散射波积分方程的Adomian分解解法

Adomian decomposition method of integral equations for scattered waves

在背景模型基础上,求解模型扰动后的地震波散射场,这是目前地震反演中的一个关键步骤.本文将计算数学中求解非线性积分方程的Adomian分解方法,应用到求解标量波散射场的Lippmann-Schwinger积分方程和Ricatti积分方程中,分别得到了散射场的Born序列解和Rytov序列解.通过一维和二维数值算例说明:在满足一定的条件下,散射场的这两种序列解稳定收敛,与传统的Born和Rytov近似解相比,引入散射序列中的高阶项可以更精确地描述地震波散射场.

During the seismic inversion,it is a key step to calculate the scattered waves after the media is perturbed.In this paper,the Adomian decomposition method for solving the integral equations in computational mathematics is applied to solve the Lippmann-Schwinger integral equation and Ricatti integral equation in seismology.As a result,the Born and Rytov scattering series solutions for the scattered waves are obtained.Numerical examples in both one and two dimensions show that these scattering series are convergent under some certain conditions.Meanwhile,compared to the conventional Born and Rytov approximate solutions,it is more accurate to describe the scattered waves under some conditions if the higher-order terms in Born or Rytov scattering series are included.