Binary recovery via phase field regularization for first-arrival traveltime tomography. (20th August 2019)

• Record Type: Journal Article
• Authors: Dunbar, Oliver R A; Elliott, Charles M
• Is Part Of: Inverse problems. Volume 35:Number 9(2019)
• Publication Date: 2019-08-20
• Subjects: seismic tomography -- binary recovery -- phase field -- finite elements -- Eikonal equation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ab1c6c
• Languages: English
• ISSNs: 0266-5611

Abstract

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 —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.