Abstract

In applying earth resistivity methods to the problem of locating and delineating subsurface structures, surface elevation variations along the surveyed terrain introduce distortions in the soundings. The analysis presented here is aimed at characterizing such terrain variations in the detection of relatively small subsurface targets such as caves, sinks, and tunnels in otherwise homogeneous earth materials. The analytical approach involves, first, the development of a suitable earth resistivity model for localized three-dimensional subsurface anomalies in a homogeneous flat half-space. Next, in order to apply the half-space resistivity model to irregular terrain, a Schwarz-Christoffel transformation is utilized to map the terrain surface variations into an equivalent flat half-space. The technique is illustrated by calculating the resistivity response of three tunnels located below a hill with 40-m valleys on either side.

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