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GravFor3D.m
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GravFor3D.m
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function [gravAnomaly] = GravFor3D(mergeFlag, parFlag, xm, ym, zm, dx, dy, dz, model, RPx, RPy, RPz)
%GRAVFOR3D calculates the gravity anomaly using input parameters.
% GRAVFOR3D(mergeFlag, parFlag, xm, ym, zm, dx, dy, dz, model, RPx, RPy, RPz)
% calculates the gravity anomalies of the model on the survey grid.
% The model info is contained in 'xm', 'ym', 'zm', 'dx', 'dy', 'dz' and 'model',
% The info of the survey grid is contained in 'RPx', 'RPy' and 'RPz'.
% User can change the parameters 'mergeFlag' and 'parFlag' to speed up
% the program.
%
% Input£º
% mergeFlag flag value of merge mode
% parFlag flag value of parallel computing mode(1 for serial, 2 for CPU parallel, 3 for GPU parallel)
% xm center coordinates of mesh cells in x direction (north is positive)
% ym center coordinates of mesh cells in y direction (east is positive)
% zm center coordinates of mesh cells in z direction (vertical down is positive)
% dx size of mesh cells in x direction
% dy size of mesh cells in y direction
% dz size of mesh cells in z direction
% model physical parameters of the model
% RPx coordinates of survey grid in x direction
% RPy coordinates of survey grid in y direction
% RPz coordinates of survey grid in z direction
%
% Output£º
% gravAnomaly gravity anomaly
%
% T. Chen 20-May-2016.
% Copyright 2016-2018 T. Chen.
nbIn = nargin;
switch nbIn
case {12}
case {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
error('GravFor3D: FunctionInput: NotEnough_ArgNum');
otherwise
error('GravFor3D: FunctionInput: TooMany_ArgNum');
end
G0 = 6.67428e-11; % gravitational constant
nd = length(RPy); % number of survey data
% mesh info
if mergeFlag == 0
index = find(model);
xm = xm(index);
ym = ym(index);
zm = zm(index);
model = model(index);
dx = dx(index);
dy = dy(index);
dz = dz(index);
mn = length(index); % number of mesh cells
else
mn = length(model); % number of mesh cells
end
switch parFlag
case 1 % serial program
gravAnomaly = zeros(nd, 1);
if mn > nd
for ip = 1 : nd
x1 = xm - dx/2.0 - RPx(ip);
x2 = x1 + dx;
y1 = ym - dy/2.0 - RPy(ip);
y2 = y1 + dy;
z1 = zm - dz/2.0 + RPz(ip);
z2 = z1 + dz;
[kenelValue] = arrayfun(@GravKernel3D, x1, x2, y1, y2, z1, z2);
G = - G0 * 1.0e+8 * kenelValue;
gravAnomaly(ip) = G' * model;
end
else
for ct = 1 : mn
x1 = xm(ct) - dx(ct)/2.0 - RPx;
x2 = x1 + dx(ct);
y1 = ym(ct) - dy(ct)/2.0 - RPy;
y2 = y1 + dy(ct);
z1 = zm(ct) - dz(ct)/2.0 + RPz;
z2 = z1 + dz(ct);
[kenelValue] = arrayfun(@GravKernel3D, x1, x2, y1, y2, z1, z2);
G = - G0 * 1.0e+8 * kenelValue;
pointAnomaly = G * model(ct);
gravAnomaly = gravAnomaly + pointAnomaly;
end
end
case 2 % multi CPU cores parallel computing
gravAnomaly = zeros(nd, 1);
if mn > nd
parfor ip = 1 : nd
x1 = xm - dx/2.0 - RPx(ip);
x2 = x1 + dx;
y1 = ym - dy/2.0 - RPy(ip);
y2 = y1 + dy;
z1 = zm - dz/2.0 + RPz(ip);
z2 = z1 + dz;
[kenelValue] = arrayfun(@GravKernel3D, x1, x2, y1, y2, z1, z2);
G = - G0 * 1.0e+8 * kenelValue;
gravAnomaly(ip) = G' * model;
end
else
parfor ct = 1 : mn
x1 = xm(ct) - dx(ct)/2.0 - RPx;
x2 = x1 + dx(ct);
y1 = ym(ct) - dy(ct)/2.0 - RPy;
y2 = y1 + dy(ct);
z1 = zm(ct) - dz(ct)/2.0 + RPz;
z2 = z1 + dz(ct);
[kenelValue] = arrayfun(@GravKernel3D, x1, x2, y1, y2, z1, z2);
G = - G0 * 1.0e+8 * kenelValue;
pointAnomaly = G * model(ct);
gravAnomaly = gravAnomaly + pointAnomaly;
end
end
case 3 % GPU parallel computing
gravAnomaly = zeros(nd, 1, 'gpuArray');
xm = gpuArray(xm);
dx = gpuArray(dx);
RPx = gpuArray(RPx);
ym = gpuArray(ym);
dy = gpuArray(dy);
RPy = gpuArray(RPy);
zm = gpuArray(zm);
dz = gpuArray(dz);
RPz = gpuArray(RPz);
model = gpuArray(model);
if mn > nd
for ip = 1 : nd
x1 = xm - dx/2.0 - RPx(ip);
x2 = x1 + dx;
y1 = ym - dy/2.0 - RPy(ip);
y2 = y1 + dy;
z1 = zm - dz/2.0 + RPz(ip);
z2 = z1 + dz;
[kenelValue] = arrayfun(@GravKernel3D, x1, x2, y1, y2, z1, z2);
G = - G0 * 1.0e+8 * kenelValue;
gravAnomaly(ip) = G' * model;
end
else
for ct = 1 : mn
x1 = xm(ct) - dx(ct)/2.0 - RPx;
x2 = x1 + dx(ct);
y1 = ym(ct) - dy(ct)/2.0 - RPy;
y2 = y1 + dy(ct);
z1 = zm(ct) - dz(ct)/2.0 + RPz;
z2 = z1 + dz(ct);
[kenelValue] = arrayfun(@GravKernel3D, x1, x2, y1, y2, z1, z2);
G = - G0 * 1.0e+8 * kenelValue;
pointAnomaly = G * model(ct);
gravAnomaly = gravAnomaly + pointAnomaly;
end
end
end
end
function [gravEffect] = GravKernel3D(x1, x2, y1, y2, z1, z2)
% GRAVKERNEL3D calculates the gravity effect of a cell on a survey point
% Input parameters contain relative distance between the cell and the survey point
%
% Reference: Li, X., Chouteau, M., 1998. Three-dimensional gravity modeling in all space. Surv.
% Geophys. 19 (4), 339¨C368.
%
% Input:
% relative distance between the cell and the survey point,
% there are: x1, x2, y1, y2, z1, z2
%
% Output:
% gravEffect gravity effect
%
% T. Chen 20-May-2016.
% Copyright 2016-2018 T. Chen.
r1 = sqrt(x1 .* x1 + y1 .* y1 + z1 .* z1);
r2 = sqrt(x1 .* x1 + y1 .* y1 + z2 .* z2);
r3 = sqrt(x1 .* x1 + y2 .* y2 + z1 .* z1);
r4 = sqrt(x1 .* x1 + y2 .* y2 + z2 .* z2);
r5 = sqrt(x2 .* x2 + y1 .* y1 + z1 .* z1);
r6 = sqrt(x2 .* x2 + y1 .* y1 + z2 .* z2);
r7 = sqrt(x2 .* x2 + y2 .* y2 + z1 .* z1);
r8 = sqrt(x2 .* x2 + y2 .* y2 + z2 .* z2);
% equation (8) in Li (1998)
gravEffect = - (x1 .* log(y1 + r1) + y1 .* log(x1 + r1) - z1 .* atan2(x1 .* y1, z1 .* r1))...
+ (x1 .* log(y1 + r2) + y1 .* log(x1 + r2) - z2 .* atan2(x1 .* y1, z2 .* r2))...
+ (x1 .* log(y2 + r3) + y2 .* log(x1 + r3) - z1 .* atan2(x1 .* y2, z1 .* r3))...
- (x1 .* log(y2 + r4) + y2 .* log(x1 + r4) - z2 .* atan2(x1 .* y2, z2 .* r4))...
+ (x2 .* log(y1 + r5) + y1 .* log(x2 + r5) - z1 .* atan2(x2 .* y1, z1 .* r5))...
- (x2 .* log(y1 + r6) + y1 .* log(x2 + r6) - z2 .* atan2(x2 .* y1, z2 .* r6))...
- (x2 .* log(y2 + r7) + y2 .* log(x2 + r7) - z1 .* atan2(x2 .* y2, z1 .* r7))...
+ (x2 .* log(y2 + r8) + y2 .* log(x2 + r8) - z2 .* atan2(x2 .* y2, z2 .* r8));
end