Spectral Factorization of Wavefield and Operator in Seismic Inverse Scattering

Abstract

AbstractThe research goal of seismic inverse scattering in this paper is to provide theoretical base for attenuating interior multiple and for suppressing the perturbation effect of seismic wavefield multiple scattering on the primary. This is of great significance for high‐frequency recovery of finely alternating layer's stratigraphic filtering, amplitude preserving elastic wave inversion, diffraction seismic exploration, and interference subtraction in oceanic seismic exploration. Based on up‐ and down‐going wave decomposition and elastic wave power reciprocity theorem, this paper derives, in a lateral velocity varying case, linear prediction operator's expression and the generalized spectral factorization equation for reflection dataset. We express the linear prediction operator, which is defined by the elements of overlaid layers' generalized reflection/transmission matrices, as a linear combination of a series of one‐way wave operators. And the linear prediction equation, under the condition of lateral velocity varying, is expressed as a connecting relation between reflection dataset, the product of linear prediction operator and its inversion. Solving the equation, the linear prediction operator of overlaid layers, then corresponding reflection/transmission operators, can be obtained. Then, the one‐dimensional linear prediction equation of vertical incident wave, under horizontally layered condition, is generalized to an oblique incident case. Using the equation as a reference, the generalized spectral factorization equation of seismic inverse scattering for reflection dataset in a laterally inhomogeneous medium is deduced. The properties of the one‐way wave operator and reflection/transmission operators of seismic inverse scattering are revealed. Numerical results for a horizontally layered medium with inclined incidence are given.