WKBJ - Compute WKBJ ray theoretic parameters, via finite differencing    

 wkbj <vfile >tfile nx= nz= xs= zs= [optional parameters]        

 Required Parameters:                                      
 <vfile     file containing velocities v[nx][nz]                 
 nx=        number of x samples (2nd dimension)            
 nz=        number of z samples (1st dimension)            
 xs=        x coordinate of source                         
 zs=        z coordinate of source                         

 Optional Parameters:                                      
 dx=1.0           x sampling interval                     
 fx=0.0           first x sample                          
 dz=1.0           z sampling interval                     
 fz=0.0           first z sample                          
 sfile=sfile      file containing sigmas sg[nx][nz]              
 bfile=bfile      file containing incident angles bet[nx][nz]          
 afile=afile      file containing propagation angles a[nx][nz]         

 Notes:                                              
 Traveltimes, propagation angles, sigmas, and incident angles in WKBJ  
 by finite differences  in polar coordinates. Traveltimes are calculated
 by upwind scheme; sigmas and incident angles by a Crank-Nicolson scheme.

 Credits:
      CWP: Zhenyue Liu, Dave Hale, pre 1992.