Lippmann-Schwinger积分方程广义超松弛迭代解法及其收敛特性  

The generalized over-relaxation iterative method for Lippmann-Schwinger equation and its convergence

作　　者：徐杨杨[1] 孙建国[1] 商耀达 孟祥羽 魏脯力 XU YangYang;SUN JianGuo;SHANG YaoDa;MENG XiangYu;WEI PuLi(College of Geo-exploration Science and Technology,Jilin University,Changchun 130026,China)

机构地区：[1]吉林大学地球探测科学与技术学院,长春130026

出　　处：《地球物理学报》2021年第1期249-262,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金(41974135)资助.

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.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.

关 键 词：散射 数值模拟 积分方程 超松弛迭代 

分 类 号：P631[天文地球—地质矿产勘探]