Wavefield extrapolation and amplitude-variation-with-angle migration in highly discontinuous media

Abstract

SUMMARY Current macromodel-based one-way wavefield extrapolation ignores the practical highly discontinuous character of rock formations. The main effects of this highly discontinuous behaviour on transmitted wavefields are angle-dependent dispersion and amplitude losses. In this paper the angle-dependent dispersion and amplitude losses are quantified by a proposed extended macro model, which is closely related to the current macro model except that two stochastic parameters on the rock formations are added. The stochastic parameters are derived based on the observation of power-law behaviour of subsurface heterogeneity. The resulting replacement medium described by the extended macro model is an anisotropic medium with anelastic losses. Explicit extrapolation operators are used to perform forward and inverse wavefield extrapolation in the inhomogeneous replacement medium, which mimics a true subsurface that is moderately inhomogeneous at the macro scale and highly discontinuous at the subwavelength scale. The stability of the inverse wavefield extrapolation is achieved through controlling the maximum angle of propagation. Also a table-driven true-amplitude pre-stack migration scheme is proposed, which can approximately eliminate the dispersion effects of the fine-layering together with the geometrical spreading effects in imaging the subsurface based on the extended macro model. A number of numerical examples are presented to illustrate the algorithms.