EIT in a layered anisotropic medium

TL;DR

This paper addresses the inverse problem of imaging layered, possibly anisotropic, subsurface structures in geophysics, focusing on identifying material properties and geometries simultaneously, modeled as nested inclusions.

Contribution

It formulates the geophysical inverse problem as a special case of nested inclusion determination in anisotropic media, advancing the mathematical framework for such imaging tasks.

Findings

Develops a mathematical model for layered anisotropic media

Provides conditions for unique reconstruction of layers and properties

Extends inverse problem theory to complex geophysical structures

Abstract

We consider the inverse problem in geophysics of imaging the subsurface of the Earth in cases where a region below the surface is known to be formed by strata of different materials and the depths and thicknesses of the strata and the (possibly anisotropic) conductivity of each of them need to be identified simultaneously. This problem is treated as a special case of the inverse problem of determining a family of nested inclusions in a medium $\Omega\subset\mathbb{R}^n$, $n \geq 3$.