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

TL;DR

This paper proves that electrical conductivity and magnetic permeability can be uniquely determined from Magneto-Telluric data on a bounded domain, even with measurements on only part of the boundary, using complex geometric optics solutions.

Contribution

It provides the first rigorous proof of unique recovery of conductivity and permeability from boundary MT data, including partial boundary measurements.

Findings

Unique recovery of conductivity and permeability from boundary data.

Extension of results to partial boundary measurements on a spherical subset.

Use of complex geometric optics solutions for the proof.

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.