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Following definition , and after explicitly
computing the half-aperture angle with equation ,
I have almost all the tools to compute the
P-incidence angle (),
and the S-reflection angle (). Snell's law, and the
P-to-S velocity ratio are the final two components for
this procedure. The final result of this process is
the mapping of the PS-ADCIGs, that are function of the half-aperture angle,
into two angle-gathers. The first one is a function
of the P-incidence angle, I refer to this angle gather as
P-ADCIG. The second angle-gather is a function of the
S-reflection angle to form an S-ADCIG.
After basic algebraic and trigonometric
manipulations, the final two expressions for this mapping are
(Appendix B):
| |
(33) |
| (34) |
Expressions and clearly
show a non-linear relation between the half-aperture angle
and both the incident and reflection angles.
The main purpose of this set of equations is
to observe and analyze the converted-wave angle-gathers
in two different domains each one corresponding to
the incidence angle and the reflection angle.
The analysis of these angle-gathers might help to
obtain residual moveout equations
for both the P-velocity and the S-velocity; therefore,
individual updates for each of the velocity models.
Next: Methodology
Up: Transformation to the angle
Previous: Transformation to the angle
Stanford Exploration Project
12/14/2006