Abstract
The electromagnetic field that generated by line current and sheet current at the surface of the earth can be expressed in analytical form. The line current created at the earth’s surface by an infinitely long line current is given by the inverse Fourier integrals over a horizontal wave number. The sheet current can be obtained by integrating the line current expansions using a Neumann and Struve functions; these functions have known mathematical properties, including the series expansions. The series expansions are exact with neglecting the displacement currents. Assuming a uniform earth and that there is no propagation, the three nonzero field components can be expressed in terms of the Neumann and Struve functions. The integrals of line current expansions are calculated by using the numerical methods. The results represented graphically and illustrated by figures. Results can be used to evaluate numerical solutions of more complicated modeling algorithms.
Highlights
In the last few decades, there has been increased interest in the behavior of electromagnetic systems which are operated near a conducting earth
Numerical computation of the electromagnetic field that generated by line current and sheet current at the surface of the earth can be performed, based on the Equations [(12), (24) and (25)] and [(44), (49) and (50)], respectively
The electromagnetic field defined as a function of x coordinate at the surface of the earth due to line current and sheet current and plotted against the distance x
Summary
In the last few decades, there has been increased interest in the behavior of electromagnetic systems which are operated near a conducting earth. Sami [14] calculated the influence of a magnetically permeable surface layer on transient electromagnetic field of a vertical magnetic dipole on a twolayer conducting earth. Neglecting the currents displacement, making the quasi-static approximation, which is always permissible in geophysical applications, and assuming a uniform earth and that there is no propagation, the three nonzero field components can be expressed in terms of the Neumann and Struve functions. These functions have known mathematical properties, including their series expansions. Sheet current having a finite width implies a more realistic model It can be obtained by integrating the line current expansions using a Neumann and Struve functions. The electric X and Z components are obtained from the magnetic Y component at the earth’s surface, we are considering the real and imaginary parts of electric field components and taking into account
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