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TRANSIENT ELECTROMAGNETIC RESPONSE OF A SPHERE IN A LAYERED MEDIUM*
- Source: Geophysical Prospecting, Volume 23, Issue 3, Jul 1975, p. 492 - 512
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- 27 Apr 2006
Abstract
The Galerkin method of solving integral equations is well suited to the solution of the integral equations describing the transient response of a sphere embedded in a layered medium, which is excited by a large co‐axial loop.
The transient response is calculated by transforming the steady state solutions obtained in the frequency domain.
The analysis shows that the scattering matrix is extremely diagonally dominant and the maximum number of modes required to obtain convergence does not rapidly increase with frequency. The number of modes required is about eight. This type of scattering matrix can be taken to be an expression of the principle of elementary superposition. This principle is reflected in the decay curves. These show that the early part of the decay curves asymptotically approach the decay curves to be expected for a layered structure without the sphere. The slope of the latter stages of the decay curve gives a decay constant that is the same as was obtained for spheres in free space excited by planar or dipolar sources.
The point of departure in time of these curves from the layered ground curves is delayed either by placing the sphere at a greater depth or by placing a more conductive overburden above the sphere.