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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2004.00321 |
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| _version_ | 1866912221442867200 |
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| author | Aspri, Andrea Beretta, Elena Mazzucato, Anna L. |
| author_facet | Aspri, Andrea Beretta, Elena Mazzucato, Anna L. |
| contents | We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting mixed-boundary-value-transmission problem, assuming only bounded elastic moduli. We establish uniqueness in the inverse problem of determining the fault surface and the slip from a unique measurement of the displacement on an open patch at the surface, assuming in addition that the Earth's crust is an isotropic, layered medium with Lamé coefficients piecewise Lipschitz on a known partition and that the fault surface is a graph with respect to an arbitrary coordinate system. These results substantially extend those of the authors in {Arch. Ration. Mech. Anal.} {\bf 263} (2020), n. 1, 71--111. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_00321 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Dislocations in a layered elastic medium with applications to fault detection Aspri, Andrea Beretta, Elena Mazzucato, Anna L. Analysis of PDEs We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting mixed-boundary-value-transmission problem, assuming only bounded elastic moduli. We establish uniqueness in the inverse problem of determining the fault surface and the slip from a unique measurement of the displacement on an open patch at the surface, assuming in addition that the Earth's crust is an isotropic, layered medium with Lamé coefficients piecewise Lipschitz on a known partition and that the fault surface is a graph with respect to an arbitrary coordinate system. These results substantially extend those of the authors in {Arch. Ration. Mech. Anal.} {\bf 263} (2020), n. 1, 71--111. |
| title | Dislocations in a layered elastic medium with applications to fault detection |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2004.00321 |