** Next:** Application
** Up:** Tisserant and Biondi: 3-D
** Previous:** Definition of the 3-D

We first present the simplest extension to 3-D: the common-azimuth case.
In 2-D, the transformation from offset-gather to angle-gather
is accomplished by applying the relation Sava and Fomel (2000)

| |
(1) |

where is the aperture angle, *k*_{hx} the in-line offset
wavenumber and *k*_{z} the vertical wavenumber.
This relation can be applied in 3-D, but it is then assumed that
the two rays propagate vertically. In 3-D however, rays can propagate
out of the vertical plane. In the common-azimuth assumption, the two
rays propagate within a slanted plane. We call the dip angle
of the slanted propagation plane. The transformation from offset to
angle needs to take into account . The new form of equation
(1) is

| |
(2) |

where *k*_{my} is the cross-line midpoint wavenumber.
We give in Appendix A a geometrical and an analytical derivation
of equation (2). This equation is valid for common-azimuth
migration, that is to say, for an in-line orientation
of the source-receiver axis and for the coplanarity of the source and
receiver rays.

** Next:** Application
** Up:** Tisserant and Biondi: 3-D
** Previous:** Definition of the 3-D
Stanford Exploration Project

7/8/2003