Analysis of a model of elastic dislocations in geophysics

We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity of the displacement. We model the Earth as an infinite, isotropic, inhomogeneous, elastic medium occupying a half space, and assume only Lipschitz continuity of the Lamé parameters. We study the well posedness of very weak solutions to the forward problem of determining the displacement by imposing traction-free boundary conditions at the surface of the Earth, continuity of the traction and a given jump on the displacement across the fault. We employ suitable weighted Sobolev spaces for the analysis. We utilize the well-posedness of the forward problem and unique-continuation arguments to establish uniqueness in the inverse problem of determining the dislocation surface and the displacement jump from measuring the displacement at the surface of the Earth. Uniqueness holds for tangential or normal jumps and under some geometric conditions on the surface.

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00205-019-01462-w

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Work Title Analysis of a model of elastic dislocations in geophysics
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Open Access
Creators
  1. Andrea Aspri
  2. Elena Beretta
  3. Anna Mazzucato
  4. Maarten V de Hoop
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Archive for Rational Mechanics and Analysis
Publication Date November 11, 2019
Publisher Identifier (DOI)
  1. https://doi.org/10.1007/s00205-019-01462-w
Deposited May 24, 2024

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Version 1
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  • Created
  • Added DRAFT_23_07v2-1.pdf
  • Added Creator Anna Mazzucato
  • Added Creator Andrea Aspri
  • Added Creator Elena Beretta
  • Added Creator Maarten V de Hoop
  • Published
  • Updated
  • Updated Creator Anna Mazzucato
  • Updated Creator Andrea Aspri
  • Updated Creator Elena Beretta