Inverse Problem of Electro-seismic Conversion

TL;DR

This paper addresses the inverse problem in electro-seismic conversion, demonstrating unique and stable reconstruction of conductivity and electro-kinetic mobility parameters from internal measurements derived from coupled Maxwell and Biot equations.

Contribution

It provides a theoretical analysis of parameter reconstruction in electro-seismic models, establishing uniqueness and stability results for the inverse problem.

Findings

Unique determination of conductivity and electro-kinetic mobility parameters.

Lipschitz stability of the reconstruction process.

Reconstruction based on internal measurements from coupled equations.

Abstract

When a porous rock is saturated with an electrolyte, electrical fields are coupled with seismic waves via the electro-seismic conversion. Pride derived the governing models, in which Maxwell equations are coupled with Biot equations through the electro-kinetic mobility parameter. The inverse problem of the linearized electro-seismic conversion consists in two step, namely the inversion of Biot equations and the inversion of Maxwell equations. We analyze the reconstruction of conductivity and electro-kinetic mobility parameter in Maxwell equations with internal measurements, while the internal measurements are provided by the results of the inversion of Biot equations. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determine these two parameters. Moreover, a Lipschitz type stability is proved based on the same sets of well-chosen boundary conditions.