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Register a new userInverse problem of electroseismic conversion. I: Inversion of Maxwells equations with internal data
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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.
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The electroseismic model describes the coupling phenomenon of the electromagnetic waves and seismic waves in fluid immersed porous rock. Electric parameters have better contrast than elastic parameters while seismic waves provide better resolution because of the short wavelength. The combination of theses two different waves is prominent in oil exploration. Under some assumptions on the physical parameters, we derived a Holder stability estimate to the inverse problem of recovery of the electric parameters and the coupling coefficient from the knowledge of the fields in a small open domain near the boundary. The proof is based on a Carleman estimate of the electroseismic model.
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This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability result is obtained by measurement data only in a suitably chosen subdomain under the assumption that the coefficients are given in a neighborhood of some subboundary.
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A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the boundary of the domain, apart from imposing that the boundary of the domain is $C^{1,1}$. The coefficients are assumed to coincide on a neighbourhood of the boundary, a natural property in applications.
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