董良国,
同济大学海洋地质国家重点实验室, 上海 200092
基金项目: 国家重点研发计划深海关键技术与装备重点专项（2019YFC0312004）和国家自然科学基金项目（41874127）联合资助
详细信息
作者简介: 汪燚林, 男, 1997年生, 同济大学地球物理学专业博士研究生, 主要从事地震波传播数值模拟与地震波反演等方面的研究.E-mail: yilin_wang1997@tongji.edu.cn
通讯作者: 董良国, 男, 教授, 博士生导师, 主要从事地震波传播理论与数值模拟、地震波反演等方面的研究.E-mail: dlg@tongji.edu.cn
中图分类号: P631收稿日期:2020-08-05
修回日期:2021-02-23
上线日期:2021-10-10
Adomian decomposition method of integral equations for scattered waves
WANG YiLin,DONG LiangGuo,
State Key Laboratory of Marine Geology, Tongji University, Shanghai 200092, China
More Information
Corresponding author: DONG LiangGuo,E-mail:dlg@tongji.edu.cn
MSC: P631--> Received Date: 05 August 2020
Revised Date: 23 February 2021
Available Online: 10 October 2021
摘要
摘要: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.
关键词: 散射波/
Lippmann-Schwinger积分方程/
Ricatti积分方程/
Adomian分解方法/
Born散射序列/
Rytov散射序列
Abstract: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.
Key words:Scattered waves/
Lippmann-Schwinger integral equation/
Ricatti integral equation/
Adomian decomposition method/
Born scattering series/
Rytov scattering series
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