INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast

doi:10.1137/21M1430200

	INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast
	LI, Jianliang 2; LI, Peijun 3; Wang, Xu 1,4
刊名	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
	2022
卷号	54 期号:5 页码:5126-5159
关键词	inverse scattering problem elastic wave equation generalized Gaussian random field pseudodifferential operator principal symbol uniqueness
ISSN号	0036-1410
DOI	10.1137/21M1430200
英文摘要	This paper is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a random potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian random field with the covariance operator being described by a classical pseudodifferential operator. The goal is to determine the principal symbol of the covariance operator from the scattered wave measured in a bounded domain which has a positive distance from the domain of the potential. For such a rough potential, the well-posedness of the direct scattering problem in the distribution sense is established by studying an equivalent LippmannSchwinger integral equation. For the inverse scattering problem, it is shown with probability one that the principal symbol of the covariance operator can be uniquely determined by the amplitude of the scattered waves averaged over the frequency band from a single realization of the random potential. The analysis employs the Born approximation in high frequency, asymptotics of the Green tensor for the elastic wave equation, and microlocal analysis for the Fourier integral operators.
资助项目	National Natural Science Foundation of China (NFSC)[12171057] ; National Science Foundation (NSF)[DMS-1912704] ; National Science Foundation (NSF)[DMS-2208256] ; NFSC[11971470] ; NFSC[11871068]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000862265300002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60926]
专题	中国科学院数学与系统科学研究院
通讯作者	LI, Jianliang
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Peoples R China 3.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA 4.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	LI, Jianliang,LI, Peijun,Wang, Xu. INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2022,54(5):5126-5159.
APA	LI, Jianliang,LI, Peijun,&Wang, Xu.(2022).INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,54(5),5126-5159.
MLA	LI, Jianliang,et al."INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 54.5(2022):5126-5159.