A level set method for shape reconstruction in seismic full waveform inversion using a linear elastic model in 2D

We present a novel shape reconstruction technique for seismic full waveform inversion that uses a linear elastic system in 2D for modeling wave propagation in the Earth and a level set technique for performing shape evolution. A cost functional is formulated and minimized by a gradient based descent technique with backtracking line search and an Armijo condition. The three distributed elastic parameter profiles are in our model assumed to follow a given reference profile inside an unknown region D, and a different reference profile outside of D. The task is to reconstruct the unknown region D from seismic data obtained at or close to the surface. We present numerical experiments that address the imaging of salt domes buried in the Earth. The results demonstrate that our new algorithm is able to reconstruct shapes with non-trivial topology from a simpler starting guess in few iterations.