|
|||||
|
|
| 散射波积分方程的Adomian分解解法 | |
| 引用本文： | 汪燚林, 董良国. 2021. 散射波积分方程的Adomian分解解法. 地球物理学报, 64(10): 3701-3717, doi: 10.6038/cjg2021O0298 |
| 作者姓名： | 汪燚林 董良国 |
| 作者单位： | 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;国家自然科学基金 |
| 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 |
| 收稿时间： | 2020-08-05 |
| 修稿时间： | 2021-02-23 |
Adomian decomposition method of integral equations for scattered waves |
|
| WANG YiLin, DONG LiangGuo. 2021. Adomian decomposition method of integral equations for scattered waves. Chinese Journal of Geophysics (in Chinese), 64(10): 3701-3717, doi: 10.6038/cjg2021O0298 | |
| Authors: | WANG YiLin DONG LiangGuo |
| Affiliation: | State Key Laboratory of Marine Geology, Tongji University, Shanghai 200092, China |
| 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. |
| Keywords: | Scattered waves Lippmann-Schwinger integral equation Ricatti integral equation Adomian decomposition method Born scattering series Rytov scattering series |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |
| 点击此处可从《地球物理学报》浏览原始摘要信息 | |
| 点击此处可从《地球物理学报》下载全文 | |