Uniqueness on recovery of Lamé constants by the same boundary measurement

Abstract

We consider the recovery of Lame constants and an unknown inner core in elastic system. In this paper, we use layer potential technique to represent the solution of the equation and analyze the obtained solution using transmission conditions across the boundary. Firstly, in a single-layer structure, using the same boundary measurements, we utilize the obtained solution to uniquely recover the Lame constant. Then, in a two-layer structure, we also prove a Calderon-type identity and use this identity to uniquely recover the piecewise Lame constant through the same boundary measurements. Finally, we prove that in a two-layer structure, the unique recovery of piecewise Lame constant in the quasi-static regime.