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ViscoElastic_2D_FDTD_SG_CPML.m
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ViscoElastic_2D_FDTD_SG_CPML.m
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clc,clear
% 2D Elastic wave simulation using finite difference.
% with staggered-grid; with Convolutional Perfectly Matched Layer;
% By zhaoqingwei
% Chengdu University of Technology (CDUT), 2021-2025
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%txx(tzz)--Vx--txx(tzz)
% | | |
% Vz------txz---vz
% | | |
%txx(tzz)--Vx--txx(tzz)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
FM=20;
DT=0.001;dt=DT;
T=4;
nx=600;
nz=600;
DH=10;dx=DH;dz=DH;
s=wavelet(FM,DT,T)*1e5;
vp=ones(nz,nx)*4000;vs=vp/2;rou=ones(600,600)*2;
lamda=rou.*(vp.*vp-vs.*vs*2);mu=rou.*vs.*vs;
c11=rou.*vp.*vp;c13=rou.*(vp.*vp-vs.*vs*2);c33=c11;c55=rou.*vs.*vs;%¸÷ÏòͬÐÔ
% Epsilon=0.25*ones(600,600);Delta=0.1*ones(600,600);
% c33=vp.*vp.*rou;c55=vs.*vs.*rou;c11=2*c33.*Epsilon+c33;c13=rou.*sqrt(((1+2*Delta).*vp.*vp-vs.*vs).*(vp.*vp-vs.*vs))-rou.*vs.*vs;%VTI
QP=100;QS=100;
c11i=c11/(QP*FM);c33i=c11i;c55i=c55/(QS*FM);c13i=c11i-2*c55i;
vx0=zeros(nz,nx);vx1=vx0;
vz0=vx0;vz1=vx0;
taoxx0=vx0;taoxx1=vx0;
taozz0=vx0;taozz1=vx0;
taoxz0=vx0;taoxz1=vx0;
z0=round(nz/2);x0=round(nx/2);
EXX0=vx0;EXX1=vx0;
EXZ0=vx0;EXZ1=vx0;
EZX0=vx0;EZX1=vx0;
EZZ0=vx0;EZZ1=vx0;
HXX0=vx0;HXX1=vx0;
HXZ0=vx0;HXZ1=vx0;
HZX0=vx0;HZX1=vx0;
HZZ0=vx0;HZZ1=vx0;
[aaz,bbz,aax,bbx] = cpml(1e-10,[nz nx],20,max(vp(:)),dt,dz);
nn=3;
dxd=FDcoeffDx(nn);ddz0=dxd';ddz1=[dxd 0]';ddx0=ddz0';ddx1=ddz1';
TX=dt/dx;TZ=dt/dz;
for t=DT:DT:T
disp(t);
k=round(t/DT);
EXX1=bbx.*EXX0+aax.*TX.*imfilter(taoxx0,ddx0)/dt;
EXZ1=bbz.*EXZ0+aaz.*TZ.*imfilter(taoxz0,ddz1)/dt;
EZX1=bbx.*EZX0+aax.*TX.*imfilter(taoxz0,ddx1)/dt;
EZZ1=bbz.*EZZ0+aaz.*TZ.*imfilter(taozz0,ddz0)/dt;
vx1=vx0+(TZ.*imfilter(taoxz0,ddz1)+TX.*imfilter(taoxx0,ddx0)+EXZ1*dt+EXX1*dt)./rou;
vz1=vz0+(TZ.*imfilter(taozz0,ddz0)+TX.*imfilter(taoxz0,ddx1)+EZZ1*dt+EZX1*dt)./rou;
vz1(z0,x0)=vz1(z0,x0)+s(k);
HXX1=bbx.*HXX0+aax.*TX.*imfilter(vx1,ddx1)/dt;
HXZ1=bbz.*HXZ0+aaz.*TZ.*imfilter(vx1,ddz0)/dt;
HZX1=bbx.*HZX0+aax.*TX.*imfilter(vz1,ddx0)/dt;
HZZ1=bbz.*HZZ0+aaz.*TZ.*imfilter(vz1,ddz1)/dt;
vzzt=TZ.*imfilter(vz1,ddz1)/dt;
vxxt=TX.*imfilter(vx1,ddx1)/dt;
vxzt=TZ.*imfilter(vx1,ddz0)/dt;
vzxt=TX.*imfilter(vz1,ddx0)/dt;
taoxx1=taoxx0+c13.*TZ.*imfilter(vz1,ddz1)+c11.*TX.*imfilter(vx1,ddx1)+c13.*HZZ1*dt+c11.*HXX1*dt+c13i.*vzzt+c11i.*vxxt;
taozz1=taozz0+c33.*TZ.*imfilter(vz1,ddz1)+c13.*TX.*imfilter(vx1,ddx1)+c33.*HZZ1*dt+c13.*HXX1*dt+c33i.*vzzt+c13i.*vxxt;
taoxz1=taoxz0+c55.*TZ.*imfilter(vx1,ddz0)+c55.*TX.*imfilter(vz1,ddx0)+c55.*HXZ1*dt+c55.*HZX1*dt+c55i.*vxzt+c55i.*vzxt;
% taoxx1(z0,x0)=taoxx1(z0,x0)+s(k);
% taozz1(z0,x0)=taozz1(z0,x0)+s(k);
EXX0=EXX1;EXZ0=EXZ1;EZX0=EZX1;EZZ0=EZZ1;
HXX0=HXX1;HXZ0=HXZ1;HZX0=HZX1;HZZ0=HZZ1;
taoxx0=taoxx1;taozz0=taozz1;taoxz0=taoxz1;
vz0=vz1;vx0=vx1;
if mod(t,0.5)==0
figure();
imagesc(vz1);
end
end