二阶Born近似及其在逆散射GRT反演中的应用

Second-order Born approximation and its application to inverse scattering GRT inversion

传统的地震逆散射广义Radon变换(GRT)保幅反演方法是建立在散射场一阶Born近似(单散射)的基础上,仅仅适用于弱扰动介质模型.本文从散射场积分方程出发,通过研究二次散射的特征,讨论和验证了基于局部二阶Born近似的GRT非线性保幅反演方法,将传统GRT线性保幅反演算子的适用范围扩展至非均匀强扰动介质.数值测试结果表明:在散射场近似模拟方面,二阶Born近似比一阶Born近似更为准确,二次散射效应主要集中在主散射点周围的局部区域内,超过这一范围,二次散射强度趋于稳定;在保幅反演方面,本文基于局部二阶Born近似的GRT非线性反演算法,明显优于传统的GRT线性反演算法,可以准确重构强扰动介质模型,而计算效率与线性反演方法相当.

The traditional seismic inverse scattering migration inversion is based on single-scattering （Born） approximation of scattered wavefield,which is only valid for weak-perturbation medium. In this paper,starting from investigating the characteristics of double scattering,we discuss and validate an amplitude-preserved nonlinear inversion method with generalized Radon transform （GRT）,which is based on local second-order Born approximation. With this nonlinear inversion approach,the application of classical GRT linear true-amplitude inversion operator is extended to inhomogeneous medium with strong perturbation. The experimental results show that the second-order Born approximation of scattered wavefield is more accurate than the Born approximation,and the effective contribution of double scattering is mainly within a local area. The GRT nonlinear approach can reconstruct strong-perturbation medium and provide more accurate amplitude restoration than the GRT linear inversion algorithm with the same computational complexity.