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The variation of seismic reflection coefficients with offset can be used
as a direct hydrocarbon indicator Ostrander (1984); Swan (1993), which
is supported in the AVO analysis theory.
The physical relation between the variation of reflection/transmission
coefficients with incident angle (and offset) and rock parameters
has been widely investigated. This relation is established in the Zoeppritz
equations, which relate reflection and transmission coefficients for plane waves
and elastic properties of the medium.
Because of the nonlinearity of the Zoeppritz equations, several approximations
have been generated, such as those presented by Aki and Richards (1997) and
Shuey (1985).
Equation (1) presents Shuey's simplification, which comprises three terms
characterizing the reflection coefficient, , at normal
incidence, at intermediated angles, and
at the approach to the critical angle:

| |
(1) |

The simplified versions of the Zoeppritz equations allow the computation of
AVO inversion to estimate elastic parameters from the observed variation
of reflection amplitude with angle.
From AVO analysis, several attributes can be generated, such as AVO intercept,
which is referred to the normal incidence reflection coefficient, and AVO
gradient, which is the coefficient of in the second term of
equation (1).
In the case of the attributes we use in this work, we call them
AVO-related attributes because
these attributes are not calculated from CMP gathers in the offset
domain but rather from CMP gathers in the offset ray parameter domain.
In this domain, the offset ray parameter is related to the
aperture angle instead of the incident angle Prucha et al. (1999).

** Next:** Seismic Data
** Up:** Introduction
** Previous:** The problem of velocity
Stanford Exploration Project

10/25/1999