP_Tyy_ya=zeros(nx,2*npml,nz); MP_Tyy_yb=zeros(nx,2*npml,nz);
MP_Tyy_za=zeros(nx,ny,2*npml); MP_Tyy_zb=zeros(nx,ny,2*npml);
MP_Tzz_xa=zeros(2*npml,ny,nz); MP_Tzz_xb=zeros(2*npml,ny,nz);
MP_Tzz_ya=zeros(nx,2*npml,nz); MP_Tzz_yb=zeros(nx,2*npml,nz);
MP_Tzz_za=zeros(nx,ny,2*npml); MP_Tzz_zb=zeros(nx,ny,2*npml);
% Update Variables in PML
UV_Txy_x =zeros(2*npml,ny+1,nz); UV_Txy_y =zeros(nx+1,2*npml,nz); UV_Txy_z =zeros(nx+1,ny+1,2*npml);
UV_Tyz_x =zeros(2*npml,ny+1,nz+1); UV_Tyz_y =zeros(nx,2*npml,nz+1); UV_Tyz_z =zeros(nx,ny+1,2*npml);
UV_Txz_x =zeros(2*npml,ny,nz+1); UV_Txz_y =zeros(nx+1,2*npml,nz+1); UV_Txz_z =zeros(nx+1,ny,2*npml);
UV_Txx_x =zeros(2*npml,ny,nz); UV_Txx_y =zeros(nx,2*npml,nz); UV_Txx_z =zeros(nx,ny,2*npml);
UV_Tyy_x =zeros(2*npml,ny,nz); UV_Tyy_y =zeros(nx,2*npml,nz); UV_Tyy_z =zeros(nx,ny,2*npml);
UV_Tzz_x =zeros(2*npml,ny,nz); UV_Tzz_y =zeros(nx,2*npml,nz); UV_Tzz_z =zeros(nx,ny,2*npml);
UV_Vx_x =zeros(2*npml,ny,nz); UV_Vx_y =zeros(nx+1,2*npml,nz); UV_Vx_z =zeros(nx+1,ny,2*npml);
UV_Vy_x =zeros(2*npml,ny+1,nz); UV_Vy_y =zeros(nx,2*npml,nz); UV_Vy_z =zeros(nx,ny+1,2*npml);
UV_Vz_x =zeros(2*npml,ny,nz+1); UV_Vz_y =zeros(nx,2*npml,nz+1); UV_Vz_z =zeros(nx,ny,2*npml);
tic
%***********************************************************************
%计算中间矩阵
%***********************************************************************
disp('Computing middle paramters for ...');
disp('Vx');
rho_r=zeros(nx+1,ny,nz); Vc_r=zeros(nx+1,ny,nz);
rho_r(1:nx,:,:)=param1; rho_r(nx+1,:,:)=param1(end,:,:);
Vc_r(1:nx,:,:)=param3; Vc_r(nx+1,:,:)=param3(end,:,:);
rho=rho_r.*rho_0; Vc=Vc_r.*Vc_0;
MP_Vx = dt./rho;
%PML
sig_max=-3*log(R)./(2*npml*dx).*Vc([1:npml nx-npml+2:nx+1],:,:);%sigma_x_max
sigx=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[2*npml,1,1]),[1,ny,nz]);%sigma_x
MP_Vx_xb=exp(-sigx.*dt);
MP_Vx_xa=1-MP_Vx_xb;
sig_max=-3*log(R)./(2*npml*dy).*Vc(:,[1:npml ny-npml+1:ny],:);
sigy=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,2*npml,1]),[nx+1,1,nz]);
MP_Vx_yb=exp(-sigy.*dt);
MP_Vx_ya=1-MP_Vx_yb;
sig_max=-3*log(R)./(2*npml*dz).*Vc(:,:,[1:npml nz-npml+1:nz]);
sigz=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,1,2*npml]),[nx+1,ny,1]);
MP_Vx_zb=exp(-sigz.*dt);
MP_Vx_za=1-MP_Vx_zb;
clear sig_max sigx sigy sigz
disp('Vy');
rho_r=zeros(nx,ny+1,nz); Vc_r=zeros(nx,ny+1,nz);
rho_r(:,1:ny,:)=param1; rho_r(:,ny+1,:)=param1(:,end,:);
Vc_r(:,1:ny,:)=param3; Vc_r(:,ny+1,:)=param3(:,end,:);
rho=rho_r.*rho_0; Vc=Vc_r.*Vc_0;
MP_Vy = dt./rho;
%PML
sig_max=-3*log(R)./(2*npml*dx).*Vc([1:npml nx-npml+1:nx],:,:);
sigx=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[2*npml,1,1]),[1,ny+1,nz]);
MP_Vy_xb=exp(-sigx.*dt);
MP_Vy_xa=1-MP_Vy_xb;
sig_max=-3*log(R)./(2*npml*dy).*Vc(:,[1:npml ny-npml+2:ny+1],:);
sigy=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,2*npml,1]),[nx,1,nz]);
MP_Vy_yb=exp(-sigy.*dt);
MP_Vy_ya=1-MP_Vy_yb;
sig_max=-3*log(R)./(2*npml*dz).*Vc(:,:,[1:npml nz-npml+1:nz]);
sigz=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,1,2*npml]),[nx,ny+1,1]);
MP_Vy_zb=exp(-sigz.*dt);
MP_Vy_za=1-MP_Vy_zb;
clear sig_max sigx sigy sigz
disp('Vz');
rho_r=zeros(nx,ny,nz+1); Vc_r=zeros(nx,ny,nz+1);
rho_r(:,:,1:nz)=param1; rho_r(:,:,nz+1)=param1(:,:,end);
Vc_r(:,:,1:nz)=param3; Vc_r(:,:,nz+1)=param3(:,:,end);
rho=rho_r.*rho_0; Vc=Vc_r.*Vc_0;
MP_Vz = dt./rho;
%PML
sig_max=-3*log(R)./(2*npml*dx).*Vc([1:npml nx-npml+1:nx],:,:);
sigx=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[2*npml,1,1]),[1,ny,nz+1]);
MP_Vz_xb=exp(-sigx.*dt);
MP_Vz_xa=1-MP_Vz_xb;
sig_max=-3*log(R)./(2*npml*dy).*Vc(:,[1:npml ny-npml+1:ny],:);
sigy=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,2*npml,1]),[nx,1,nz+1]);
MP_Vz_yb=exp(-sigy.*dt);
MP_Vz_ya=1-MP_Vz_yb;
sig_max=-3*log(R)./(2*npml*dz).*Vc(:,:,[1:npml nz-npml+2:nz+1]);
sigz=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[1,1,2*npml]),[nx,ny,1]);
MP_Vz_zb=exp(-sigz.*dt);
MP_Vz_za=1-MP_Vz_zb;
clear sig_max sigx sigy sigz
disp('Txy');
rho_r=zeros(nx+1,ny+1,nz);
% sig= zeros(nx+1,ny+1,nz);
Vc_r=zeros(nx+1,ny+1,nz);
Vs_r=zeros(nx+1,ny+1,nz);
rho_r(1:nx,1:ny,:)=param1; rho_r(nx+1,1:ny,:)=param1(end,:,:);rho_r(:,ny+1,:)=rho_r(:,ny,:);
Vc_r(1:nx,1:ny,:)=param3; Vc_r(nx+1,1:ny,:)=param3(end,:,:); Vc_r(:,ny+1,:)=Vc_r(:,ny,:);
Vs_r(1:nx,1:ny,:)=param4; Vs_r(nx+1,1:ny,:)=param4(end,:,:); Vs_r(:,ny+1,:)=Vs_r(:,ny,:);
rho=rho_r.*rho_0; Vc=Vc_r.*Vc_0; Vs=Vs_r.*Vs_0;
MP_Txy=Vs.^2.*rho.*dt; %mu*dt
%PML
sig_max=-3*log(R)./(2*npml*dx).*Vc([1:npml nx-npml+2:nx+1],:,:);
sigx=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[2*npml,1,1]),[1,ny+1,nz]);
MP_Txy_xb=exp(-sigx.*dt);
MP_Txy_xa=1-MP_Txy_xb;
sig_max=-3*log(R)./(2*npml*dy).*Vc(:,[1:npml ny-npml+2:ny+1],:);
sigy=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[1,2*npml,1]),[nx+1,1,nz]);
MP_Txy_yb=exp(-sigy.*dt);
MP_Txy_ya=1-MP_Txy_yb;
sig_max=-3*log(R)./(2*npml*dz).*Vc(:,:,[1:npml nz-npml+1:nz]);
sigz=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,1,2*npml]),[nx+1,ny+1,1]);
MP_Txy_zb=exp(-sigz.*dt);
MP_Txy_za=1-MP_Txy_zb;
clear rho_r sig Vs_r Vc_r rho Vs Vc sig_max sigx sigy sigz
disp('Tyz');
rho_r = zeros(nx,ny+1,nz+1);
%sig = zeros(nx,ny+1,nz+1);
Vc_r = zeros(nx,ny+1,nz+1);
Vs_r = zeros(nx,ny+1,nz+1);
rho_r(:,1:ny,1:nz)=param1; rho_r(:,1:ny,nz+1)=param1(:,:,end); rho_r(:,ny+1,:)=rho_r(:,ny,:);
Vc_r(:,1:ny,1:nz)=param3; Vc_r(:,1:ny,nz+1)=param3(:,:,end); Vc_r(:,ny+1,:)=Vc_r(:,ny,:);
Vs_r(:,1:ny,1:nz)=param4; Vs_r(:,1:ny,nz+1)=param4(:,:,end); Vs_r(:,ny+1,:)=Vs_r(:,ny,:);
rho=rho_r.*rho_0; Vc=Vc_r.*Vc_0; Vs=Vs_r.*Vs_0;
MP_Tyz=Vs.^2.*rho.*dt;
sig_max=-3*log(R)./(2*npml*dx).*Vc([1:npml nx-npml+1:nx],:,:);
sigx=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[2*npml,1,1]),[1,ny+1,nz+1]);
MP_Tyz_xb=exp(-sigx.*dt);
MP_Tyz_xa=1-MP_Tyz_xb;
sig_max=-3*log(R)./(2*npml*dy).*Vc(:,[1:npml ny-npml+2:ny+1],:);
sigy=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[1,2*npml,1]),[nx,1,nz+1]);
MP_Tyz_yb=exp(-sigy.*dt);
MP_Tyz_ya=1-MP_Tyz_yb;
sig_max=-3*log(R)./(2*npml*dz).*Vc(:,:,[1:npml nz-npml+2:nz+1]);
sigz=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[1,1,2*npml]),[nx,ny+1,1]);
MP_Tyz_zb=exp(-sigz.*dt);
MP_Tyz_za=1-MP_Tyz_zb;
clear rho_r sig Vs_r Vc_r rho Vs Vc sig_max sigx sigy sigz
disp('Txz');
rho_r=zeros(nx+1,ny,nz+1);
% sig= zeros(nx+1,ny,nz+1);
Vc_r=zeros(nx+1,ny,nz+1);
Vs_r=zeros(nx+1,ny,nz+1);
rho_r(1:nx,:,1:nz)=param1; rho_r(1:nx,:,nz+1)=param1(:,:,end); rho_r(nx+1,:,:)=rho_r(nx,:,:);
Vc_r(1:nx,:,1:nz)=param3; Vc_r(1:nx,:,nz+1)=param3(:,:,end); Vc_r(nx+1,:,:)=Vc_r(nx,:,:);
Vs_r(1:nx,:,1:nz)=param4; Vs_r(1:nx,:,nz+1)=param4(:,:,end); Vs_r(nx+1,:,:)=Vs_r(nx,:,:);
rho=rho_r.*rho_0; Vc=Vc_r.*Vc_0; Vs=Vs_r.*Vs_0;
MP_Txz=Vs.^2.*rho.*dt;
%CPML
sig_max=-3*log(R)./(2*npml*dx).*Vc([1:npml nx-npml+2:nx+1],:,:);
sigx=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[2*npml,1,1]),[1,ny,nz+1]);
MP_Txz_xb=exp(-sigx.*dt);
MP_Txz_xa=1-MP_Txz_xb;
sig_max=-3*log(R)./(2*npml*dy).*Vc(:,[1:npml ny-npml+1:ny],:);
sigy=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[1,2*npml,1]),[nx+1,1,nz+1]);
MP_Txz_yb=exp(-sigy.*dt);
MP_Txz_ya=1-MP_Txz_yb;
sig_max=-3*log(R)./(2*npml*dz).*Vc(:,:,[1:npml nz-npml+2:nz+1]);
sigz=sig_max.*repmat(reshape((([npml:-1:1 1:npml])./npml).^m,[1,1,2*npml]),[nx+1,ny,1]);
MP_Txz_zb=exp(-sigz.*dt);
MP_Txz_za=1-MP_Txz_zb;
clear rho_r sig Vs_r Vc_r rho Vs Vc sigmax sigx sigy sigz
disp('Txx');
rho=param1.*rho_0;
Vc=param3.*Vc_0;
Vs=param4.*Vs_0;
MP_Txx1=Vc.^2.*rho.*dt; %lambda+2mu=rho*Vp^2
MP_Txx2=(Vc.^2-2*Vs.^2).*rho.*dt; %lambda=rho*(Vp^2-2*Vs^2)
disp('Tyy');
MP_Tyy1=Vc.^2.*rho.*dt; %lambda+2mu=rho*Vp^2
MP_Tyy2=(Vc.^2-2*Vs.^2).*rho.*dt; %lambda=rho*(Vp^2-2*Vs^2)
disp('Tzz');
MP_Tzz1=Vc.^2.*rho.*dt; %lambda+2mu=rho*Vp^2
MP_Tzz2=(Vc.^2-2*Vs.^2).*rho.*dt; %lambda=rho*(Vp^2-2*Vs^2)
%pml
sig_max=-3*log(R)./(2*npml*dx).*Vc([1:npml nx-npml+1:nx],:,:);
sigx=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[2*npml,1,1]),[1,ny,nz]);
MP_Txx_xb=exp(-sigx.*dt); MP_Txx_xa=1-MP_Txx_xb;
MP_Tyy_xb=exp(-sigx.*dt); MP_Tyy_xa=1-MP_Tyy_xb;
MP_Tzz_xb=exp(-sigx.*dt); MP_Tzz_xa=1-MP_Tzz_xb;
sig_max=-3*log(R)./(2*npml*dy).*Vc(:,[1:npml ny-npml+1:ny],:);
sigy=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,2*npml,1]),[nx,1,nz]);
MP_Txx_yb=exp(-sigy.*dt); MP_Txx_ya=1-MP_Txx_yb;
MP_Tyy_yb=exp(-sigy.*dt); MP_Tyy_ya=1-MP_Tyy_yb;
MP_Tzz_yb=exp(-sigy.*dt); MP_Tzz_ya=1-MP_Tzz_yb;
sig_max=-3*log(R)./(2*npml*dz).*Vc(:,:,[1:npml nz-npml+1:nz]);
sigz=sig_max.*repmat(reshape((([npml-0.5:-1:0.5 0.5:npml-0.5])./npml).^m,[1,1,2*npml]),[nx,ny,1]);
MP_Txx_zb=exp(-sigz.*dt); MP_Txx_za=1-MP_Txx_zb;
MP_Tyy_zb=exp(-sigz.*dt); MP_Tyy_za=1-MP_Tyy_zb;
MP_Tzz_zb=exp(-sigz.*dt); MP_Tzz_za=1-MP_Tzz_zb;
clear rho Vc Vs param1 param2 param3 param4 sigmax sigx sigy sigz
%***********************************************************************
%更新系数
%***********************************************************************
myavi=VideoWriter('3D_Elastic_waves.avi','Motion JPEG AVI');
myavi.FrameRate=5;
% myavi.Height=1024;
% myavi.Width=1920;
open(myavi);
for j=1:nt %Time iteration
disp([num2str(j) '/' num2str(nt)]);
Vx(fsx,fsy,fsz)=Vx(fsx,fsy,fsz) + source(j);
Vy(fsx,fsy,fsz)=Vy(fsx,fsy,fsz) + source(j);
Vz(fsx,fsy,fsz)=Vz(fsx,fsy,fsz) + source(j);
Txx=Txx + MP_Txx1.*( Vx(2:nx+1,:,:)-Vx(1:nx,:,:) )./dx ...
+ MP_Txx2.* ( (Vy(:,2:ny+1,:)-Vy(:,1:ny,:))./dy + (Vz(:,:,2:nz+1)-Vz(:,:,1:nz))./dz );
UV_Txx_x=MP_Txx_xb.*UV_Txx_x+MP_Txx_xa.*(Vx([2:npml+1 nx-npml+2:nx+1],:,:)-Vx([1:npml nx-npml+1:nx],:,:))./dx;
Txx([1:npml nx-npml+1:nx],:,:)=Txx([1:npml nx-npml+1:nx],:,:) - MP_Txx1([1:npml nx-npml+1:nx],:,:).*UV_Txx_x;
UV_Txx_y=MP_Txx_yb.*UV_Txx_y+MP_Txx_ya.*(Vy(:,[2:npml+1 ny-npml+2:ny+1],:)-Vy(:,[1:npml ny-npml+1:ny],:))./dy;
Txx(:,[1:npml ny-npml+1:ny],:)=Txx(:,[1:npml ny-npml+1:ny],:) - MP_Txx2(:,[1:npml ny-npml+1:ny],:).*UV_Txx_y;
UV_Txx_z=MP_Txx_zb.*UV_Txx_z+MP_Txx_za.*(Vz(:,:,[2:npml+1 nz-npml+2:nz+1])-Vz(:,:,[1:npml nz-npml+1:nz]))./dz;
Txx(:,:,[1:npml nz-npml+1:nz])=Txx(:,:,[1:npml nz-npml+1:nz]) - MP_Txx2(:,:,[1:npml nz-npml+1:nz]).*UV_Txx_z;
Tyy=Tyy + MP_Tyy1.*( Vy(:,2:ny+1,:)-Vy(:,1:ny,:) )./dy...
+ MP_Tyy2.* ( (Vx(2:nx+1,:,:)-Vx(1:nx,:,:))./dx + (Vz(:,:,2:nz+1)-Vz(:,:,1:nz))./dz );
UV_Tyy_x=MP_Tyy_xb.*UV_Tyy_x+MP_Tyy_xa.*(Vx([2:npml+1 nx-npml+2:nx+1],:,:)-Vx([1:npml nx-npml+1:nx],:,:))./dx;
Tyy([1:npml nx-npml+1:nx],:,:)=Tyy([1:npml nx-npml+1:nx],:,:) - MP_Tyy2([1:npml nx-npml+1:nx],:,:).*UV_Tyy_x;
UV_Tyy_y=MP_Tyy_yb.*UV_Tyy_y+MP_Tyy_ya.*(Vy(:,[2:npml+1 ny-npml+2:ny+1],:)-Vy(:,[1:npml ny-npml+1:ny],:))./dy;
Tyy(:,[1:npml ny-npml+1:ny],:)=Tyy(:,[1:npml ny-npml+1:ny],:) - MP_Tyy1(:,[1:npml ny-npml+1:ny],:).*UV_Tyy_y;
UV_Tyy_z=MP_Tyy_zb.*UV_Tyy_z+MP_Tyy_za.*(Vz(:,:,[2:npml+1 nz-npml+2:nz+1])-Vz(:,:,[1:npml nz-npml+1:nz]))./dz;
Tyy(:,:,[1:npml nz-npml+1:nz])=Tyy(:,:,[1:npml nz-npml+1:nz]) - MP_Tyy2(:,:,[1:npml nz-npml+1:nz]).*UV_Tyy_z;
Tzz=Tzz + MP_Tzz1.*( Vz(:,:,2:nz+1)-Vz(:,:,1:nz) )./dz...
+ MP_Tzz2.* ( (Vx(2:nx+1,:,:)-Vx(1:nx,:,:))./dx + (Vy(:,2:ny+1,:)-Vy(:,1:ny,:))./dy );
UV_Tzz_x=MP_Tzz_xb.*UV_Tzz_x+MP_Tzz_xa.*(Vx([2:npml+1 nx-npml+2:nx+1],:,:)-Vx([1:npml nx-npml+1:nx],:,:))./dx;
Tzz([1:npml nx-npml+1:nx],:,:)=Tzz([1:npml nx-npml+1:nx],:,:) - MP_Tzz2([1:npml nx-npml+1:nx],:,:).*UV_Tzz_x;
UV_Tzz_y=MP_Tzz_yb.*UV_Tzz_y+MP_Tzz_ya.*(Vy(:,[2:npml+1 ny-npml+2:ny+1],:)-Vy(:,[1:npml ny-npml+1:ny],:))./dy;
Tzz(:,[1:npml ny-npml+1:ny],:)=Tzz(:,[1:npml ny-npml+1:ny],:) - MP_Tzz2(:,[1:npml ny-npml+1:ny],:).*UV_Tzz_y;
UV_Tzz_z=MP_Tzz_zb.*UV_Tzz_z+MP_Tzz_za.*(Vz(:,:,[2:npml+1 nz-npml+2:nz+1])-Vz(:,:,[1:npml nz-npml+1:nz]))./dz;
Tzz(:,:,[1:npml nz-npml+1:nz])=Tzz(:,:,[1:npml nz-npml+1:nz]) - MP_Tzz1(:,:,[1:npml nz-npml+1:nz]).*UV_Tzz_z;
Txy(2:nx,2:ny,:)=Txy(2:nx,2:ny,:)+ MP_Txy(2:nx,2:ny,:).*( (Vx(2:nx,2:ny,:)-Vx(2:nx,1:ny-1,:))./dy + (Vy(2:nx,2:ny,:)-Vy(1:nx-1,2:ny,:))./dx );
UV_Txy_x=MP_Txy_xb.*UV_Txy_x+MP_Txy_xa.*(Vy([2:npml+1 nx-npml+1:nx],:,:)-Vy([1:npml nx-npml:nx-1],:,:))./dx;
Txy([2:npml+1 nx-npml+1:nx],:,:)=Txy([2:npml+1 nx-npml+1:nx],:,:) - MP_Txy([2:npml+1 nx-npml+1:nx],:,:).*UV_Txy_x;
UV_Txy_y=MP_Txy_yb.*UV_Txy_y+MP_Txy_ya.*(Vx(:,[2:npml+1 ny-npml+1:ny],:)-Vx(:,[1:npml ny-npml:ny-1],:))./dy;
Txy(:,[2:npml+1 ny-npml+1:ny],:)=Txy(:,[2:npml+1 ny-npml+1:ny],:) - MP_Txy(:,[2:npml+1 ny-npml+1:ny],:).*UV_Txy_y;
Txy([1 nx+1],2:ny,:)=Txy([2 nx],2:ny,:); Txy(:,[1 ny+1],:)=Txy(:,[2 ny],:);
Tyz(:,2:ny,2:nz)=Tyz(:,2:ny,2:nz)+ MP_Tyz(:,2:ny,2:nz).*( (Vy(:,2:ny,2:nz)-Vy(:,2:ny,1:nz-1))./dz + (Vz(:,2:ny,2:nz)-Vz(:,1:ny-1,2:nz))./dy );
UV_Tyz_y=MP_Tyz_yb.*UV_Tyz_y+MP_Tyz_ya.*(Vz(:,[2:npml+1 ny-npml+1:ny],:)-Vz(:,[1:npml ny-npml:ny-1],:))./dy;
Tyz(:,[2:npml+1 ny-npml+1:ny],:)=Tyz(:,[2:npml+1 ny-npml+1:ny],:) - MP_Tyz(:,[2:npml+1 ny-npml+1:ny],:).*UV_Tyz_y;
UV_Tyz_z=MP_Tyz_zb.*UV_Tyz_z+MP_Tyz_za.*(Vy(:,:,[2:npml+1 nz-npml+1:nz])-Vy(:,:,[1:npml nz-npml:nz-1]))./dz;
Tyz(:,:,[2:npml+1 nz-npml+1:nz])=Tyz(:,:,[2:npml+1 nz-npml+1:nz]) - MP_Tyz(:,:,[2:npml+1 nz-npml+1:nz]).*UV_Tyz_z;
Tyz(:,2:ny,[1 nz+1])=Tyz(:,2:ny,[2 nz]); Tyz(:,[1 ny+1],:)=Tyz(:,[2 ny],:);
Txz(2:nx,:,2:nz)=Txz(2:nx,:,2:nz)+ MP_Txz(2:nx,:,2:nz).*( (Vx(2:nx,:,2:nz)-Vx(2:nx,:,1:nz-1))./dz + (Vz(2:nx,:,2:nz)-Vz(1:nx-1,:,2:nz))./dx );
UV_Txz_x=MP_Txz_xb.*UV_Txz_x+MP_Txz_xa.*(Vz([2:npml+1 nx-npml+1:nx],:,:)-Vz([1:npml nx-npml:nx-1],:,:))./dx;
Txz([2:npml+1 nx-npml+1:nx],:,:)=Txz([2:npml+1 nx-npml+1:nx],:,:) - MP_Txz([2:npml+1 nx-npml+1:nx],:,:).*UV_Txz_x;
UV_Txz_z=MP_Txz_zb.*UV_Txz_z+MP_Txz_za.*(Vx(:,:,[2:npml+1 nz-npml+1:nz])-Vx(:,:,[1:npml nz-npml:nz-1]))./dz;
Txz(:,:,[2:npml+1 nz-npml+1:nz])=Txz(:,:,[2:npml+1 nz-npml+1:nz]) - MP_Txz(:,:,[2:npml+1 nz-npml+1:nz]).*UV_Txz_z;
Txz([1 nx+1],:,2:nz)=Txz([2 nx],:,2:nz); Txz(:,:,[1 nz+1])=Txz(:,:,[2 nz]);
Vx(2:nx,:,:)=Vx(2:nx,:,:)+ MP_Vx(2:nx,:,:).* ( (Txx(2:nx,:,:)-Txx(1:nx-1,:,:))./dx ...
+ (Txy(2:nx,2:ny+1,:)-Txy(2:nx,1:ny,:))./dy + (Txz(2:nx,:,2:nz+1)-Txz(2:nx,:,1:nz))./dz );
UV_Vx_x=MP_Vx_xb.*UV_Vx_x+MP_Vx_xa.*(Txx([2:npml+1 nx-npml+1:nx],:,:)-Txx([1:npml nx-npml:nx-1],:,:))./dx;
Vx([2:npml+1 nx-npml+1:nx],:,:)=Vx([2:npml+1 nx-npml+1:nx],:,:) - MP_Vx([2:npml+1 nx-npml+1:nx],:,:).*UV_Vx_x;
UV_Vx_y=MP_Vx_yb.*UV_Vx_y+MP_Vx_ya.*(Txy(:,[2:npml+1 ny-npml+2:ny+1],:)-Txy(:,[1:npml ny-npml+1:ny],:))./dy;
Vx(:,[1:npml ny-npml+1:ny],:)=Vx(:,[1:npml ny-npml+1:ny],:) - MP_Vx(:,[1:npml ny-npml+1:ny],:).*UV_Vx_y;
UV_Vx_z=MP_Vx_zb.*UV_Vx_z+MP_Vx_za.*(Txz(:,:,[2:npml+1 nz-npml+2:nz+1])-Txz(:,:,[1:npml nz-npml+1:nz]))./dz;
Vx(:,:,[1:npml nz-npml+1:nz])=Vx(:,:,[1:npml nz-npml+1:nz]) - MP_Vx(:,:,[1:npml nz-npml+1:nz]).*UV_Vx_z;
Vx([1 nx+1],:,:)=Vx([2 nx],:,:);
Vy(:,2:ny,:)=Vy(:,2:ny,:)+MP_Vy(:,2:ny,:).* ( (Txy(2:nx+1,2:ny,:)-Txy(1:nx,2:ny,:))./dx...
+ (Tyy(:,2:ny,:)-Tyy(:,1:ny-1,:))./dy + (Tyz(:,2:ny,2:nz+1)-Tyz(:,2:ny,1:nz))./dz );
UV_Vy_x=MP_Vy_xb.*UV_Vy_x+MP_Vy_xa.*(Txy([2:npml+1 nx-npml+2:nx+1],:,:)-Txy([1:npml nx-npml+1:nx],:,:))./dx;
Vy([1:npml nx-npml+1:nx],:,:)=Vy([1:npml nx-npml+1:nx],:,:) - MP_Vy([1:npml nx-npml+1:nx],:,:).*UV_Vy_x;
UV_Vy_y=MP_Vy_yb.*UV_Vy_y+MP_Vy_ya.*(Tyy(:,[2:npml+1 ny-npml+1:ny],:)-Tyy(:,[1:npml ny-npml:ny-1],:))./dy;
Vy(:,[2:npml+1 ny-npml+1:ny],:)=Vy(:,[2:npml+1 ny-npml+1:ny],:) - MP_Vy(:,[2:npml+1 ny-npml+1:ny],:).*UV_Vy_y;
UV_Vy_z=MP_Vy_zb.*UV_Vy_z+MP_Vy_za.*(Tyz(:,:,[2:npml+1 nz-npml+2:nz+1])-Tyz(:,:,[1:npml nz-npml+1:nz]))./dz;
Vy(:,:,[1:npml nz-npml+1:nz])=Vy(:,:,[1:npml nz-npml+1:nz]) - MP_Vy(:,:,[1:npml nz-npml+1:nz]).*UV_Vy_z;
Vy(:,[1 ny+1],:)=Vy(:,[2 ny],:);
Vz(:,:,2:nz)=Vz(:,:,2:nz)+MP_Vz(:,:,2:nz).* ( (Txz(2:nx+1,:,2:nz)-Txz(1:nx,:,2:nz))./dx...
+ (Tyz(:,2:ny+1,2:nz)-Tyz(:,1:ny,2:nz))./dy + (Tzz(:,:,2:nz)-Tzz(:,:,1:nz-1))./dz );
UV_Vz_x=MP_Vz_xb.*UV_Vz_x+MP_Vz_xa.*(Txz([2:npml+1 nx-npml+2:nx+1],:,:)-Txz([1:npml nx-npml+1:nx],:,:))./dx;
Vz([1:npml nx-npml+1:nx],:,:)=Vz([1:npml nx-npml+1:nx],:,:) - MP_Vz([1:npml nx-npml+1:nx],:,:).*UV_Vz_x;
UV_Vz_y=MP_Vz_yb.*UV_Vz_y+MP_Vz_ya.*(Tyz(:,[2:npml+1 ny-npml+2:ny+1],:)-Tyz(:,[1:npml ny-npml+1:ny],:))./dy;
Vz(:,[1:npml ny-npml+1:ny],:)=Vz(:,[1:npml ny-npml+1:ny],:) - MP_Vz(:,[1:npml ny-npml+1:ny],:).*UV_Vz_y;
UV_Vz_z=MP_Vz_zb.*UV_Vz_z+MP_Vz_za.*(Tzz(:,:,[2:npml+1 nz-npml+1:nz])-Tzz(:,:,[1:npml nz-npml:nz-1]))./dz;
Vz(:,:,[2:npml+1 nz-npml+1:nz])=Vz(:,:,[2:npml+1 nz-npml+1:nz]) - MP_Vz(:,:,[2:npml+1 nz-npml+1:nz]).*UV_Vz_z;
Vz(:,:,[1 nz+1])=Vz(:,:,[2 nz]);
if mod(j,100)==0 %出图和动画
figure(2);
set(gcf,'outerposition',get(0,'screensize')); %全屏
subplot(1,2,1);
imagesc(squeeze(Vx(npml+1:nx+1-npml,1+npml:ny-npml,fsz)));
colorbar;
shading interp;
axis equal tight;
set(gca,'fontsize',12,'fontweight', 'Bold');
subplot(1,2,2);
imagesc(squeeze(Vx(fsx,1+npml:ny-npml,1+npml:nz-npml)));
colorbar('horiz');
set(gca,'fontsize',12,'fontweight', 'Bold');
axis equal tight;
h=suptitle(['Vx at step = ',num2str(j), ', time = ',num2str(j*dt),' sec']);
set(h,'fontsize',18,'fontweight', 'Bold');
writeVideo(myavi,getframe(gcf));
end
end
close(myavi);
toc