Notice the dark halo around the reconstruction in Figure 3.
It was suppressed in Figure 5 by the subroutine `halfdif()`.
Recall that slant-stack inversion (see IEI for example)
requires an filter.
Without doing any formal analysis I guessed that the same filter
would be helpful here
because the dark halo has a strong spectral component at which would be extinguished by an filter.
Because of the close relation to wave propagation and causality,
I found it appealing to factor into a causal
part and an anticausal
part.
I applied a causal after generating
the (*t*,*x*)-space and an anticausal before making the -space.
I implemented the causality by taking
the square root of a Fourier domain representation
of causal differentiation, namely (1-*Z*)^{1/2}.
The listing of this half-order differentiator is straightforward.

Notice also that `vspray()` includes a scaling variable
named `scale`.
I did not develop a theory for this scale factor,
but if you omit it, amplitudes in the reconstructions
will be far out of amplitude balance with the input.

1/13/1998