A Semismooth Newton-CG Method for Constrained Parameter Identification in Seismic Tomography

Seismic tomography is a technique to determine the material properties of the Earth's subsurface based on the observation of seismograms. This can be stated as a PDE-constrained optimization problem governed by the elastic wave equation. We present a semismooth Newton-PCG method with a trust-region globalization for full-waveform seismic inversion that uses a Moreau-Yosida regularization to handle additional constraints on the material parameters. We establish results on the differentiability of the parameter-to-state operator and analyze the proposed optimization method in a function space setting. The elastic wave equation is discretized by a high-order continuous Galerkin method in space and an explicit Newmark time-stepping scheme. The matrix-free implementation relies on the adjoint-based computation of the gradient and Hessian-vector products and on an MPI-based parallelization. Numerical results are shown for an application in geophysical exploration at reservoir scale.