Smoothing in velocity

To get smoother results I took the time axis to be continuous and the signal value at (t,x) to be distributed between the two points $t_-=t-\Delta t/2$ and $t_+=t+\Delta t/2$.The two time points $t_{\pm}$ and the x-value are mapped to two slownesses $s_{\pm}$.The signal from the (t,x)-pixel is sprayed into the horizontal line $(\tau,s_{\pm})$.To enable you to reproduce the result, I include the program below:

subroutine vspray( conj,  nt,dt,t0,  nx,dx,x0, tx,  ns,ds,s0, zs)
integer conj, it, nt, iz, nz, ix, nx, is, ns, isp, ism
real	tx(nt,nx), zs(nt,ns), scale
real	z,dz,z0, t,dt,t0, x,dx,x0, s,ds,s0, sm,sp, xm,xp, tm,tp
nz=nt;	dz=dt;	z0=t0;
if( conj == 0 ) { do is=1,ns;  do iz=1,nz;  zs(iz,is) = 0.}
else 		{ do ix=1,nx;  do it=1,nt;  tx(it,ix) = 0.}
if( conj == 0)  { do ix=1,nx;  call halfdif ( 1, nt, tx(1,ix), tx(1,ix) )}
do iz=  1, nz {  z = z0 + dz*(iz-1)
do ix=  1, nx {  x = x0 + dx*(ix-1)
do it= iz, nt {  t = t0 + dt*(it-1)
	tm = t-dt/2;	xm = x
	tp = t+dt/2;	xp = x
	sm = (tm**2 -z**2)/xp**2;  ism = 1.5+(sm-s0)/ds
	sp = (tp**2 -z**2)/xm**2;  isp = 1.5+(sp-s0)/ds
	if( ism<2 ) next
	if( isp>ns) next
	scale = sqrt( t / (1.+isp-ism) ) / x
	do is= ism, isp {
		if( conj == 0)
			zs(iz ,is) = zs(iz ,is) + tx(it ,ix) * scale
		else 
			tx(it ,ix) = tx(it ,ix) + zs(iz ,is) * scale
		}
	} } }
if( conj != 0)  { do ix=1,nx;  call halfdif ( 0, nt, tx(1,ix), tx(1,ix) )}
return; end

Figure 5 shows the result on the same inputs as in Figures 3 and 4.

 

vspray4
Figure 5 Horizontal line method. Compare the left to Figure 3 and the right to 4.