In a previous report, Sava and Fomel (2000) presented a method for computing angle-domain common-image gathers by a radial-trace transform in the Fourier domain. The method converts offset-domain common-image gathers, which are computed using 2-D prestack wave-equation migration Prucha et al. (1999) into true reflection angle-domain common-image gathers.
Obtaining the output images in angle-domain is very attractive for amplitude versus angle (AVA) analysis. However, because the application of AVA analysis is to detect anomalous amplitude behavior, we need to understand how the relative amplitudes are affected by the method in order to guarantee that the method itself is not a source of amplitude distortions.
According to the AVA analysis theory, the variation of seismic reflection coefficients with angle (and offset) can be used as a direct hydrocarbon indicator Ostrander (1984); Swan (1993). The physical relationship between the variation of reflection/transmission coefficients with incident angle and rock parameters has been widely investigated. This relationship is established in the Zoeppritz equations Mavko et al. (1998), which relate reflection and transmission coefficients for plane waves and elastic properties of the medium.
In this note, I investigate the amplitude behavior of angle gathers using two synthetic data sets. I compare the resulting amplitudes from angle-domain common-image gathers with the amplitudes from offset-ray parameter images obtained using two different approaches: prestack wave-equation migration Prucha et al. (1999) and migration/inversion Prucha et al. (2000).