Geoelectric Axial Dipole Sounding Curves for a Class of Two‐dimensional Earth Structures*

Abstract

PATELLA, D. and TRAMACERE, A. 1986 Geoelectric Axial Dipole Sounding Curves For a Class of Geophysical Prospecting 34, With the aim of studying the behaviour of geoelectric axial dipole vertical soundings over complex geology, a systematic theoretical approach is presented for a class of earth structures characterized by horizontal and vertical parallel boundary planes. The twodimensional cylindrical bodies of infinite length and rectangular cross-section are constrained to have resistivities satisfying Alfano's condition at every intersection line of the graticule, in order to adopt the image-point theory. A detailed analysis is performed for models with any number of horizontal boundaries and two vertical discontinuities. The apparent resistivity formulas are obtained and selected apparent resistivity curves are drawn for different parameter combinations and various directions of the sounding expansion axis. The class under consideration contains as a particular case the HVC model elaborated in Alpin's monograph, where only a small collection of master curves is available for the axial array. The reconstruction of those curves by the present formulation shows the existence of large discrepancies. A test based on the transformation to equivalent half-Schlumberger sounding curves supports the conclusion that an unidentified error must exist in some part of the theoretical approach of the Russian researchers. Finally, some field sounding curves based on geothermal and volcanological surveys are presented and interpreted by complete curve matching, essentially to show the applicability of the theoretical solutions.