Journal of Mathematical Sciences: Advances and ApplicationsAuthor's: Warin Sripanya and Suabsagun Yooyuanyong
Pages: [37] - [56]
Received Date: December 30, 2010
Submitted by:
We derive analytical solutions of the electric potential resulting from a direct current point source located anywhere within two types of multilayered earth structures including layers having linearly varying conductivities and layers having binomially varying conductivities. Our solutions are obtained by solving a boundary value problem in the wave number domain and then transforming the solution back to the spatial domain. The propagator matrix technique is used to formulate the upward-downward recurrences for solving the problems. One of these recurrences is applicable to general cases in which, the layers have constant, linearly or binomially varying conductivities. The equations derived for the electric potential can be used to interpret the hole-to-hole, hole-to-surface, and conventional surface array data. The inverse problems via the use of the Newton-Raphson and quasi-Newton optimization techniques are introduced for finding the conductivity parameters.
Hankel transform, inverse problem, electric potential, buried current source.
