地震逆散射波场和算子的谱分解

Spectral factorization of wavefield and operator in seismic inverse scattering

本文对地震逆散射的研究,旨在于为抑制层间多次波和地震波场多重散射对一次反射干扰效应提供理论依据.这对薄互层地层滤波的高频恢复、保幅弹性反演、衍射地震勘探及海洋地震勘探中的干扰消除皆具重要意义.本文基于上下行波分解及弹性波互易定理,导出横向变速介质条件下线性预测算子的表达式和反射数据的广义谱分解方程.文中先由上覆地层广义反射透射矩阵的元素定义线性预测算子,并将其表示成一系列单程波算子的线性组合,之后将横向变速介质条件下线性预测方程表达为反射数据与线性预测算子及其逆的乘积.对该方程的求解可获得上覆地层的线性预测算子,从而可借以求出相应的反射透射算子.本文先将水平层状介质条件下垂直入射的一维线性预测方程推广到斜入射的情况,以此为参照,导出横向非均匀介质条件下反射数据的地震逆散射广义谱分解方程.文中也揭示了单程波地震逆散射算子、反射透射算子的性态.本文还针对水平层状介质条件,给出斜入射的数值结果.

The 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 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 the 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 layer＇s 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 oblique incident case. Using the equation as a reference, the generalized spectral factorization equation of seismic inverse scattering for reflection dataset in a lateral 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 horizontally layered media with inclined incidence are given.