长方体、台阶通过MATLAB生成的三维重力异常正演图形代码

以下是生成长方体、台阶三维重力异常正演图形的MATLAB代码：

% 生成长方体、台阶三维重力异常正演图形
clear all; clc; close all;
G = 6.67e-11; % 万有引力常数
rho = 2670; % 密度
Lx = 1000; Ly = 1000; Lz = 2000; % 长方体的长、宽、高
dx = 50; dy = 50; dz = 50; % 网格间距
x = -Lx/2:dx:Lx/2; y = -Ly/2:dy:Ly/2; z = 0:dz:Lz;
[X,Y,Z] = meshgrid(x,y,-z);
% 计算长方体的重力异常
gx = zeros(size(X)); gy = zeros(size(Y)); gz = zeros(size(Z));
gx(abs(X)<=Lx/2) = 2*pi*G*rho*Lx*(Y(abs(Y)<=Ly/2)*Lz^2)./((X(abs(X)<=Lx/2).^2 + Y(abs(Y)<=Ly/2).^2 + Lz^2).^(3/2));
gy(abs(Y)<=Ly/2) = 2*pi*G*rho*Ly*(X(abs(X)<=Lx/2)*Lz^2)./((X(abs(X)<=Lx/2).^2 + Y(abs(Y)<=Ly/2).^2 + Lz^2).^(3/2));
gz = 2*pi*G*rho*(Lx*Ly*Z - (X(abs(X)<=Lx/2)*Y(abs(Y)<=Ly/2)*Lz));
% 生成台阶
zt = 500; % 台阶高度
W = 800; % 台阶宽度
x1 = -Lx/2; x2 = x1+W; x3 = x2; x4 = x1;
y1 = -Ly/2; y2 = y1; y3 = y1+W; y4 = y3;
z1 = -zt; z2 = z1; z3 = 0; z4 = z3;
zt1 = z1+zt/2; % 台阶上方的一层网格
[Xt,Yt,Zt] = meshgrid(x1:dx:x2,y1:dy:y3,z1:dz:zt1);
% 计算台阶的重力异常
gxt = zeros(size(Xt)); gyt = zeros(size(Yt)); gzt = zeros(size(Zt));
gxt(Xt<=x2) = 2*pi*G*rho*W*(zt-Zt(Xt<=x2))./(Xt(Xt<=x2).^2 + (zt-Zt(Xt<=x2)).^2);
gyt(Yt<=y3) = 2*pi*G*rho*W*(zt-Zt(Yt<=y3))./(Yt(Yt<=y3).^2 + (zt-Zt(Yt<=y3)).^2);
gzt1 = 2*pi*G*rho*W*(zt1-Zt)./(Xt.^2 + Yt.^2 + (zt1-Zt).^2);
gzt(Xt<=x2 & Yt<=y3 & Zt<=zt1) = gzt1(Xt<=x2 & Yt<=y3 & Zt<=zt1);
% 绘制三维重力异常正演图形
figure;
subplot(1,2,1); 
p1 = patch(isosurface(X,Y,Z,gx,0)); set(p1,'FaceColor','r','EdgeColor','none','FaceAlpha',0.5);
p2 = patch(isosurface(X,Y,Z,gy,0)); set(p2,'FaceColor','g','EdgeColor','none','FaceAlpha',0.5);
p3 = patch(isosurface(X,Y,Z,gz,0)); set(p3,'FaceColor','b','EdgeColor','none','FaceAlpha',0.5);
axis equal; view(3); xlabel('X'); ylabel('Y'); zlabel('Z'); 
legend([p1 p2 p3],'gx','gy','gz'); title('长方体的重力异常');
subplot(1,2,2); 
p4 = patch(isosurface(Xt,Yt,Zt,gxt,0)); set(p4,'FaceColor','r','EdgeColor','none','FaceAlpha',0.5);
p5 = patch(isosurface(Xt,Yt,Zt,gyt,0)); set(p5,'FaceColor','g','EdgeColor','none','FaceAlpha',0.5);
p6 = patch(isosurface(Xt,Yt,Zt,gzt,0)); set(p6,'FaceColor','b','EdgeColor','none','FaceAlpha',0.5);
axis equal; view(3); xlabel('X'); ylabel('Y'); zlabel('Z'); 
legend([p4 p5 p6],'gx','gy','gz'); title('台阶的重力异常');

在上述代码中，首先定义了万有引力常数和长方体、台阶的参数，然后使用meshgrid函数生成三维网格，并根据重力公式计算出长方体、台阶的重力异常。最后使用isosurface函数绘制三维重力异常正演图形。两个子图分别展示了长方体和台阶的重力异常。可以通过修改参数来生成不同形状和大小的模型，并进行三维重力异常正演计算和图形绘制。