A boundary perturbation method for recovering interface shapes in layered media
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Malcolm - boundary.pdf
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191.18 KB
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Author(s)
Malcolm, Alison E.
Nicholls, David P.
Date Issued
August 2011
Journal
Inverse Problems
Publisher
Institute of Physics Publishing
Citation
Malcolm, Alison, and David P Nicholls. “A Boundary Perturbation Method for Recovering Interface Shapes in Layered Media.” Inverse Problems 27.9 (2011): 095009. Web.
Version
Author's final manuscript
Abstract
The scattering of linear acoustic radiation by a periodic layered structure is a fundamental model in the geosciences as it closely approximates the propagation of pressure waves in the earth's crust. In this contribution, the authors describe new algorithms for (1) the forward problem of prescribing incident radiation and, given the known structure, determining the scattered field, and (2) the inverse problem of approximating the form of the structure given prescribed incident radiation and measured scattered data. Each of these algorithms is based upon a novel statement of the problem in terms of boundary integral operators (Dirichlet–Neumann operators), and a boundary perturbation algorithm (the method of operator expansions) for their evaluation. Detailed formulas and numerical simulations are presented to demonstrate the utility of these new approaches.
MIT Department
Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1088/0266-5611/27/9/095009
