The inverse problem for electroseismic conversion: Stable recovery of the conductivity and the electrokinetic mobility parameter

Jie  Chen; Maarten de  Hoop

doi:10.3934/ipi.2016015

Article Contents

2016, Volume 10, Issue 3: 641-658. Doi: 10.3934/ipi.2016015

This issue Previous Article Solving monotone inclusions involving parallel sums of linearly composed maximally monotone operators Next Article Local inverse scattering at fixed energy in spherically symmetric asymptotically hyperbolic manifolds

The inverse problem for electroseismic conversion: Stable recovery of the conductivity and the electrokinetic mobility parameter

Jie Chen^1, and
Maarten de Hoop^2,

1.
8817 234th St. SW, Edmonds, WA 98026
2.
Computational and Applied Mathematics, Rice University, Houston, TX 77005

Received: April 30, 2015

Revised: April 30, 2016

Published: July 2016

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Abstract

Pride (1994, Phys. Rev. B 50 15678-96) derived the governing model of electroseismic conversion, in which Maxwell's equations are coupled with Biot's equations through an electrokinetic mobility parameter. The inverse problem of electroseismic conversion was first studied by Chen and Yang (2013, Inverse Problem 29 115006). By following the construction of Complex Geometrical Optics (CGO) solutions to a matrix Schrödinger equation introduced by Ola and Somersalo (1996, SIAM J. Appl. Math. 56 No. 4 1129-1145), we analyze the recovering of conductivity, permittivity and the electrokinetic mobility parameter in Maxwell's equations with internal measurements, while allowing the magnetic permeability $\mu$ to be a variable function. We show that knowledge of two internal data sets associated with well-chosen boundary electrical sources uniquely determines these parameters. Moreover, a Lipschitz-type stability is obtained based on the same set.

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Mathematics Subject Classification: Primary: 65N21, 35Q61, 35J10.

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