Abstract

The method of R.W. Moore for determining subsurface interfacial depths bymeans of integrated curves of apparent resistivity has been analyzedtheoretically. It is found that the only unique tangents that can be drawn tosuch curves are the asymptotes at infinite electrode spacing and the tangentsthrough the origin at vanishing electrode spacing. Explicit expressions havebeen derived for the relationship between the electrode spacing at the pointsof intersection of these tangents and the thickness of the surface strata as afunction of the conductivity parameters for the two-layer and three-layerearths. It is found that in all cases the electrode spacing at the points ofintersection will exceed 3/2 of the thickness of the surface layer, and mayeven become indefinitely large as the resistivity of the deepest layersincreases as compared with that of the surface layer. These results do notagree with the empirical findings of Moore that the intersection of the tangentlines fall at an electrode spacing very approximately equal to the thickness ofthe surface layer.

Introduction

In a recent paper, R.W. Moore proposed a new method for the analysis andinterpretation of earth-resistivity measurements. This consists essentially inplotting against the electrode separation of a Gish-Rooney system the integralof the apparent resistivity with respect to the electrode spacing, andobserving the breaks in the integral curves. Specifically, tangents are drawnto the various segments of the integral curves, which show appreciablydifferent slopes, and the intersections of these tangents are used asindications of the depths of the various underlying strata. By numerousexamples Moore has shown that the electrode separation at the firstintersection so found agrees very closely with the depth of the bottom of thesurface layer. Moreover, in a number of instances the intersections for greaterelectrode spacings seemed to correspond to the depths of deeper beds.

T.P. 1761

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