initial upload
This commit is contained in:
BIN
DRTP-v31-08-05/rtpdemodata.mat
Normal file
BIN
DRTP-v31-08-05/rtpdemodata.mat
Normal file
Binary file not shown.
167
DRTP-v31-08-05/rtpvariable.m
Normal file
167
DRTP-v31-08-05/rtpvariable.m
Normal file
@@ -0,0 +1,167 @@
|
||||
function varrtp=rtpvariable(magc,incv);
|
||||
% *****************************************************************
|
||||
% *** RTP with variable geomagnetic parameters
|
||||
% *** Uses a Taylor series expansion in the space domain
|
||||
% *** GRJ Cooper July 2002
|
||||
% ******************************************************************
|
||||
% *** magc ; input data (even no of datapoints in each dir)
|
||||
% *** incv ; dataset of field inc over dataset - must be exactly
|
||||
% *** the same size as magc. If omitted then inc is specified only
|
||||
% *** at the dataset corners, and interpolated from there
|
||||
% ******************************************************************
|
||||
% *** Type rtpvariable with no input parameters for demo application
|
||||
% ******************************************************************
|
||||
|
||||
dtr=pi/180; azimuth=0;
|
||||
|
||||
% interpolate inc variation over dataset using linear polynomial
|
||||
|
||||
if nargin==0
|
||||
disp('Loading demo data');
|
||||
load rtpdemodata;
|
||||
end;
|
||||
[nr,nc]=size(magc);
|
||||
if nargin<2 % Specify inc variation only at corners
|
||||
disp('Generating grid of inclination data from values at grid corners');
|
||||
a=zeros(4,3); yval=zeros(4,1);
|
||||
a(1,1)=1; a(1,2)=nr; a(1,3)=1; yval(1,1)=-30;
|
||||
a(2,1)=1; a(2,2)=nr; a(2,3)=nc; yval(2,1)=-30;
|
||||
a(3,1)=1; a(3,2)=1; a(3,3)=1; yval(3,1)=-90;
|
||||
a(4,1)=1; a(4,2)=1; a(4,3)=nc; yval(4,1)=-90;
|
||||
p=pinv(a)*yval;
|
||||
[xi,yi]=meshgrid(1:nc,1:nr);
|
||||
incv=p(1)+p(2)*yi+p(3)*xi;
|
||||
end;
|
||||
incv=incv*dtr; inc=incv(nr/2,nc/2); % inclination at centre of grid
|
||||
|
||||
nmax=max([nr nc]); npts=(2^nextpow2(nmax));
|
||||
cdiff=floor((npts-nc)/2); rdiff=floor((npts-nr)/2);
|
||||
disp('Computing rtp');
|
||||
rtpdata=rtp(magc,npts,nr,nc,rdiff,cdiff,azimuth,inc);
|
||||
incv=incv-inc;
|
||||
disp('Computing dx1');
|
||||
drtp1=taylortp1(magc,npts,nr,nc,rdiff,cdiff,azimuth,inc);
|
||||
disp('Computing dx2');
|
||||
drtp2=taylortp1(drtp1,npts,nr,nc,rdiff,cdiff,azimuth,inc);
|
||||
disp('Computing dx3');
|
||||
drtp3=taylortp1(drtp2,npts,nr,nc,rdiff,cdiff,azimuth,inc);
|
||||
disp('Computing rtpvar');
|
||||
varrtp=rtpdata+drtp1.*incv+0.5*drtp2.*incv.^2+0.1666666*drtp3.*incv.^3; % 3 terms - modify as required
|
||||
figure(1);
|
||||
subplot(1,2,1); imagesc(magc); axis equal; axis tight; axis xy; title('Data'); axis off;
|
||||
hold on; contour(magc,6,'k'); hold off;
|
||||
subplot(1,2,2); imagesc((incv+inc)/dtr); axis equal; axis tight; axis xy; title('Inclination Variation');
|
||||
axis off; colorbar;
|
||||
currfig=get(0,'CurrentFigure'); set(currfig,'numbertitle','off');
|
||||
set(currfig,'name','RTP Datasets');
|
||||
figure(2);
|
||||
subplot(1,3,1); imagesc(drtp1); axis equal; axis tight; axis xy; title('1st Derivative'); axis off;
|
||||
subplot(1,3,2); imagesc(drtp2); axis equal; axis tight; axis xy; title('2nd Derivative'); axis off;
|
||||
subplot(1,3,3); imagesc(drtp3); axis equal; axis tight; axis xy; title('3rd Derivative'); axis off;
|
||||
currfig=get(0,'CurrentFigure'); set(currfig,'numbertitle','off');
|
||||
set(currfig,'name','RTP Derivatives');
|
||||
figure(3);
|
||||
subplot(1,2,1); imagesc(rtpdata); axis equal; axis tight; axis xy; title('After Standard RTP'); axis off;
|
||||
hold on; contour(rtpdata,6,'k'); hold off;
|
||||
subplot(1,2,2); imagesc(varrtp); axis equal; axis tight; axis xy; title('c) After Differential RTP'); axis off;
|
||||
hold on; contour(varrtp,6,'k'); hold off;
|
||||
colormap('jet');
|
||||
currfig=get(0,'CurrentFigure'); set(currfig,'numbertitle','off');
|
||||
set(currfig,'name','RTP with Variable Inclination Over Survey Area');
|
||||
|
||||
%**************************************************************************
|
||||
function drtp=taylortp1(magc,npts,nr,nc,rdiff,cdiff,azimuth,inc); % Rtp derivatives
|
||||
|
||||
dtheta=0.01; dtr=pi/180;
|
||||
rtpdata1=rtp(magc,npts,nr,nc,rdiff,cdiff,azimuth,inc);
|
||||
rtpdata2=rtp(magc,npts,nr,nc,rdiff,cdiff,azimuth,inc+dtheta);
|
||||
drtp=(rtpdata2-rtpdata1)/dtheta;
|
||||
|
||||
% *************************************************************************
|
||||
function rtpdata=rtp(magc,npts,nr,nc,rdiff,cdiff,azimuth,inc);
|
||||
|
||||
gf=taper2d(magc,npts,nc,nr,cdiff,rdiff);
|
||||
f=fft2(gf,npts,npts);
|
||||
fx=f;
|
||||
|
||||
% Direction cosines
|
||||
|
||||
L=cos(azimuth)*cos(inc);
|
||||
M=sin(azimuth)*cos(inc);
|
||||
N=sin(inc);
|
||||
|
||||
wn=2.0*pi/(npts-1);
|
||||
for I=1:npts/2
|
||||
for J=1:npts/2
|
||||
U=I*wn; V=J*wn;
|
||||
temp=U*U+V*V;
|
||||
temp1=L*U+M*V;
|
||||
temp2=N*N*temp-temp1*temp1;
|
||||
base=temp2*temp2+4.0*N*N*temp1*temp1*temp;
|
||||
Rpart=temp*temp2/base;
|
||||
Ipart=-2.0*N*temp1*(temp^1.5)/base;
|
||||
temp3=real(f(I,J));
|
||||
temp4=imag(f(I,J));
|
||||
fx(I,J)=real(Rpart*temp3-temp4*Ipart)+i*real(Rpart*temp4+Ipart*temp3);
|
||||
|
||||
temp1=-L*U+M*V;
|
||||
temp2=N*N*temp-temp1*temp1;
|
||||
base=temp2*temp2+4.0*N*N*temp1*temp1*temp;
|
||||
Rpart=temp*temp2/base;
|
||||
Ipart=-2.0*N*temp1*(temp^1.5)/base;
|
||||
temp3=real(f(npts-I+1,J));
|
||||
temp4=imag(f(npts-I+1,J));
|
||||
fx(npts-I+1,J)=real(Rpart*temp3-temp4*Ipart)+i*real(Rpart*temp4+Ipart*temp3);
|
||||
|
||||
temp1=L*U-M*V;
|
||||
temp2=N*N*temp-temp1*temp1;
|
||||
base=temp2*temp2+4.0*N*N*temp1*temp1*temp;
|
||||
Rpart=temp*temp2/base;
|
||||
Ipart=-2.0*N*temp1*(temp^1.5)/base;
|
||||
temp3=real(f(I,npts-J+1));
|
||||
temp4=imag(f(I,npts-J+1));
|
||||
fx(I,npts-J+1)=real(Rpart*temp3-temp4*Ipart)+i*real(Rpart*temp4+Ipart*temp3);
|
||||
|
||||
temp1=-L*U-M*V;
|
||||
temp2=N*N*temp-temp1*temp1;
|
||||
base=temp2*temp2+4.0*N*N*temp1*temp1*temp;
|
||||
Rpart=temp*temp2/base;
|
||||
Ipart=-2.0*N*temp1*(temp^1.5)/base;
|
||||
temp3=real(f(npts-I+1,npts-J+1));
|
||||
temp4=imag(f(npts-I+1,npts-J+1));
|
||||
fx(npts-I+1,npts-J+1)=real(Rpart*temp3-temp4*Ipart)+i*real(Rpart*temp4+Ipart*temp3);
|
||||
end;
|
||||
end;
|
||||
fxinv=ifft2(fx); rtpdata=real(fxinv(1+rdiff:nr+rdiff,1+cdiff:nc+cdiff));
|
||||
|
||||
%**************************************************************************
|
||||
function gf=taper2d(g,npts,nc,nr,cdiff,rdiff);
|
||||
|
||||
gf=zeros(npts); gf(rdiff+1:rdiff+nr,cdiff+1:cdiff+nc)=g;
|
||||
for J=cdiff+1:cdiff+nc
|
||||
for I=1:rdiff
|
||||
gf(I,J)=gf(2*rdiff-I+1,J)*((1+sin(-pi/2+(I-1)*pi/rdiff))*0.5);
|
||||
gf(npts-I+1,J)=gf(npts-2*rdiff+I,J)*((1+sin(-pi/2+(I-1)*pi/rdiff))*0.5);
|
||||
end;
|
||||
end;
|
||||
|
||||
for I=rdiff+1:rdiff+nr
|
||||
for J=1:cdiff
|
||||
gf(I,J)=gf(I,2*cdiff-J+1)*((1+sin(-pi/2+(J-1)*pi/(cdiff)))*0.5);
|
||||
gf(I,npts-J)=gf(I,npts-2*cdiff+J)*((1+sin(-pi/2+(J-1)*pi/(cdiff)))*0.5);
|
||||
end;
|
||||
end;
|
||||
|
||||
for J=1:cdiff
|
||||
for I=1:rdiff
|
||||
gf(I,J)=gf(rdiff+1,J)*((1+sin(-pi/2+(I-1)*pi/(rdiff)))*0.5);
|
||||
gf(npts-I,J)=gf(npts-rdiff,J)*((1+sin(-pi/2+(I-1)*pi/(rdiff)))*0.5);
|
||||
end;
|
||||
end;
|
||||
|
||||
for J=cdiff+nc:npts
|
||||
for I=1:rdiff
|
||||
gf(I,J)=gf(rdiff+1,J)*((1+sin(-pi/2+(I-1)*pi/(rdiff)))*0.5);
|
||||
gf(npts-I,J)=gf(npts-rdiff,J)*((1+sin(-pi/2+(I-1)*pi/(rdiff)))*0.5);
|
||||
end;
|
||||
end;
|
||||
Reference in New Issue
Block a user