Abstract

The electromagnetic field components are expressed in terms of Sommerfeld-type improper integrals, the integrands of which depend upon the solution of a nonlinear differential equation. Combining a collection of Runge-Kutta numerical integration methods with the extrapolation to the limit, a desired accuracy in the final result is obtained by varying the step-size along the structure according to the local error.Actual calculations were performed for: (1) A homogeneous half-space having on top several layers with linearly varying conductivity sandwiching a very conductive or a very resistive layer. (2) A stack of homogeneous layers over a resistive or a conductive half-space. (3) A transition layer in a stack of homogeneous layers. The ratios of the field components to corresponding components for a half-space as functions of 'numerical distance' are strongly correlated to the variation of resistivity with depth. (The main portions of the graphs of the absolute values and phases for all the ratios show a striking similarity for a given model.) This characteristic curve, called loosely 'model line' starts with a maximum for a resistive half-space and a minimum for a conductive one. Further maxima and minima reflect the conductivity of the various layers. A similar behavior occurs when transition layers are present, although the model lines show lower peaks and are smoother.

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