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

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 Schrodinger 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.