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I produce angle gathers for shot-profile migrations by combining
de Bruin et al.'s 1990 approach with that of
Sava and Fomel (2000).
Rather than extracting a single zero-offset/zero-time reflectivity
image, I extract multiple zero-time images with a range of offsets.
In 2-D this can be performed with the following sum over frequency:
| |
(128) |

Gathers produced this way contain off-diagonal elements of Berkhout's
reflectivity matrix 1985, and are equivalent to those
produced by imaging multiple non-zero offsets in an offset-midpoint
shot-geophone migration.
Consequently, the offset axes can be mapped to angle with Sava
and Fomel's 2000 transformation, which is
based on the relationship
| |
(129) |

where is the half-opening angle.
The imaging condition (*t*=0) provides the constant *t*, and the
common midpoint nature of CIGs provides the constant *x*, allowing
to be obtained directly from CIGs.

** Next:** Shot to midpoint transformations
** Up:** Common-image gathers for shot-profile
** Previous:** Introduction
Stanford Exploration Project

5/27/2001