Inverse problem of electroseismic conversion. I: Inversion of Maxwells equations with internal data

Pride (1994, Phys. Rev. B 50 15678-96) derived the governing model of electroseismic conversion, in which Maxwells equations are coupled with Biots 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 reconstruction of conductivity, permittivity and the electrokinetic mobility parameter in Maxwells 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 electric sources uniquely determines these parameters. Moreover, a Lipschitz-type stability is obtained based on the same set.