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We propose a double obstacle phase field methodology for binary recovery ofthe slowness function of an Eikonal equation found in first traveltimetomography. We treat the inverse problem as an optimization problem withquadratic misfit functional added to a phase field relaxation of the perimeterpenalization functional. Our approach yields solutions as we account for wellposedness of the forward problem by choosing regular priors. We obtain aconvergent finite difference and mixed finite element based discretization anda well defined descent scheme by accounting for the non-differentiability ofthe forward problem. We validate the phase field technique with a $\Gamma$ -convergence result and numerically by conducting parameter studies for thescheme, and by applying it to a variety of test problems with differentgeometries, boundary conditions, and source - receiver locations.

Binary recovery via phase field regularization for first traveltime tomography