Kantorovich-Rubinstein metric based level-set methods for inverting modulus of gravity-force data

Abstract

We propose to use the Kantorovich-Rubinstein (K-R) metric as a novel misfit function for the level-set based inverse gravity problems, where modulus of gravity-force data is used. By using the modulus data, we can satisfy the non-negativity requirement of distribution for the K-R metric naturally. Moreover, the K-R metric based level-set method can tolerate high level noise in the modulus data so that we can solve the domain inverse problem of gravimetry to high resolution. We develop the computational framework systematically. Numerical examples demonstrate the performance and effectiveness of the proposed algorithms.