INVERSE RESONANCE PROBLEM FOR LOVE SEISMIC SURFACE WAVES
(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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https://lup.lub.lu.se/record/ea4b742c-bd7e-4511-9503-c855b2ed832e
- author
- Sottile, Samuele LU
- organization
- publishing date
- 2024-08
- 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}}, }