Sharp-interface imaging in full waveform inversion using finite elements

Summary In this work we present an optimization methodology that inverts for the sharp interface of a salt body by recasting full waveform inversion as a shape optimization problem. In this framework, a shape representing the salt body can morph throughout the optimization process while preserving the model discontinuity between the salt and background sediment. We employ a distributed expression of the shape derivative instead of a boundary expression; this allows working with non-smooth domains, low regularity functions and often offers better accuracy than the boundary expression for numerical approximation. For a better resolution of these sharp interfaces, we utilize a finite element method with unstructured triangular meshes and variable mesh resolution to solve the optimization problem. All developments are available in an open-source coding package called spyro which uses the finite element library Firedrake.