burg.m

Univ. of Calgary CREWS的免费地震研究软件

function [specb,fb]=burg(trin,t,lc,n)

% [specb,fb]= burg(trin,t,lc,n)
% [specb,fb]= burg(trin,t,lc)
%
% Returns a the Burg (Maximum Entropy) amplitude spectral estimate. 
% If the input trace (time series) is actually a matrix, then one
% trace per column is assumned and this routine
% will compute an ensemble Burg spectrum by averaging the prediction
% filters.
%
% trin= input trace or trace matrix. If a single trace, it is best
% 	to use a column vector. Must be regularly sampled.
% t= time coordinate vector for trin. Should be a column vector with
%	the same number of rows as trin.
% lc= number of points in prediction filter (number of
%     significant spectral features?)
% n= number of points in final Burg spectral estimate
%    *********** default = length(trin/2+1) ************
% specb= Burg amplitude spectrum
% fb= frequency coordinate vector for specb
%
% adapted from Claerbout 1976: Fundamentals of Geophysical Data
% Processing, p 137
%
% by G.F. Margrave, May 1991
%
% 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
 
% set defaults
 if nargin<4
  n=length(trin);
 end
%
 specb=zeros(1,n);
 lx=max(size(trin));
 ntraces=min(size(trin));
 [n1,n2]=size(trin);
 if n2==ntraces, trin=trin.';end
 %[lx,ntraces]=size(trin);
% loop over traces in the ensemble
sbar= zeros(1,lc);
for itr=1:ntraces,
%
 a=[1.0 zeros(1,lc-1)];
 c=zeros(1,lc);
 em=trin(itr,:);
 ep=trin(itr,:);
 for j=2:lc
   bot=ep(j:lx)*ep(j:lx)'+em(1:lx-j+1)*em(1:lx-j+1)';
   top=ep(j:lx)*em(1:lx-j+1)';
   c(j)=2.*top/bot;
   epp=[ep(1:j-1) ep(j:lx)-c(j)*em(1:lx-j+1)];
   em=[em(1:lx-j+1)-conj(c(j))*ep(j:lx) em(lx-j+2:lx)];
   ep=epp;
   s(1:j)=a(1:j)-c(j)*conj(a(j:-1:1));
   a(1:j)=s(1:j);
 end
 sbar=sbar+s;
end
% here ends the ensemble loop
 sbar=sbar/ntraces;
 %[spec,fb]=fftrl(sbar,t(1:length(sbar)),0,2*(n-1));
 [spec,fb]=fftrl(sbar,t(1:length(sbar)),0,n);
 specb=1. ./abs(spec);
 
 %impose parseval's relation
 specb=specb*norm(trin)/norm(specb);