Figure illustrates the fact that in a v(z) medium, there
exists a single offset xp such that a pegleg with offset x and primary with
offset xp are physically invariant with respect to AVO behavior and, assuming
perfect elasticity in the top layer (often water), to anelastic attenuation.
Since the pegleg multiple and primary in Figure
have the
same emergence angle,
, the time dip, or ``stepout'' of the two events
is the same at x and xp. In Appendix
, I derive
the following expression for xp, where
,
, and
were defined in Section
:
schem-snell
Figure 4 A primary and pegleg multiple with the same emergence angle ( ![]() ![]() | ![]() |
![]() |
(21) |
Figure illustrates application of Snell Resampling to a
synthetic CMP gather. From the Figure, we see that Snell Resampling is an
important vehicle for the exploitation of the additional information contained in
the multiples. Notice how energy from the multiples is spread into the coverage
gaps at near offsets and at 1.0 km offset. Snell Resampling moves energy from
the multiples to the offset corresponding to its reflection angle at the target.
![]() |
Graphically (Figure ), we may infer that the shift in
midpoint,
, of the reflection points of the primary and first-order
pegleg is:
![]() |
(22) |
For peglegs arising from sub-seabed reflectors, the assumption of perfect elasticity for the multiple bounce breaks down. To some extent, however, the additional attenuation suffered by the multiple can, to first order, be treated as a decrease in reflection coefficient.