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 vspray() subroutine. 

subroutine vspray( adj,  nt,dt,t0,  nx,dx,x0, tx,  ns,ds,s0, zs)
integer adj, 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;
call adjnull( adj, 0,              tx, nt*nx,     zs, nz*ns)
if( adj == 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) ) / ( abs(x) + abs(dx)/2.)
        do is= ism, isp {
                if( adj == 0)
                        zs(iz ,is) = zs(iz ,is) + tx(it ,ix) * scale
                else 
                        tx(it ,ix) = tx(it ,ix) + zs(iz ,is) * scale
                }
        } } }
if( adj != 0)  { do ix=1,nx;  call halfdif ( 0, nt, tx(1,ix), tx(1,ix) )}
return; end

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

 

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