In this paper, the solution of magnetic field response from DC source located on a two layered uniform conductive host medium is formulated. For the first layer, the conductivity of overburden is a function of depth () z and denoted by () 2 () 2 1 0 is given by () 2 0 z σ σ =. The Hankel transforms are introduced to solve the magnetic fields which are expressed in the form of integral expressions. In order to determine the magnetic fields, numerical solutions are computed to show the behavior of the field while some parameters are given approximately. The graphs of computation results perform the same relationship to the conductivity profile of the ground.

We derive an analytical solution of the steady state magnetic field due to a direct current source on a two layered earth with having exponentially varying conductivity. The solution is achieved by solving a boundary value problem in the wave number domain. The Hankel transform is used to transform to the spatial domain. The solutions are expressed in the form of integral expressions. The inversion process via the use of the Newton-Raphson optimization technique is introduced for finding the conductivity parameter of the conductivity variation. The optimal results of our sample test converge very fast to the true values with misfits less than 10 −12 (A • m −1).

In this paper, the analytical solution of normalized apparent resistivity from DC source located on a two layered earth model is formulated. The conductivity of overburden is denoted by σ over (z) = σ 0 e −b(z−l) 2 /2 , 0 ≤ z ≤ d, where b and l are positive constants and l is used to locate the peak of the bulge, d is the thickness of overburden and σ 0 is a positive constant. The conductivity of host medium, z > d, is denoted by a constant and is given by σ host (z) = σ 0. The Hankel transforms and power series method are used to solve the partial differential equation to find the potential functions. The expression for the Wenner configuration is introduced to formulate the normalized apparent resistivity. In order to determine the normalized apparent resistivity, numerical solutions are computed to show the behavior of the curves by using Chave's algorithm while some parameters are given. The curves of computation results of normalized apparent resistivity are plotted against electrode spacing. The curves could be able to predict the depth of the underground water that could damage to the foundation of old building.

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