孙建国,,
商耀达,
孟祥羽,
魏脯力
吉林大学地球探测科学与技术学院, 长春 130026
基金项目: 国家自然科学基金（41974135）资助
详细信息
作者简介: 徐杨杨, 女, 1991年生, 在读博士, 主要从事地震散射波场正演技术与快速算法研究.E-mail:846208564@qq.com
通讯作者: 孙建国, 男, 1956年生, 博士, 教授, 博士生导师, 目前主要从事地下波动理论与成像技术、计算地球物理、科学计算方法与技术、海洋反射地震资料处理、地下天线理论以及岩石物理等方面的教学和研究工作.E-mail:sun_jg@jlu.edu.cn
中图分类号: P631收稿日期:2020-03-16
修回日期:2020-09-09
上线日期:2021-01-10
The generalized over-relaxation iterative method for Lippmann-Schwinger equation and its convergence
XU YangYang,SUN JianGuo,,
SHANG YaoDa,
MENG XiangYu,
WEI PuLi
College of Geo-exploration Science and Technology, Jilin University, Changchun 130026, China
More Information
Corresponding author: SUN JianGuo,E-mail:sun_jg@jlu.edu.cn
MSC: P631--> Received Date: 16 March 2020
Revised Date: 09 September 2020
Available Online: 10 January 2021
摘要
摘要:为克服Born级数只适用于弱散射和短程传播的弱点，从光学散射理论中引入了针对强光学散射问题的Lippmann-Schwinger方程广义超松弛迭代解法，并对这种方法在反射地震条件下的算法表现、收敛特点、计算效率以及计算精度等问题进行了分析和讨论.理论分析和数值计算结果均表明：（1）与散射级数重整化相比，超松弛法具有更坚实的数学基础；（2）超松弛法可以有效地克服Born级数的弱点，得到与有限差分相当的数值模拟结果；（3）在反射地震条件下LS方程超松弛法表现优异，完全可以解决反射地震数值模拟中的强散射问题.
关键词: 散射/
数值模拟/
积分方程/
超松弛迭代
Abstract:To overcome the shortcomings of the traditional Born scattering series,which is only applicable to weak scattering and short-range propagation,we introduce a generalized over-relaxation iterative method for the Lippmann-Schwinger equation from the optical theory. It is a numerical simulation method for strong scattering to solve forward modeling and inversion problems of strong optical scattering. The applicability and convergence characteristics of the over-relaxation method under the condition of seismic reflection were analyzed in this work. Results show that (1) compared with scattering series renormalisation,the over-relaxation method has a more solid mathematics basis. (2) The over-relaxation method can effectively overcome the shortcomings of the Born series and obtain numerical simulation results equivalent to that of the finite-difference method. And (3) under the condition of seismic reflection,the over-relaxation method can be used to fully solve the problem of strong scattering.
Key words:Wave scattering/
Seismic modeling/
Integral equation/
Over-relaxation iteration
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