Unique recovery of electrical conductivity and magnetic permeability from Magneto-Telluric data

Abstract

We present a comprehensive mathematical study of the Magneto-Telluric (MT) method, on bounded domain in $\mathbb{R}^3$. We show that electrical conductivity and magnetic permeability, assumed to be $C^2$, can be uniquely recovered from MT data measured on the boundary of the domain. The proof is based on the construction of complex geometric optics solutions. Furthermore, we obtain a unique determination result in the case when the MT data are measured only on an open subset of the boundary. Here, we assume that the part of the boundary inaccessible for measurements is a subset of a sphere.