We investigate the structure of a two layered earth by presenting a mathematical model of electromagnetic response. The integral expressions provide the electric fields on the ground surface, and Taylor-series expansion are used to find the solution of the electric field. Numerical solutions are computed and plotted to show the behaviors of the electric field while some parameters are assigned approximately. The responses of electric field from the ground surface are influenced by the conductivity of overburden.
In this paper, we study the nonhomogeneous second order differential equation of Cauchy-Euler equation with a bulge function. The reduction of order and Taylor series expansion of a bulge function are used to obtain the general solution.
The purpose of this paper is to study the structure of the earth by constructing a mathematical model of electromagnetic response of a half-space earth with a positively skewed bulge conductivity. Taylorseries expansion and approximation are used to find the solution of the homogeneous differential equation. The Hankel transform is introduced to the problems and analytical result is achieved. The responses of electric field from the ground surface show some subject matter to the variations of conductivity and are compelled by the conductivity ground profile.
In this paper, we show that the one solution of the second-order homogeneous linear differential equation can be obtained by using the method of Frobenius.Mathematics Subject Classification: 34B05, 34G10, 34A30, 35L05
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