On the reconstruction of conductivity of bordered two-dimensional surface in R from electrical currents measurements on its boundary
نویسندگان
چکیده
0. Introduction 0.1. Reduction of inverse boundary value problem on a surface in R to the corresponding problem on affine algebraic Riemann surface in C. Let X be bordered oriented two-dimensional manifold in R. Manifold X is equiped by complex (conformal) structure induced by Euclidean metric of R. We say that X possesses an isotropic conductivity function σ > 0, if any electric potential u on bX generates electrical potential U on X , solving the Dirichlet problem:
منابع مشابه
Reconstruction of Thin Tubular Inclusions in Three-Dimensional Domains Using Electrical Impedance Tomography
We consider the inverse problem of reconstructing thin tubular inclusions inside a three-dimensional body from measurements of electrostatic currents and potentials on its boundary. By inclusions we mean objects with an electrical conductivity differing from that of the background material of the body. We apply an asymptotic expansion of the electrostatic potential on the boundary of the body a...
متن کاملA simple form of MT impedance tensor analysis to simplify its decomposition to remove the effects of near surface small-scale 3-D conductivity structures
Magnetotelluric (MT) is a natural electromagnetic (EM) technique which is used for geothermal, petroleum, geotechnical, groundwater and mineral exploration. MT is also routinely used for mapping of deep subsurface structures. In this method, the measured regional complex impedance tensor (Z) is substantially distorted by any topographical feature or small-scale near-surface, three-dimensional (...
متن کاملUnited Kingdom.
An integral equation method for the inverse conductivity problem. Abstract: We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced boundary potentials, as well as the boundary values of the electrical conductivity....
متن کاملThree-dimensional Magnetotelluric Modeling of data from Northeast of Gorgan Plain
Magnetotelluric measurements have been conducted in the period range of 0.005-128 s along five parallel east-west directed profiles including 85 sites totally in the north-eastern part of Gorgan Plain, Golestan Province, North of Iran; with the aim of exploring iodine. Distortion and dimensionality analysis of data imply the existence of a north-south elongated two-dimensional model with some l...
متن کاملBoundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method
In this paper, we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linea...
متن کامل