Increasing stability in acoustic and elastic inverse source problems

Abstract

We study increasing stability in the inverse scattering source problem for the Helmholtz equation and the classical Lamé system in the three dimensional space from boundary data at multiple wave numbers. As additional data for source identification we use pressure or displacement at the boundary of the reference domain which are natural and minimal data. By using the Fourier transform with respect to the wave numbers, explicit bounds for analytic continuation, Huygens principle, and sharp bounds for initial boundary value problems, increasing (with larger wave number intervals) stability estimates are obtained.