INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES

doi:10.1137/16M1088922

	INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES
	Bao, Gang 1; Chen, Chuchu2 ; Li, Peijun 3
	2017
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	55 期号:6 页码:2616-2643
摘要	This paper is concerned with the direct and inverse random source scattering problems for elastic waves, where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the displacement of the random wave field. The inverse problem is to reconstruct the mean and variance of the random source from the boundary measurement of the wave field at multiple frequencies. The direct problem is shown to have a unique mild solution by using a constructive proof. Based on the explicit mild solution, Fredholm integral equations of the first kind are deduced for the inverse problem. The regularized block Kaczmarz method is developed to solve the ill-posed integral equations. The convergence is proved for the method. Numerical experiments are shown to demonstrate the effectiveness of the proposed method.
关键词	inverse source scattering problem elastic wave equation stochastic partial differential equation Fredholm integral equation
DOI	10.1137/16M1088922
语种	英语
资助项目	Key Project of the Major Research Plan of NSFC[91130004] ; NSFC A3 project[11421110002] ; NSFC Tianyuan project[11426235] ; NSFC Tianyuan project[11526211] ; NSFC Innovative Group Fund[11621101] ; Zhejiang University ; NSFC[91130003] ; NSFC[11021101] ; NSFC[11290142] ; NSF grant[DMS-1151308]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000418663500005
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/27089
专题	计算数学与科学工程计算研究所
通讯作者	Li, Peijun
作者单位	1.Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
推荐引用方式 GB/T 7714	Bao, Gang,Chen, Chuchu,Li, Peijun. INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(6):2616-2643.
APA	Bao, Gang,Chen, Chuchu,&Li, Peijun.(2017).INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(6),2616-2643.
MLA	Bao, Gang,et al."INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.6(2017):2616-2643.