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Uniqueness for a seismic inverse source problem modeling a subsonic rupture

de Hoop, MV; Oksanen, L; Tittelfitz, J; (2016) Uniqueness for a seismic inverse source problem modeling a subsonic rupture. Communications in Partial Differential Equations , 41 (12) pp. 1895-1917. 10.1080/03605302.2016.1240183. Green open access

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Abstract

We consider an inverse source problem for an inhomogeneous wave equation with discrete-in-time sources, modeling a seismic rupture. The inverse source problem, with an arbitrary source term on the right-hand side of the wave equation, is not uniquely solvable. Here we formulate conditions on the source term that allow us to show uniqueness and that provide a reasonable model for the application of interest. We assume that the source term is supported on a finite set of times and that the support in space moves with subsonic velocity. Moreover, we assume that the spatial part of the source is singular on a hypersurface, an application being a seismic rupture along a fault plane. Given data collected over time on a detection surface that encloses the spatial projection of the support of the source, we show how to recover the times and locations of sources microlocally and then reconstruct the smooth part of the source assuming that it is the same at each source location.

Type: Article
Title: Uniqueness for a seismic inverse source problem modeling a subsonic rupture
Open access status: An open access version is available from UCL Discovery
DOI: 10.1080/03605302.2016.1240183
Publisher version: http://dx.doi.org/10.1080/03605302.2016.1240183
Language: English
Additional information: Copyright © 2016 Taylor & Francis. This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Partial Differential Equations on 28 September 2016, available online: http://dx.doi.org/10.1080/03605302.2016.1240183
Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Geophysics, inverse problems, partial differential equations, wave equation, Source-scanning Algorithm, Thermoacoustic Tomography, Earthquake Sources, Hyperbolic Problem, Speed, Theorem, Continuation, Radiation, Boundary, Valley
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI: https://discovery.ucl.ac.uk/id/eprint/1535200
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