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RESISTIVITY ANALYSIS FOR MODELS OF A SPHERE IN A HALF‐SPACE WITH BURIED CURRENT SOURCES *
Author(s) -
MERKEL R. H.,
ALEXANDER S. S.
Publication year - 1971
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1971.tb00907.x
Subject(s) - electrical conductor , current (fluid) , limiting current , surface (topology) , conductor , conductivity , spheres , electrode , electrical resistivity and conductivity , boundary value problem , flow (mathematics) , mechanics , geometry , materials science , physics , mathematics , thermodynamics , composite material , electrochemistry , quantum mechanics , astronomy
A bstract Boundary‐value problems in steady‐state current flow were solved numerically in bispherical coordinates for a sphere of arbitrary conductivity in a half‐space. Solutions for the potential on the surface of the half‐space were examined for the cases where both current sources were on the surface, one source on the surface and the second between the surface and the sphere, and one source on the surface and the other in the sphere. Results show a great similarity with the layered case when the buried electrode is placed between the surface and the conducting region. Such a buried electrode configuration makes it possible to obtain an accurate measurement of the depth to the conductor in both cases. A model with the current electrode placed in a conductive sphere is compared with a three‐layered model with the source in a conductive intermediate layer, and results indicate that the lateral extent of a finite anomalous zone can be estimated using these limiting curves. The validity of these theoretical calculations for buried spheres was confirmed experimentally by tests conducted on an analog model.