Abstract
The purpose of this paper is to give a mathematical model and methods for uncovering the conductivity, the conductance, the thickness, and the depth of a circular body buried under the ground surface with a normal curve conductivity profile. The solution of electric field for this model earths structure is obtained by using the Hankel transforms and integral equations. The Cauchy-Euler method and the method of variation of parameter are intro- duced. Chave's algorithm is used for numerical computing the inverse Hankel transforms of the electric field solution. The operations on matrices are applied for resolving the linear system of equations. The conducts of electric field are shown in graphical forms.
Highlights
The electromagnetic method is the most ordinarily employed in geophysicalReceived: May 4, 2014 c 2014 Academic Publications, Ltd. url: www.acadpubl.euP
The intention of this paper is to acquaint with a mathematical model and methods for studying the structure of the earth which has a circular cylinder body buried under the ground
We study the ground which has a circular body buried under the ground with a normal curve conductivity profile and given by σ(z) = σ0e−b(z−l)2, where σ0 a is positive constant, b is constant, and l is positive which is used to locate the peak of the bulge
Summary
Lee and Ignetik [4] considered the forward problem of the transient electromagnetic response of a half-space with an exponentially varying conductivity profiles. Yooyuanyong and Chumchob [6] derived mathematical modelling of electromagnetic sounding for a conductive 3-D circular cylinder body embedded in a conducting half-space. The intention of this paper is to acquaint with a mathematical model and methods for studying the structure of the earth which has a circular cylinder body buried under the ground. The conductivity ground profile used in this paper is distinct from the models used by Lee and Ignetik [4] and Yooyuanyong and Siew [7], Ketchanwit [3] and Yooyuanyong and Chumchob [6]
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