# Kirchhoff migration and diffraction.  (greased lightning)
#
subroutine kirchfast( conj, add,  velhalf, t0,dt,dx, modl,nt,nx, data)
integer ix,iz,it,ih,  conj, add,                          nt,nx,    xstart, xend
real	amp,t,z,h,                velhalf, t0,dt,dx, modl(nt,nx),data(nt,nx)
call conjnull(        conj, add,                     modl,nt*nx, data,nt*nx)
do ih= -nx, nx {	h = dx * ih 			# h = offset
	do iz= 2, nt {	z = t0 + dt * (iz-1)		# z = travel-time depth
			t = sqrt( z**2  +  (h/velhalf)**2 )
			it = 1.5 + (t - t0) / dt
	     if( it > nt )  break
		amp = (z / t)  *  sqrt( nt*dt / t )
		xstart =  1-ih;		xstart = max0(  1, xstart)
		xend   = nx-ih;		xend   = min0( nx, xend)
		if( conj == 0 )
			do ix= xstart, xend
				data(it,ix+ih)=data(it,ix+ih)+modl(iz,ix   )*amp
		else
			do ix= xstart, xend
				modl(iz,ix   )=modl(iz,ix   )+data(it,ix+ih)*amp
		}
	}
return; end