event_pwlinh.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.

function amat=event_pwlinh(amat,t,x,v,xhyp,zhyp,ahyp,flag,dx,noversamp)
% EVENT_PWLINH: diffraction superposition along a piecewise linear track
%
% amat=event_pwlinh(amat,t,x,v,xhyp,zhyp,ahyp,flag,dx,noversamp)
%
% EVENT_PWLINH constructs the exploding reflector response from a piecewise 
% linear structure by superposition of hyperbolae.
%
% amat ... the matrix of size nrows by ncols
% t ... vector of length nrows giving the matrix t coordinates
% x ... vector of length ncols giving the matrix x coordinates
% v ... velocity (scalar)
% xhyp ... vector of x coordinates of piecewise linear structure
% zhyp ... vector of z coordinates of piecewise linear structure
% ahyp ... vector of amplitudes of piecewise linear structure
%    ahyp, xhyp, and zhyp must all be the same size
% flag ... if 1, then amplitudes are divided by cos(theta) where theta is the
%		local dip [tan(theta)=diff(zhyp)./diff(xhyp)]
%				otherwise no effect
%      ******** default = 1 *********
% dx ... nominal spacing of hyperbolae. Between each pair of xhyp, hyperbolae
%		will be placed at this horizontal increment if the local dip is zero. For
%		nonzero dip the horizontal spacing is dx*cos(theta). Setting dx to 0 will
%		cause hyperbolae to be placed only at the exact coordinates in (xhyp,zhyp)
%		and not at interpolated locations.
%      ******** default = abs(x(2)-x(1)) ********
% noversamp ... each output trace is created by nearest-neighbor interpolation into
%		a temporary over-sampled trace that is then properly resampled. The greater the
%		oversampling, the better the result.
%      ******** default = 10 *********
%
% G.F. Margrave, CREWES, 2000
%
% 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

if(nargin<10) noversamp=10; end
if(nargin<9) dx=abs(x(2)-x(1)); end
if(nargin<8) flag=1; end

%loop over columns
%nc= between(xlims(1),xlims(2),x,2);
[nr,nc]=size(amat);

v=v/2;%exploding reflector

tmin=t(1);
tmax=t(length(t));
dt=t(2)-t(1);
dt2=dt/noversamp;
ttmp=tmin:dt2:tmax;

costheta=ones(size(xhyp));
if(flag==1) 
	tantheta=diff(zhyp)./diff(xhyp);
	costh=sqrt(1 ./(1+tantheta.^2));
	%costheta(2:end-1)=.5*(costh(1:end-1)+costh(2:end));
	%costheta(1)=costheta(2);costheta(end)=costheta(end-1);
	costheta(1:end-1)=costh;
	costheta(end)=costh(end);
end

% costheta is intended to be piecewise constant. That is, costheta(k)
% applies to all x such that xhyp(k)<= x < xhyp(k-1)

%ahyp=ahyp./costheta;

%resample such that the samples are dx apart measured along dip

%estimate number of samples needed
if(dx~=0)
	dxest=dx*mean(costheta);
	nxest=round(2*abs(xhyp(end)-xhyp(1))/dxest);
	xh2=nan*1:nxest;

	%calculate new x locations
	nx2=0;
	for k=1:length(xhyp)-1
		x1=xhyp(k);x2=xhyp(k+1);
		dir=sign(x2-x1);
		dxk=dx*costheta(k)*dir;
		if(dir*(x1+dxk)<dir*x2)
			xnext=x1;
			while dir*xnext<dir*x2
				nx2=nx2+1;
				xh2(nx2)=xnext;
				xnext=xnext+dxk;
			end
		else
			nx2=nx2+1;
			xh2(nx2)=x1;
		end
	end

	ind=find(isnan(xh2));
	if(~isempty(ind))
		xh2(ind(1):end)=[];
	end

	%interpolate depths, amplitudes, and dips
	%zh2=interp1(xhyp,zhyp,xh2);
	%ah2=interp1(xhyp,ahyp,xh2);
	zh2=pwlint(xhyp,zhyp,xh2);
	ah2=pwlint(xhyp,ahyp,xh2);
	csth2=pcint(xhyp,costheta,xh2);
else
	xh2=xhyp;
	zh2=zhyp;
	ah2=ahyp;
	csth2=costheta;
end

%adjust amplitudes for dip
ah2=ah2./csth2;
			
tnot=zh2/v;	

for k=1:nc %loop over traces
	trctmp=zeros(size(ttmp))';
	tk=sqrt(tnot.^2+((x(k)-xh2)/v).^2);
	ak=ah2.*tnot.*(tk.^(-1.5));
	ind2=between(tmin,tmax,tk);
	if(ind2~=0)
		ik=round(tk(ind2)/dt2)+1;
		for kh=1:length(ik)
			trctmp(ik(kh))=trctmp(ik(kh))+ak(ind2(kh));
		end
	
		%amat(:,k)=amat(:,k) + resample(trctmp,1,noversamp)/costheta;
		amat(:,k)=amat(:,k) + resample(trctmp,1,noversamp);
	end
end