AVO theory

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, $R\left(\theta\right)$, at normal incidence, at intermediated angles, and at the approach to the critical angle:

 

$$R\left(\theta\right)= R_0 + \left[ A_0R_0 + \frac{ \Delta\si... ...ac{\Delta{V_p}}{V_p} \left( \tan^2\theta - \sin^2\theta \right)$$ (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 $\sin^2\theta$ 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).