function [K]=ray_kernel(r_path,t_phase,R,r,w,cs,wcs);
% MATLAB HELP:
%
% function [K]=ray_kernel(r_path,t_phase,R,r,w,cs,wcs);
%
% inputs:
%  r_path, radius along the ray
%  t_phase, phase time along the ray
%  R, solar radius
%  r, radius grid
%  w, frequency of the ray
%  cs, square of the sound speed
%  wcs, square of the acoustic cutoff frequency
%
% output:
%  K, travel-time kernel for the square of the sound speed
%
% see ray_codes.ps for more details
%
% aaron birch may 22 2002


%
% square of the sound speed along the path
%
c_path=interp1(r,sqrt(cs),r_path);

%
% have to be careful about the twos here,
% we want a kernel for the perturbation to the
% the travel time by pert. to SQUARE of sound speed
%
K=-R*(1+wcs./(w^2-wcs)).*interp1(r_path,gradient(t_phase,r_path),r);

%
% put zeros below the lower turning point
%
I=find(isnan(K));K(I)=zeros(size(I));