Attenuation function for propagation over a nonparallel stratified ground

Abstract

The directional dependence of the calculated surface impedance on a nonparallel stratified conductor is pointed out. In spite of this dependence, the reciprocity theorem is not violated when the mutual coupling between two dipoles is considered.

Line source over a nonuniform stratified Earth

“…On applying the reciprocity relationships, we see that the results given in Figure 13 are consistent with those considered in Figure 11. It is in.teresting to note here that, contrary to earlier conjectures [Schlak and Wait, 1968], King and Hustig [1971] demonstrated experimentally that the surface impedance derived by the geometrical-optical method is less valid for 8 --tan 1 ø than for 8 = --tan 1 ø .…”

“…The contributions from each of the terms satisfying (26) do not peak for precisely the same value of the angle Oo r. However, when the average gradient of the overburden depth 8 is very small, all these contributions tend to overlap, particularly for small values of t (Schlak and Wait [1968] restrict their attention to wedge-shaped overburdens with small 8.) Finally, we note that in Figures 2 through 13 the pen movement of the automatic plotter saturates at --40 db.…”

“…Since.an increase in $ results in an increase in A0•, there is a larger shift in the principal lobe for • ---tan 5 ø . (The geometrical-optical approach is restricted to small $ [Schlak and Wait, 1968]. )…”

“…In this case, we also find • narrowing of the lobe width as L increases (equations 20c and d). The geometrical-optical solutions of Schlak and Wait [1968] improve as the separation between the transmitter and receiver increases.…”

“…this solution to a critical reciprocity test, which pointed up some of the restrictions of the geometrical-optical method. To obtain greater insight into this problem, Schlak and Wait [1968] and King and Hustig [1971] conducted some preliminary laboratory experiments. Although Schlak and Wait's experimental results were not considered sufficiently accurate to resolve the problems, King and Hustig concluded that the equivalent surface impedance cannot, in general, be evaluated by the geometrical-optical approach.…”