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Direct and inverse time-harmonic elastic scattering from point-like and extended obstacles

Hu, Guanghui and Mantile, Andrea and Sini, Mourad and Yin, Tao (2020) Direct and inverse time-harmonic elastic scattering from point-like and extended obstacles. Inverse Problems and Imaging, 14 (6). pp. 1025-1056. ISSN 1930-8345. doi:10.3934/ipi.2020054.

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This paper is concerned with the time-harmonic direct and inverse elastic scattering by an extended rigid elastic body surrounded by a finite number of point-like obstacles. We first justify the point-interaction model for the Lamé operator within the singular perturbation approach. For a general family of pointwise-supported singular perturbations, including anisotropic and non-local interactions, we derive an explicit representation of the scattered field. In the case of isotropic and local point-interactions, our result is consistent with the ones previously obtained by Foldy's formal method as well as by the renormalization technique. In the case of multiple scattering with pointwise and extended obstacles, we show that the scattered field consists of two parts: one is due to the diffusion by the extended scatterer and the other one is a linear combination of the interactions between the point-like obstacles and the interaction between the point-like obstacles with the extended one. As to the inverse problem, the factorization method by Kirsch is adapted to recover simultaneously the shape of an extended elastic body and the location of point-like scatterers in the case of isotropic and local interactions. The inverse problems using only one type of elastic waves (i.e. pressure or shear waves) are also investigated and numerical examples are presented to confirm the inversion schemes.

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Additional Information:© 2020 American Institute of Mathematical Sciences. Part of this work was finished when G. Hu and A. Mantile visited the Johann Radon Institute for Computational and Applied Mathematics (RICAM) in October, 2019. The hospitality of the institute is appreciated. The authors are grateful to the two anonymous referees for their valuable suggestions and comments, which helped improve this paper. The authors were partially supported by the Austrian Science Fund (FWF) P28971-N32 and the NSFC grant 11671028.
Funding AgencyGrant Number
FWF Der WissenschaftsfondsP28971-N32
National Natural Science Foundation of China11671028
Subject Keywords:Linear elasticity, point-like scatterers, Navier equation, Green's tensor, far field pattern
Issue or Number:6
Classification Code:2020 Mathematics Subject Classification: 74B05, 78A45, 81Q10
Record Number:CaltechAUTHORS:20201214-092120750
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Official Citation:Direct and inverse time-harmonic elastic scattering from point-like and extended obstacles, Inverse Problems & Imaging, 14, 6, 1025-1056, 2020-8-28, Guanghui Hu, Andrea Mantile, Mourad Sini, Tao Yin. DOI: 10.3934/ipi.2020054
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107059
Deposited By: Tony Diaz
Deposited On:14 Dec 2020 20:44
Last Modified:16 Nov 2021 18:59

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