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mt2dforward_TM.m
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clear;
clc;
%geo
X_length = 1000;
Y_length = -1000;
NXTM = 55; % X方向 即横向 间隔数
NYTM = 50; % Y方向 即纵向 间隔数
NETM = NXTM * NYTM; % 总单元个数
NPSUMTM = (NXTM + 1) * (NYTM + 1); %总节点个数
a = 100; % 单元的 横向长度
h = 100; % % 单元的 纵向长度
PaTM = [100, 1500]; % 需要设定的电阻率值
f=logspace(3, -3, 20); % 频率
xTM = zeros(NPSUMTM, length(f));
X = linspace(0, 1000, NXTM+1);
Y = linspace(0, -1000, NYTM+1);
XY = zeros(2, NPSUMTM); %节点坐标表格
for ix = 1:NXTM+1
for iy = 1:NYTM+1
N = (ix-1)*(NYTM+1) + iy;
XY(1, N) = X(ix);
XY(2, N) = Y(iy);
end
end
BHXY = zeros(4, NETM); %单元的 节点索引表
for IX=1:NXTM
for IY=1:NYTM
N=(IX-1)*NYTM+IY;%单元编号
N1=N+(IX-1);%每个单元的第一个节点编号
BHXY(1,N)=N1;%每个单元的第一个节点编号
BHXY(2,N)=N1+1;%每个单元的第二个节点编号
BHXY(3,N)=N1+NYTM+2;%每个单元的第三个节点编号
BHXY(4,N)=N1+NYTM+1;%每个单元的第四个节点编号
end
end
%%%%%%%构建地电模型%%%%%%
rhoTM = zeros(NETM, 1); % 单元的 电阻率信息
% 以下为 定义地电模型 呈层状结构
% for i=1:30
% for j=1:NYTM
% m=(i-1)*NYTM+j;%单元编号
% rhoTM(m)=PaTM(1);
% end
% end
% for i=31:60
% for j=1:NYTM
% m=(i-1)*NYTM+j;%单元编号
% rhoTM(m)=PaTM(2);
% end
% end
% for i=1:NXTM
% for j=1:NYTM
% m=(i-1)*NYTM+j;
% rhoTM(m)=100;
% end
% end
% for i=16:24%异常体
% for j=2:18
% m=(i-1)*NYTM+j;
% rhoTM(m)=400;
% end
% end
% for i=26:30%异常体
% for j=1:10
% m=(i-1)*NYTM+j;
% rhoTM(m)=800;
% end
% end
for i = 1:NXTM
for j = 1:5
m=(i-1)*NYTM+j;
rhoTM(m) = 10;
end
end
for i = 1:NXTM
for j = 6:15
m=(i-1)*NYTM+j;
rhoTM(m) = 100;
end
end
for i = 1:NXTM
for j = 16:40
m=(i-1)*NYTM+j;
rhoTM(m) = 10;
end
end
for i = 1:NXTM
for j = 41:NYTM
m=(i-1)*NYTM+j;
rhoTM(m) = 100;
end
end
%%%%%%%%%%%%%%
for ff=1:size(f,2)
K1TM=zeros(NPSUMTM); %
K2TM=zeros(NPSUMTM); %
K3TM=zeros(NPSUMTM); %
PTM=zeros(NPSUMTM,1); %
u=(4e-7)*pi;%电、磁性参数
w=2*pi*f(ff);
TAOTM=rhoTM;
LMTM=sqrt(-1)*w*u;
%%%% K1
for m=1:NETM
A=(h/a)/6;
B=(a/h)/6;
K1e=A*[2 1 -1 -2;1 2 -2 -1;-1 -2 2 1;-2 -1 1 2]+B*[2 -2 -1 1;-2 2 1 -1;-1 1 2 -2;1 -1 -2 2];
for j=1:4
NJ=BHXY(j,m);
for k=1:4
NK=BHXY(k,m);
K1TM(NJ,NK)=K1TM(NJ,NK)+K1e(j,k)*TAOTM(m);
end
end
end
%%%% K2
for m=1:NETM
K2e=[4 2 1 2;2 4 2 1;1 2 4 2;2 1 2 4];
for j=1:4
NJ=BHXY(j,m);
for k=1:4
NK=BHXY(k,m);
K2TM(NJ,NK)=K2TM(NJ,NK)+K2e(j,k)*LMTM*a*h/36;
end
end
end
%%%%% K3
for n1=NYTM:NYTM:NETM
i=BHXY(1,n1); j=BHXY(2,n1);
kn=sqrt(-sqrt(-1)*w*u/rhoTM(n1));
mk=TAOTM(n1)*kn*a/6;%???????????????????????????
Kjj=2*mk;
K3TM(j,j)=K3TM(j,j)+Kjj;
K3TM(i,i)=K3TM(i,i)+Kjj;
Kji=1*mk;
K3TM(j,i)=K3TM(j,i)+Kji;
K3TM(i,j)=K3TM(i,j)+Kji;
end
%%%%% 组装总体刚度矩阵
vTM=sparse(K1TM-K2TM+K3TM);
PTM=zeros(NPSUMTM,1);
for i=1:NXTM+1
j=1+(i-1)*(NYTM+1);
vTM(j,j)=vTM(j,j)*10^10;
PTM(j)=vTM(j,j)*1;
end
vvTM=vTM;
%xTM=zeros(size(PTM),2);
tol=1e-15;
maxsteps=100;
[LTM,UTM]=luinc(vvTM,'0');
xTM(:,ff)=bicgstab(vvTM,PTM,tol,maxsteps,LTM,UTM);
end
%%%%%%
vect=1:NYTM+1:NPSUMTM-NYTM;%这是地表节点的标号
% du/dy = (-11*u1 + 18*u2 - 9u3 + 2u4)
u1=zeros(size(vect,2),size(f,2));
u2=zeros(size(vect,2),size(f,2));
u3=zeros(size(vect,2),size(f,2));
u4=zeros(size(vect,2),size(f,2));
z=zeros(size(vect,2),size(f,2)); %%阻抗
pc=zeros(size(vect,2),size(f,2)); %视电阻率
phase=zeros(size(vect,2),size(f,2)); %阻抗相位
ve=[1:NYTM:(NYTM*NXTM-NYTM+1),NYTM*NXTM-NYTM+1];
%多加一个单元是为了补偿向量ve的长度与vect相同，方便后面计算
% 求取地表的 阻抗 视电阻率 阻抗相位
for ff=1:size(f,2)
for i=1:size(vect,2)
u=(4e-7)*pi;
w=2*pi*f(ff);
u1(i,ff)=xTM(vect(i),ff);
u2(i,ff)=xTM(vect(i)+1,ff);
u3(i,ff)=xTM(vect(i)+2,ff);
u4(i,ff)=xTM(vect(i)+3,ff);
%四个节点的边长
l=3*h;
ux(i,ff)=(-11*u1(i,ff)+18*u2(i,ff)-9*u3(i,ff)+2*u4(i,ff))/(2*l); %近似求导数
z(i,ff)=(rhoTM(ve(i))*ux(i,ff))/xTM(vect(i),ff);%阻抗
pc(i,ff)=(abs((rhoTM(ve(i))*ux(i,ff))/xTM(vect(i),ff))^2)/(w*u); %视电阻率
phase(i,ff)=-atan(imag(z(i,ff))/real(z(i,ff)))*180/pi; %阻抗相位
HEY(i,ff)=ux(i,ff)*rhoTM(ve(i));%EY
end
end
% semilogx（x1，y1，选项1，x2，y2，选项2，…）
% plot(f,pc(20,:));
semilogx(1./f, pc(20, :));