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August  2016, 10(3): 641-658. doi: 10.3934/ipi.2016015

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

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

Received  May 2015 Revised  May 2016 Published  August 2016

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.
Citation: Jie Chen, Maarten de Hoop. The inverse problem for electroseismic conversion: Stable recovery of the conductivity and the electrokinetic mobility parameter. Inverse Problems & Imaging, 2016, 10 (3) : 641-658. doi: 10.3934/ipi.2016015
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