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Binary recovery via phase field regularization for first-arrival traveltime tomography

Dunbar, Oliver R. A. and Elliott, Charles M. (2019) Binary recovery via phase field regularization for first-arrival traveltime tomography. Inverse Problems, 35 (9). Art. No. 095004. ISSN 0266-5611. https://resolver.caltech.edu/CaltechAUTHORS:20190820-105232050

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Abstract

We propose a double obstacle phase field methodology for binary recovery of the slowness function of an Eikonal equation found in first-arrival traveltime tomography. We treat the inverse problem as an optimization problem with quadratic misfit functional added to a phase field relaxation of the perimeter penalization functional. Our approach yields solutions as we account for well posedness of the forward problem by choosing regular priors. We obtain a convergent finite difference and mixed finite element based discretization and a well defined descent scheme by accounting for the non-differentiability of the forward problem. We validate the phase field technique with a Γ—convergence result and numerically by conducting parameter studies for the scheme, and by applying it to a variety of test problems with different geometries, boundary conditions, and source—receiver locations.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/1361-6420/ab1c6cDOIArticle
https://arxiv.org/abs/1811.02865arXivDiscussion Paper
ORCID:
AuthorORCID
Dunbar, Oliver R. A.0000-0001-7374-0382
Additional Information:© 2019 IOP Publishing Ltd. Published 20 August 2019. The work of CME was partially supported by the Royal Society via a Wolfson Research Merit Award; the work of ORAD and CME by the EPSRC Programme Grant EQUIP.
Funders:
Funding AgencyGrant Number
Royal SocietyUNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)EQUIP
Issue or Number:9
Record Number:CaltechAUTHORS:20190820-105232050
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190820-105232050
Official Citation:Oliver R A Dunbar and Charles M Elliott 2019 Inverse Problems 35 095004
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98037
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Aug 2019 18:28
Last Modified:03 Oct 2019 21:37

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