A boundary perturbation method for recovering interface shapes in layered media
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 presc...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Physics Publishing
2012
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| Online Access: | http://hdl.handle.net/1721.1/75751 |
| _version_ | 1811092011850137600 |
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| author | Malcolm, Alison E. Nicholls, David P. |
| author2 | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Malcolm, Alison E. Nicholls, David P. |
| author_sort | Malcolm, Alison E. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:11:30Z |
| format | Article |
| id | mit-1721.1/75751 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:11:30Z |
| publishDate | 2012 |
| publisher | Institute of Physics Publishing |
| record_format | dspace |
| spelling | mit-1721.1/757512022-10-02T01:14:55Z A boundary perturbation method for recovering interface shapes in layered media Malcolm, Alison E. Nicholls, David P. Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Malcolm, Alison E. Malcolm, Alison E. 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. National Science Foundation (U.S.) (DMS-0810958) United States. Dept. of Energy (award no DE-SC0001549) Massachusetts Institute of Technology. Earth Resources Laboratory 2012-12-17T21:36:15Z 2012-12-17T21:36:15Z 2011-08 2011-07 Article http://purl.org/eprint/type/JournalArticle 0266-5611 1361-6420 http://hdl.handle.net/1721.1/75751 Malcolm, Alison, and David P Nicholls. “A Boundary Perturbation Method for Recovering Interface Shapes in Layered Media.” Inverse Problems 27.9 (2011): 095009. Web. en_US http://dx.doi.org/10.1088/0266-5611/27/9/095009 Inverse Problems Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Physics Publishing Malcolm via Michael Noga |
| spellingShingle | Malcolm, Alison E. Nicholls, David P. A boundary perturbation method for recovering interface shapes in layered media |
| title | A boundary perturbation method for recovering interface shapes in layered media |
| title_full | A boundary perturbation method for recovering interface shapes in layered media |
| title_fullStr | A boundary perturbation method for recovering interface shapes in layered media |
| title_full_unstemmed | A boundary perturbation method for recovering interface shapes in layered media |
| title_short | A boundary perturbation method for recovering interface shapes in layered media |
| title_sort | boundary perturbation method for recovering interface shapes in layered media |
| url | http://hdl.handle.net/1721.1/75751 |
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