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This appendix presents the derivation of the main
equation for this paper, that is, the transformation
from the subsurface offset domain into the angle domain
for converted-wave data.
Rosales and Biondi (2005) present the
derivation for the angle-domain transformation.
Biondi (2005) and Shragge et al. (2005)
present similar equations for different applications,
for anisotropic case and for the forward-scatter case,
respectively.
Throughout this Appendix we will use the following
defintions:
In this definitions, is the *pseudo-reflection* angle,
and is field for the local image dips. The bases for this
definition resides in the conventional PP case. For that
case, the *pseudo-reflection* angle represents the
reflection angle, and the field represents the
geological dip Fomel (1996).
Based on this definition,
the angle equations from
Biondi (2005); Rosales and Biondi (2005); Shragge et al. (2005)
can be rewritten as:
| |
(6) |

| (7) |

Following basic algebra, equation 7 can be rewritten as:
| |
(8) |

Substituing equation 8 into equation 6,
and following basic algebraic manipulations, we obtain equation 4
in the paper.

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Stanford Exploration Project

4/5/2006