kirk_mig2.m

基于matlab的反演程序,用于地球物理勘探中射线追踪及偏移成像程序.

<<<<<<< kirk_mig2.m
function [arymig,tmig,xmig]=kirk_mig2(aryin,aryvel,dt,dx,params)
%
% [arymig,tmig,xmig]=kirk_mig2(aryin,aryvel,dt,dx,params)
%
% KIRK_MIG2 is a kirchhoff time migration routine.
%
% aryin ... matrix of zero offset data. One trace per column.
% aryvel ... velocity information. The are 3 possibilities:
%            1) if a scalar, then a constant velocity migration with
%               velocity=aryvel is performed.
%            2) if a vector, then it must be the same length as the number
%               of rows in aryin. In this case it is assumed to be an rms 
%               velocity function (of time) which is applied at all positions
%               along the section.
%            3) if a matrix, then it must be the same size as aryin. Here it
%               is assumed to give the rms velocity for each sample location.
% t ... if a scalar, this is the time sample rate in SECONDS.
%       If a vector, it gives the time coordinates for the rows of aryin.
% x ... if a scalar, this is the spatial sample rate (in units 
%       consistent with the velocity information. If a vector, then
%       it gives the x coordinates of the columns of aryin
%
% params ... vector of migration parameters
%
%    params(1--3) : migration aperture and its taper
%       params(1) ... physical length aperture
%	          default is the length of the section in length
%       params(2) ... width of the aperture taper
%                 default is 0.05*params(1)
%       params(3) ... = 0, linear taper
%                     = 1, cosine taper   
%                 default is 1 (cosine taper)
%
%    params(4-6) : angle limit in degree
%       params(4) ... maximum dip limte
%                 default = 60
%       params(5) ... width of angle limit taper
%                 default = 0.15*params(4)
%       params(6) ... taper type:
%                     = 0: linear taper;
%                     = 1: cosine taper.
%                 default = 1.
%
%    params(7) : relative to sample interpolation
%       params(7) ... = 1, linear interpolation
%                     = 2, cubic interpolation
%                     = 3, spline interpolation
%                     = 4, sinc interpolation
%                 default = 1
%
%    params(8--11) : relative to migration target window
%	params(8) ... tmin of migration target window
%	          default = 0.0 
%	params(9) ... tmax of migration target window
%	          default is maximum input time 
%       params(10) ... xm target window
%	          default is the minimum input coordinate 
%       params(11) ... xmax of migration target window
%	          default is the maximum input coordinate 
%
%    params(12) : box-car anti-aliasing filter
%       params(12) ... = 0, no box-car filter used;
%                      = 1, box-car filter will be used.
%                 default is 0.
%
% OUTPUT argument
%
%    arymig ... the output migrated time section
%    tmig ... t coordinates of migrated data
%    xmig ... x coordinates of migrated data
%
% By Xinxiang Li, modified from kirk.m by Dr. G.F. Margrave
% CREWES Project, U of Calgary, 1996
%
% NOTE: It is illegal for you to use this software for a purpose other
% than non-profit education or research UNLESS you are employed by a CREWES
% Project sponsor. By using this software, you are agreeing to the terms
% detailed in this software's Matlab source file.
 
% BEGIN TERMS OF USE LICENSE
%
% This SOFTWARE is maintained by the CREWES Project at the Department
% of Geology and Geophysics of the University of Calgary, Calgary,
% Alberta, Canada.  The copyright and ownership is jointly held by 
% its author (identified above) and the CREWES Project.  The CREWES 
% project may be contacted via email at:  [e-mail]
% 
% The term 'SOFTWARE' refers to the Matlab source code, translations to
% any other computer language, or object code
%
% Terms of use of this SOFTWARE
%
% 1) Use of this SOFTWARE by any for-profit commercial organization is
%    expressly forbidden unless said organization is a CREWES Project
%    Sponsor.
%
% 2) A CREWES Project sponsor may use this SOFTWARE under the terms of the 
%    CREWES Project Sponsorship agreement.
%
% 3) A student or employee of a non-profit educational institution may 
%    use this SOFTWARE subject to the following terms and conditions:
%    - this SOFTWARE is for teaching or research purposes only.
%    - this SOFTWARE may be distributed to other students or researchers 
%      provided that these license terms are included.
%    - reselling the SOFTWARE, or including it or any portion of it, in any
%      software that will be resold is expressly forbidden.
%    - transfering the SOFTWARE in any form to a commercial firm or any 
%      other for-profit organization is expressly forbidden.
%
% END TERMS OF USE LICENSE


[nsamp,ntr]=size(aryin);
[nvsamp,nvtr]=size(aryvel);

% check the validity input arguments

%  ---- check dt  ----
if(length(dt)>1)
	if(length(dt)~=nsamp)
		error('Incorrect time specification')
	end
	t=dt(:);
	[nrow,nvol] = size(t) ;
	if nrow < nvol
		t = t' ;
	end
	dt=t(2)-t(1);
else
 t=((0:nsamp-1)*dt)';
end

%  ---- checck dx ----
if(length(dx)>1)
	if(length(dx)~=ntr)
		error('Incorrect x specification')
	end
	x=dx;
	[nrow,nvol] = size(x) ;
	if nrow > nvol
		x = x' ;
	end
	dx=x(2)-x(1);
else
 x=(0:ntr-1)*dx;
end

%  ---- test velocity info ----

if(nvsamp==1 & nvtr~=1)
	%might be transposed vector
	if(nvtr==nsamp)
		aryvel=aryvel';
	else
		error('Velocity vector is wrong size');
	end
	%make velocity matrix
	aryvel=aryvel*ones(1,ntr);
elseif( nvsamp==1 & nvtr==1)
	aryvel=aryvel*ones(nsamp,ntr);
else
	if(nvsamp~=nsamp)
		error('Velocity matrix has wrong number of rows');
	elseif(ntr~=nvtr)
		error('Velocity matrix has wrong number of columns');
	end
end
%
%ok, we now have a velocity matrix the same size as the data matrix
%

%  ---- examine parameters ----
nparams=12; 				% number of defined parameters
					
if(nargin<5) 				% no parameters inputted
	params= nan*ones(1,nparams); 
end 	 	

if(length(params)<nparams) 
	params = [params nan*ones(1,nparams-length(params))];
end

%assign parameter defaults

if( isnan(params(1)) ) 
	aper = abs(max(x)-min(x));
else
        aper = params(1);
end

if( isnan(params(2)) )
		width1 = aper/20;
else
		width1 = params(2);
end

if( isnan(params(3)) )
		itaper1 = 1;
else
		itaper1 = params(3);
end

if( isnan(params(4)) )
	ang_limit = pi/3;
else
	ang_limit = params(4)*pi/180;
end

if( isnan(params(5)) )
	width2 = 0.15*ang_limit;
else
	width2 = params(5)*pi/180;
end
angle1 = ang_limit + width2;

if( isnan(params(6)) )
	itaper2 = 1;
else
	itaper2 = params(6);
end
if itaper2 ~= 1 & itaper2 ~= 0
	error('the angle limit taper type: params(6) should be 0 and 1 !');
end

if( isnan(params(7)) )
	interp_type = 1;
else
	interp_type = params(7);
end
if interp_type < 1 | interp_type > 4
	error('the interpolation indexx paarams(7) should be 1, 2, 3 and 4 !');
end

if( isnan(params(8)) ) 
		tmig1 = min(t);
else
		tmig1 = params(8);
end

if( isnan(params(9)) ) 
		tmig2 = max(t);
else
		tmig2 = params(9);
end
if tmig2 < tmig1
	error('the target time window start time should be smaller than the end time !');
	error('i.e. paraams(8) < params(9)');
end

if( isnan(params(10)) ) 
		xmig1 = min(x);
else
		xmig1 = params(10);
end
if( isnan(params(11)) ) 
		xmig2 = max(x);
else
		xmig2 = params(11);
end
if xmig2 < xmig1
 	error('the start location of target trace range should be prerior to the end location');
	error('i.e. params(10) < params(11)');
end

if( isnan(params(12)) )
		ibcfilter = 0;
else
		ibcfilter = params(12);
end

if ibcfilter 
	% get a cumulative array from aryin
	arycum=cumsum(aryin);
end
	

%aperture in traces and the taper coefficient
traper0 = .5*aper/dx;
traper1 = width1/dx;
traper = round(traper0+traper1);
if itaper1 == 0
	coef1 = lin_taper(traper0,traper0+traper1);
else
	coef1 = cos_taper(traper0,traper0+traper1);
end

%one way time
dt1=.5*dt;
t1=t/2;
t2= t1.^2;

%compute maximum time needed
vmin=min(min(aryvel));
vmax=max(max(aryvel));
tmax=sqrt( .25*tmig2^2 + ((.5*aper+width1)/vmin)^2);

%pad input to tmaxin
npad=ceil(tmax/dt1)-nsamp+5;
if( npad > 0)
	aryin= [aryin; zeros(npad,ntr)];
	t1 = [t1',(nsamp+1:nsamp+npad)*dt1]';
	if ibcfilter
		for j=1:npad
			arycum=[arycum; arycum(nsamp,:)];
		end
	end
end

%output samples targeted
samptarget=near(t,tmig1,tmig2);
tmig=t(samptarget);

%output traces desired
trtarget= near(x,xmig1,xmig2);
xmig=x(trtarget);

%initialize output array
arymig=zeros(length(samptarget),length(trtarget));

%loop over migrated traces
%
kmig=0;

disp([' ']);
disp([' --- Total number of traces to be migrated : ' int2str(length(trtarget)) ' ---']);
disp([' ']);

flops1=flops;
clock1=clock;

for ktr=trtarget 			% ktr--the location of output trace
	kmig=kmig+1; 			% numerator

	%determine traces in aperture
	n1=max([1 ktr-traper]);
	n2=min([ntr ktr+traper]);
	truse=n1:n2;

	%offsets and velocity 
	offset2=((truse-ktr)*dx).^2;
	v2 = aryvel(:,ktr).^2;
	
	% loop over traces in aperture
	disp([' --- Trace No.' ,int2str(kmig) ,' The traces in aperture : ' ,int2str(length(truse))]);
	for kaper=1:length(truse)
	
		% offset times
		t_aper = sqrt( offset2(kaper)./v2(samptarget) + t2(samptarget) );

		%cosine theta amplitude correction
		if truse(kaper) == ktr
			costheta = ones(size(samptarget'));
			tanalpha = zeros(size(samptarget'));
		else
			costheta = 0.5*tmig./t_aper;
			tanalpha = sqrt(1-costheta.^2);
					
			%angle limit and the taper
		
			ind = find( costheta < cos(angle1) );
			i1 = ind(length(ind));
			ind = find( costheta < cos(ang_limit) );
			i2 = ind(length(ind));
		
			if i1 < i2
			        if itaper2  ==  0
					coef2 = lin_taper(i2,i1);
				else
					coef2 = cos_taper(i2,i1);
				end
				costheta(1:i1) = zeros(i1,1);
				costheta(i1+1:i2) = coef2(i2-i1:-1:1)'.*costheta(i1+1:i2);
			end
		end
	
		% boxcar anti-aliasing filter
		if ibcfilter
			lt0=(dx*tanalpha./aryvel(samptarget,ktr)/dt1);
			indt = (t_aper/dt1)+1;
			lentr = nsamp+npad;
			lt = ones(lentr,1)*max(lt0);
			lt(indt)=lt0;
			lt(max(indt)+1:lentr) = ones(lentr-max(indt),1)*min(lt0);
			it = (1:lentr)';
			l1=it-lt-1;
			l2=it+lt;
			ind = find(l1 < 1);
			l1(ind) = ones(length(ind),1);
			ind = find(l2> lentr);
			l2(ind)=ones(length(ind),1)*lentr;
			tmp0=t1;
			tmp0(1) = arycum(1,truse(kaper));
			ind = 2:lentr;
			tmp0(ind) = (arycum(l2(ind),truse(kaper))-arycum(l1(ind),truse(kaper)))...
				    ./(l2(ind)-l1(ind));
		else
			tmp0 = aryin(:,truse(kaper));
		end	

		%interpolation
		% Linear
		if interp_type == 1
			tnumber = t_aper/dt1;
			it0 = floor( tnumber ) + 1;
			it1 = it0+1; 
			xt0 = tnumber - it0 + 1;
			xt1 = it0-tnumber;
			tmp = xt1.*tmp0(it0)+xt0.*tmp0(it1);
		end
		% Spline
		if interp_type == 2
			tmp = interp1(t1,tmp0,t_aper,'spline');
		end
		% Cubic
		if interp_type == 3
			tmp = interp1(t1,tmp0,t_aper,'cubic');
		end
		% Sinc
		if interp_type == 4
			tmp = sinci(tmp0,t1,t_aper);
		end

		% aperture taper
		ccoef = 1. ;
		if abs(truse(kaper)-ktr)*dx > 0.5*aper
			ccoef = coef1( round(abs(truse(kaper)-ktr)-traper0) );
		end
		if abs(1-ccoef) > 0.05
			tmp = tmp .* ccoef;
		end
		
		ind = find( costheta < 0.999);
		costheta(ind) = sqrt(costheta(ind).^3);
		tmp(ind) = tmp(ind) .* costheta(ind);

		arymig(:,kmig)= arymig(:,kmig)+tmp;
		
	end
	
	% scaling and 45 degree phase shift
	scalemig = aryvel(samptarget,kmig).*sqrt(pi.*(tmig+0.0001)) ;
	arymig(:,kmig) = arymig(:,kmig)./scalemig ;

end

% 45 degree phase shift
arymig = conv45(arymig);
runtime=etime(clock,clock1);


disp(['Total floating operation2 --' int2str(flops2-flops1)]);
disp(['Total run time --' int2str(runtime)]);
=======
function [arymig,tmig,xmig]=kirk_mig2(aryin,aryvel,dt,dx,params)
%
% [arymig,tmig,xmig]=kirk_mig2(aryin,aryvel,dt,dx,params)
%
% KIRK_MIG is a kirchhoff time migration routine.
%
% aryin ... matrix of zero offset data. One trace per column.
% aryvel ... velocity information. The are 3 possibilities:
%            1) if a scalar, then a constant velocity migration with
%               velocity=aryvel is performed.
%            2) if a vector, then it must be the same length as the number
%               of rows in aryin. In this case it is assumed to be an rms 
%               velocity function (of time) which is applied at all positions
%               along the section.
%            3) if a matrix, then it must be the same size as aryin. Here it
%               is assumed to give the rms velocity for each sample location.
% dt ... if a scalar, this is the time sample rate in SECONDS.
%       If a vector, it gives the time coordinates for the rows of aryin.
% dx ... if a scalar, this is the spatial sample rate (in units 
%       consistent with the velocity information. If a vector, then
%       it gives the x coordinates of the columns of aryin
%
% params ... vector of migration parameters
%
%    params(1--3) : migration aperture and its taper
%       params(1) ... physical length aperture
%	          default is the length of the section in length
%       params(2) ... width of the aperture taper
%                 default is 0.05*params(1)
%       params(3) ... = 0, linear taper
%                     = 1, cosine taper   
%                 default is 1 (cosine taper)
%
%    params(4-6) : angle limit in degree
%       params(4) ... maximum dip limte
%                 default = 60
%       params(5) ... width of angle limit taper
%                 default = 0.15*params(4)
%       params(6) ... taper type:
%                     = 0: linear taper;
%                     = 1: cosine taper.
%                 default = 1.
%
%    params(7) : relative to sample interpolation
%       params(7) ... = 1, linear interpolation
%                     = 2, cubic interpolation
%                     = 3, spline interpolation
%                     = 4, sinc interpolation
%                 default = 1
%
%    params(8--11) : relative to migration target window
%	params(8) ... tmin of migration target window
%	          default = 0.0 
%	params(9) ... tmax of migration target window
%	          default is maximum input time 
%       params(10) ... xm target window
%	          default is the minimum input coordinate 
%       params(11) ... xmax of migration target window
%	          default is the maximum input coordinate 
%
%    params(12) : box-car anti-aliasing filter
%       params(12) ... = 0, no box-car filter used;
%                      = 1, box-car filter will be used.
%                 default is 0.
%
% OUTPUT argument
%
%    arymig ... the output migrated time section
%    tmig ... t coordinates of migrated data
%    xmig ... x coordinates of migrated data
%
% By Xinxiang Li, modified from kirk.m by Dr. G.F. Margrave
% CREWES Project, U of Calgary, 1996
%
% NOTE: It is illegal for you to use this software for a purpose other
% than non-profit education or research UNLESS you are employed by a CREWES
% Project sponsor. By using this software, you are agreeing to the terms
% detailed in this software's Matlab source file.
 
% BEGIN TERMS OF USE LICENSE
%
% This SOFTWARE is maintained by the CREWES Project at the Department
% of Geology and Geophysics of the University of Calgary, Calgary,
% Alberta, Canada.  The copyright and ownership is jointly held by 
% its author (identified above) and the CREWES Project.  The CREWES 
% project may be contacted via email at:  [e-mail]
% 
% The term 'SOFTWARE' refers to the Matlab source code, translations to
% any other computer language, or object code
%
% Terms of use of this SOFTWARE
%
% 1) Use of this SOFTWARE by any for-profit commercial organization is
%    expressly forbidden unless said organization is a CREWES Project
%    Sponsor.
%
% 2) A CREWES Project sponsor may use this SOFTWARE under the terms of the 
%    CREWES Project Sponsorship agreement.
%
% 3) A student or employee of a non-profit educational institution may 
%    use this SOFTWARE subject to the following terms and conditions:
%    - this SOFTWARE is for teaching or research purposes only.
%    - this SOFTWARE may be distributed to other students or researchers 
%      provided that these license terms are included.
%    - reselling the SOFTWARE, or including it or any portion of it, in any
%      software that will be resold is expressly forbidden.
%    - transfering the SOFTWARE in any form to a commercial firm or any 
%      other for-profit organization is expressly forbidden.
%
% END TERMS OF USE LICENSE
%flops(0);
[nsamp,ntr]=size(aryin);
[nvsamp,nvtr]=size(aryvel);
% check the validity input arguments
%  ---- check dt  ----
if(length(dt)>1)
	if(length(dt)~=nsamp)
		error('Incorrect time specification')
	end
	t=dt(:);
	[nrow,nvol] = size(t) ;
	if nrow < nvol
		t = t' ;
	end
	dt=t(2)-t(1);
else
 t=((0:nsamp-1)*dt)';
end
%  ---- checck dx ----
if(length(dx)>1)
	if(length(dx)~=ntr)
		error('Incorrect x specification')
	end
	x=dx;
	[nrow,nvol] = size(x) ;
	if nrow > nvol
		x = x' ;
	end
	dx=x(2)-x(1);
else
 x=(0:ntr-1)*dx;
end
%  ---- test velocity info ----
if(nvsamp==1 & nvtr~=1)
	%might be transposed vector
	if(nvtr==nsamp)
		aryvel=aryvel';
	else
		error('Velocity vector is wrong size');
	end
	%make velocity matrix
	aryvel=aryvel*ones(1,ntr);
elseif( nvsamp==1 & nvtr==1)
	aryvel=aryvel*ones(nsamp,ntr);
else
	if(nvsamp~=nsamp)
		error('Velocity matrix has wrong number of rows');
	elseif(ntr~=nvtr)
		error('Velocity matrix has wrong number of columns');
	end
end
%
%ok, we now have a velocity matrix the same size as the data matrix
%
%  ---- examine parameters ----
nparams=12; 				% number of defined parameters
					
if(nargin<5) 				% no parameters inputted
	params= nan*ones(1,nparams); 
end 	 	
if(length(params)<nparams) 
	params = [params nan*ones(1,nparams-length(params))];
end
%assign parameter defaults
if( isnan(params(1)) ) 
	aper = abs(max(x)-min(x));
else
        aper = params(1);
end
if( isnan(params(2)) )
		width1 = aper/20;
else
		width1 = params(2);
end
if( isnan(params(3)) )
		itaper1 = 1;
else
		itaper1 = params(3);
end
if( isnan(params(4)) )
	ang_limit = pi/3;
else
	ang_limit = params(4)*pi/180;
end
if( isnan(params(5)) )
	width2 = 0.15*ang_limit;
else
	width2 = params(5)*pi/180;
end
angle1 = ang_limit + width2;
if( isnan(params(6)) )
	itaper2 = 1;
else
	itaper2 = params(6);
end