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INVERSE RESONANCE PROBLEM FOR LOVE SEISMIC SURFACE WAVES

Sottile, Samuele LU (2024) In SIAM Journal on Applied Mathematics 84(4). p.1288-1311
Abstract

In this paper, we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb's problem. Using a semiclassical approach, we are able to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schr\"odinger equation with Robin boundary conditions on the half-line. We obtain asymptotic values on the number and the location of the resonances with respect to the wave number. Moreover, we prove that the mapping from real compactly supported potentials to the Jost functions in a suitable class of entire functions is one-to-one and onto and we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
inverse problems, Love surface waves, resonances, Sturm-Liouville problem
in
SIAM Journal on Applied Mathematics
volume
84
issue
4
pages
24 pages
publisher
Society for Industrial and Applied Mathematics
external identifiers
  • scopus:85198007505
ISSN
0036-1399
DOI
10.1137/23M155877X
language
English
LU publication?
yes
id
ea4b742c-bd7e-4511-9503-c855b2ed832e
date added to LUP
2024-09-23 15:35:23
date last changed
2024-09-23 15:35:45
@article{ea4b742c-bd7e-4511-9503-c855b2ed832e,
  abstract     = {{<p>In this paper, we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb's problem. Using a semiclassical approach, we are able to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schr\"odinger equation with Robin boundary conditions on the half-line. We obtain asymptotic values on the number and the location of the resonances with respect to the wave number. Moreover, we prove that the mapping from real compactly supported potentials to the Jost functions in a suitable class of entire functions is one-to-one and onto and we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances.</p>}},
  author       = {{Sottile, Samuele}},
  issn         = {{0036-1399}},
  keywords     = {{inverse problems; Love surface waves; resonances; Sturm-Liouville problem}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1288--1311}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  series       = {{SIAM Journal on Applied Mathematics}},
  title        = {{INVERSE RESONANCE PROBLEM FOR LOVE SEISMIC SURFACE WAVES}},
  url          = {{http://dx.doi.org/10.1137/23M155877X}},
  doi          = {{10.1137/23M155877X}},
  volume       = {{84}},
  year         = {{2024}},
}