Dislocations in a layered elastic medium with applications to fault detection
Andrea Aspri
Università degli Studi di Pavia, ItalyElena Beretta
New York University Abu Dhabi, United Arab EmiratesAnna Mazzucato
Penn State University, University Park, USA
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Abstract
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 satisfies certain geometric conditions. These results substantially extend those of the authors in [Arch. Ration. Mech. Anal. 263, 71–111 (2020)].
Cite this article
Andrea Aspri, Elena Beretta, Anna Mazzucato, Dislocations in a layered elastic medium with applications to fault detection. J. Eur. Math. Soc. 25 (2023), no. 3, pp. 1091–1112
DOI 10.4171/JEMS/1243