Although the use of the critical horizontal slowness to perform the separation between P and S waves is effective for shallow reflectors, the finite size of the cable restricts its application to deep reflectors because a converted wave with horizontal slowness larger than the P wave critical slowness will be received at very large offsets.

A possible way to overcome the limitations associated with
the finiteness of the field aperture is to use a criterion
that somehow takes into account the depth of the reflector.
Transforming the data into the *- p * domain provides
the necessary flexibility for use of a variable slowness cutoff.
Tatham and Goolsbee (1984) showed also that better
results can be achieved when a hyperbolic velocity filtering is used
during the -

As we will see, the separation of the data into ranges of *Snell rays *
would seem to be another appropriate way to perform the
slowness filtering with a variable-slowness cutoff.

A Snell ray (Ottolini, 1982) can be defined for a plane-layered
earth as a ray that keeps a constant horizontal slowness (obeys the Snell
law) while it propagates through the subsurface,
as illustrated in Figure . The reflection
points corresponding to a Snell ray with ray parameter (or horizontal
slowness) *p* are defined by

For the simple case of a plane-layered earth, the horizontal slowness of a
P wave will always be lower than the horizontal slowness of a converted
wave recorded at the same position in the *x-t * domain.
It is possible then to choose a set of ray parameters and
divide the data into regions whose P waves Snell rays are
limited by two adjacent values (Figure ).
Since the converted waves inside each region will have higher horizontal
slownesses than the P waves, a different filter can be applied
to each region; the cutoff value is given by the ray parameter
of the Snell ray that defines the upper limit of that region.

1/13/1998