Factorization method in inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves

Guanghui Hu; Andreas Kirsch; Tao  Yin

doi:10.3934/ipi.2016.10.103

Article Contents

2016, Volume 10, Issue 1: 103-129. Doi: 10.3934/ipi.2016.10.103

This issue Previous Article Common midpoint versus common offset acquisition geometry in seismic imaging Next Article The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain

Factorization method in inverse interaction problems with bi-periodic interfaces between acoustic and elastic waves

1.
Weierstrass Institute, Mohrenstr. 39, 10117 Berlin
2.
Department of Mathematics, Karlsruhe Institute of Technology (KIT), 76131 Karlsruhe
3.
College of Mathematics and Statistics, Chongqing University

Received: October 31, 2014

Revised: May 31, 2015

Published: January 2016

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Abstract

Consider a time-harmonic acoustic wave incident onto a doubly periodic (biperiodic) interface from a homogeneous compressible inviscid fluid. The region below the interface is supposed to be an isotropic linearly elastic solid. This paper is concerned with the inverse fluid-solid interaction (FSI) problem of recovering the unbounded periodic interface separating the fluid and solid. We provide a theoretical justification of the factorization method for precisely characterizing the region occupied by the elastic solid by utilizing the scattered acoustic waves measured in the fluid. A computational criterion and a uniqueness result are presented with infinitely many incident acoustic waves having common quasiperiodicity parameters. Numerical examples in 2D are demonstrated to show the validity and accuracy of the inversion algorithm.

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Mathematics Subject Classification: Primary: 74J25; Secondary: 74J20, 35R30, 35Q74.

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References

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