Zero-offset seismic amplitude decomposition and migration

Abstract

In an anisotropic medium, a normal-incidence wave is multiply transmitted and reflected down to a reflector where the phase velocity vector is parallel to the interface normal. The ray code of the up-going wave is equal to the ray code of the down-going wave in reverse order. The geometrical spreading, KMAH index and transmission and reflection coefficients of the normal-incidence ray can be simply expressed in terms of products or sums of the corresponding quantities of the one-way normal and NIP waves. Here we show that the amplitude of the ray-theoretic Green's function for the reflected wave also follow a similar decomposition in terms of the amplitude of the Green's function of the NIP wave and the normal wave. We use this property to propose three schemes for true-amplitude post-stack depth migration in anisotropic media where the image represents an estimate of the zero-offset reflection coefficient. The first is a map migration procedure in which selected primary zero-offset reflections are converted into depth with attached true amplitudes. The second is a ray-based, Kirchhoff type full migration. Finally, a wave equation continuation algorithm can be used to reverse-propagate the recorded wavefield in a half-velocity model with half the elastic constants and double the density. The image is formed by taking the reverse-propagated wavefield at time equal zero followed by a geometrical spreading correction.