A shape derivative algorithm for reconstructing elastic dislocations in geophysics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914965738225664 |
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| author | Aspri, Andrea Beretta, Elena Lee, Arum Mazzucato, Anna |
| author_facet | Aspri, Andrea Beretta, Elena Lee, Arum Mazzucato, Anna |
| contents | We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a distributed as well as a boundary shape derivative that encodes the change in a misfit functional between the measured and the computed surface displacement under infinitesimal movements of the dislocation and infinitesimal changes in the slip vector, which gives the displacement jump across the dislocation. We employ the shape derivative in an iterative reconstruction algorithm. We present some numerical test of the reconstruction algorithm in a simplified 2D setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04273 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A shape derivative algorithm for reconstructing elastic dislocations in geophysics Aspri, Andrea Beretta, Elena Lee, Arum Mazzucato, Anna Analysis of PDEs 35R30, 74G75, 65N30 We consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a distributed as well as a boundary shape derivative that encodes the change in a misfit functional between the measured and the computed surface displacement under infinitesimal movements of the dislocation and infinitesimal changes in the slip vector, which gives the displacement jump across the dislocation. We employ the shape derivative in an iterative reconstruction algorithm. We present some numerical test of the reconstruction algorithm in a simplified 2D setting. |
| title | A shape derivative algorithm for reconstructing elastic dislocations in geophysics |
| topic | Analysis of PDEs 35R30, 74G75, 65N30 |
| url | https://arxiv.org/abs/2410.04273 |