Theory; Proceedings Of Thru-The-Earth Electromagnetics Workshop
Description:A general analytical solution of the effect of an inclined contact separating two media of differing electrical properties on a normally incident plane electromagnetic field has been given (Geyer, 1972). These solutions for the electromagnetic response at any observation point P(r, [u]) are given in the form of inverse Lebedev-Kontorovich transforms. Two modes of excitation are considered: (1) case where current density flows across strike of the contact separating the media of differing electrical properties (only Er , E [u] , and Hx differ from zero) and (2) case where current density flows along-strike (only Hr , H [u] , and Ex differ from zero). The electromagnetic fields in the frequency range of interest and for the rock conductivities under consideration are quasi-static in nature so that to a first-order approximation the horizontal magnetic field at the surface of the earth is constant and continuous across the discrete discontinuity in resistivity for case (1) above, and so that the tangential derivative of the horizontal electric field at the surface of the earth is constant and continuous across the discrete discontinuity for case (2) above. Of course, it is well known that where large horizontal gradients in conductivity exist, there also exists large anomalous components of the vertical magnetic field (Weaver, 1963). The recognition of such anomalous components and their magnitudes due to the presence of lateral resistivity changes in the overburden becomes very important in any wavetilt type measurement which may be used to locate a miner. When the lateral change in resistivity becomes quite large, the integral solutions (expressed as Lebedev-Kontorovich transforms) simplify considerably and allow ready numerical evaluation. Examples of the amplitude and phase responses of the radial electric, horizontal electric, and vertical magnetic field in the vicinity of the contrast in resistivity are shown in Figures 2, 3, and 4. Of particular significance is the fact that the anomalous vertical magnetic field is three orders of magnitude larger near the contact than far from the contact. This fact implies that where large resistivity contrasts do occur in the rocks overlying mine workings, that significant errors may be present in wavetilt measurements as used above for location criteria! Another observation insofar as the anomalous vertical magnetic field is concerned is the linear variation of phase as one proceeds away from strike in induction number (increased distance or frequency). For a pulse-excited communications system this phenomena would have a bearing on where the zero crossings would occur (i.e., 'pulse breadth') in the transient coupling between any given source-receiver configuration and at any given receiver site.
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