** Next:** A Kirchhoff perspective for
** Up:** Imaging of converted-wave Ocean-bottom
** Previous:** PS angle-domain transformation

# Mapping of PS-ADCIGs

This appendix presents the derivation for the equations that allow to
map the existing PS-ADCIGs that are a function of the
half-aperture angle into two angle-domain common-image gathers.
The first angle gather is a function of the P-incidence angle,
the second angle gather depends on the S-reflection angle.
The first element to obtain these mapping equations
is Snell's law:

| |
(72) |

The angles and are the incidence and
reflection angles, respectively.
From the definition of the *full-aperture* angle, ,(equation ), I obtain the following:
| |
(73) |

| (74) |

Introducing equations and
into equation ,
and using the P-to-S velocity ratio (), I obtain:

| |
(75) |

| (76) |

Using simple trigonometric relations and basic algebra,
from equations and , I get, respectively,

| |
(77) |

| (78) |

Equations and translate into
equations and , in Chapter 3.

** Next:** A Kirchhoff perspective for
** Up:** Imaging of converted-wave Ocean-bottom
** Previous:** PS angle-domain transformation
Stanford Exploration Project

12/14/2006