Abstract

Solutions of Laplace’s equation in prolate and oblate spheroidal coordinates are applied to problems that arise in resistivity surveys over filled hemispheroidal sinks. Comprehensive sets of theoretical curves are presented for both horizontal and vertical profiles in the vicinity of filled sinks. The effectiveness of these theoretical curves is demonstrated not only for the interpretation of resistivity data but also for the planning of proper field techniques in resistivity surveying over such sinks. Excellent correlation between theoretical and observed field resistivity curves is shown over a shale sink in the Tri‐State lead‐zinc mining district, near Joplin, Missouri. It is shown that a filled sink can be approximated in its resistivity edge effects by 1) a vertical dike if the width of the sink is small in comparison with its length and its depth; and 2) a vertical fault if the sink is large in comparison with the electrode separation. A study of the Lee and Wenner configurations indicates that the former gives additional information that more than justifies the extra time and expense involved.

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