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chapter1_Rayleigh_ts.m
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chapter1_Rayleigh_ts.m
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function []= chapter1_Rayleigh_ts()
clc; clear all
snapshot_time = input('请输入一个波场快照时间(单位:ms):')
tic
%%% 参数设置 %%%
N = 400;
fm = 30;
space_x = 0.5; space_z = 0.5; % 网格步长
sample_t = 0.05/1000; % 时间步长0.05ms
T = 250/1000; % 总时间为250ms
K = T/sample_t; % 外层时间循环总次数:250/0.05 = 5000次
layer = 20*space_x; % 吸收层的厚度
coefficientR = 0.0001; % 理想的反射系数：基本不反射
C1 = 1.125;
C2 = -0.04166667;
%%% 均匀半空间模型的初始化 %%%
% 预分配提速:
VP = zeros(400,400)+1000;
VS = zeros(400,400)+570;
Density = zeros(400,400)+2000;
lame1 = zeros(400,400);
lame2 = zeros(400,400);
for i = 1:N
j = 1:N; % 矢量化加速
lame1(i,j) = Density(i,j) .* (VP(i,j).^2 - 2*VS(i,j).^2);
lame2(i,j) = Density(i,j) .* VS(i,j).^2;
end
%%% U、V、P、Q、R：速度、应力全空间初始化 %%%
% 预分配:全x向参数
U_x = zeros(400,400);
V_x = zeros(400,400);
P_x = zeros(400,400);
Q_x = zeros(400,400);
R_x = zeros(400,400);
% 预分配:全y向的参数
U_y = zeros(400,400);
V_y = zeros(400,400);
P_y = zeros(400,400);
Q_y = zeros(400,400);
R_y = zeros(400,400);
% 预分配:总参数
U = zeros(400,400);
V = zeros(400,400);
P = zeros(400,400);
Q = zeros(400,400);
R = zeros(400,400);
% 预分配:间距
dx = zeros(1,400);
dy = zeros(1,400);
%%% AEA 自由表面边界条件 %%%
% 其实就是把原始空间的前4行拿出来，用来做自由空间层！
% 所以差分计算时，i和j都是从4开始
for i = 1:4
j = 1:N % 矢量化加速
Density(i,j) = 0.5*Density(i,j);
lame1(i,j) = 0;
lame2(i,j) = lame2(i,j);
end
%%% 开始有限差分的计算 %%%
for k = 1:K % 时间是最外层循环：相当于总的迭代次数/传播的时间
fprintf('迭代计算开始,当前是第%d次"时间"大循环!\n',k)
mibinbin = k;
% AEA 自由边界设置：
for i = 1:N
Q(i,4) = 0;
end
% 差分计算：各点的速度更新
for i = 4:(N-4)
for j = 4:(N-4)
% 区域边界的设置
if i <= 4 + layer/space_x
dx(i) = (2*VP(i,j)/layer)*log(1/coefficientR)*((4+layer/space_x-i)*space_x/layer)^4;
end
if i >= N-4-layer/space_x
dx(i) = (2*VP(i,j)/layer)*log(1/coefficientR)*((i-(N-4-layer/space_x))*space_x/layer)^4;
end
if j >= N-4-layer/space_x % 400 - 4 - 10/0.5 = 346 每一个i下，j要在346之后才会不等于0
%fprintf('第%d次"行循环"已进入j>=346阶段,当前:j=%d\n',i,j);
%pause(1);
dy(j) = (2*VP(i,j)/layer)*log(1/coefficientR)*((j-(N-4-layer/space_x))*space_x/layer)^4;
end
% 速度迭代计算
U_x(i,j) = ( (1-0.5*sample_t*dx(i))/(1+0.5*sample_t*dx(i)))*U_x(i,j) + ...
(1/(1+0.5*sample_t*dx(i)))*(1/Density(i,j))*(sample_t/space_x)*...
( C1*(P(i+1,j)-P((i),j))+C2*( P((i+2),j)-P((i-1),j))); % 已检查
U_y(i,j) = ((1-0.5*sample_t*dy(j))/(1+0.5*sample_t*dy(j)))*U_y(i,j) + ...
(1/(1+0.5*sample_t*dy(j)))*(1/Density(i,j))*(sample_t/space_z)* ...
( C1*(R(i,j)-R(i,j-1))+C2*(R(i,(j+1))-R(i,(j-2))));
U(i,j) = U_x(i,j) + U_y(i,j);
V_x(i,j) = ((1-0.5*sample_t*dx(i))/(1+0.5*sample_t*dx(i)))*V_x(i,j) + ...
(1/(1+0.5*sample_t*dx(i)))*(1/Density(i,j))*(sample_t/space_x)*...
( C1*(R(i,j)-R(i-1,j))+C2*(R((i+1),j)-R(i-2,j)));
V_y(i,j) = ((1-0.5*sample_t*dy(j))/(1+0.5*sample_t*dy(j)))*V_y(i,j) + ...
(1/(1+0.5*sample_t*dy(j)))*(1/Density(i,j))*(sample_t/space_z)* ...
( C1*(Q(i,(j+1))-Q(i,j))+C2*( Q(i,(j+2))-Q(i,(j-1))));
V(i,j) = V_x(i,j) + V_y(i,j);
end
end
% 差分计算：各点的应力更新
for i = 4:(N-4)
for j = 4:(N-4)
if i <= 4 + layer/space_x
dx(i) = (2*VP(i,j)/layer)*log(1/coefficientR)*((4+layer/space_x-i)*space_x/layer)^4;
end
if i >= N-4-layer/space_x
dx(i) = (2*VP(i,j)/layer)*log(1/coefficientR)*((i-(N-4-layer/space_x))*space_x/layer)^4;
end
if j >= N-4-layer/space_x
dy(j) = (2*VP(i,j)/layer)*log(1/coefficientR)*((j-(N-4-layer/space_x))*space_x/layer)^4;
end
% 中心震源的位置:
V(200,4) = 100*(1-2*(pi*fm*(k-1000)*sample_t)^2)*...
exp(-(pi*fm*(k-1000)*sample_t)^2);
% 震源的设置:
P_x(i,j) = ((1-0.5*sample_t*dx(i))/(1+0.5*sample_t*dx(i)))*P_x(i,j) + ...
(1/(1+0.5*sample_t*dx(i)))*(lame1(i,j)+2*lame2(i,j))*(sample_t/space_x)*...
(C1*(U((i),j)-U(i-1,j))+C2*(U((i+1),j)-U((i-2),j)));
P_y(i,j) = ((1-0.5*sample_t*dy(j))/(1+0.5*sample_t*dy(j)))*P_y(i,j) + ...
(1/(1+0.5*sample_t*dy(j)))*lame1(i,j)*(sample_t/space_z)*...
(C1*(V(i,j)-V(i,(j-1))) + C2*( V(i,(j+1))-V(i,(j-2))));
P(i,j) = P_x(i,j) + P_y(i,j);
Q_x(i,j) = ((1-0.5*sample_t*dx(i))/(1+0.5*sample_t*dx(i)))*Q_x(i,j) + ...
(1/(1+0.5*sample_t*dx(i)))*lame1(i,j)*(sample_t/space_x)*...
(C1*(U((i),j)-U(i-1,j))+C2*(U((i+1),j)-U((i-2),j)));
Q_y(i,j) = ((1-0.5*sample_t*dy(j))/(1+0.5*sample_t*dy(j)))*Q_y(i,j) + ...
(1/(1+0.5*sample_t*dy(j)))*(lame1(i,j)+2*lame2(i,j))*(sample_t/space_z)*...
(C1*(V(i,j)-V(i,(j-1)))+C2*(V(i,j+1)-V(i,(j-2))));
Q(i,j) = Q_x(i,j) + Q_y(i,j);
R_x(i,j) = ((1-0.5*sample_t*dx(i))/(1+0.5*sample_t*dx(i)))*R_x(i,j) + ...
(1/(1+0.5*sample_t*dx(i)))*lame2(i,j)*(sample_t/space_x)*...
(C1*(V(i+1,j)-V((i),j)) + C2*( V((i+2),j)-V((i-1),j)));
R_y(i,j) = ((1-0.5*sample_t*dy(j))/(1+0.5*sample_t*dy(j)))*R_y(i,j) + ...
(1/(1+0.5*sample_t*dy(j)))*lame2(i,j)*(sample_t/space_z)*...
(C1*(U(i,(j+1))-U(i,j)) + C2*(U(i,(j+2))-U(i,(j-1))));
R(i,j) = R_x(i,j) + R_y(i,j);
end
end
% snapshot时的波场快照：k = snapshot_time*20
if k == snapshot_time*20
figure('name','总速度V的波场快照');
colormap(jet);
imagesc(V');
figure('name','速度分量V_x的波场快照');
colormap(jet);
imagesc(V_x');
figure('name','速度分量V_y的波场快照');
colormap(jet);
imagesc(V_y');
break;
end
end
toc
xlswrite('result_rayleigh.xls', V, 'sheet1')
xlswrite('result_rayleigh.xls', V_x, 'sheet2')
xlswrite('result_rayleigh.xls', V_y, 'sheet3')