Abstract
A new method designated TDS (transverse differential sounding) is proposed for obtaining high resolution direct current resistivity soundings in the field. The measured apparent resistivity is designated TDR (transverse differential resistivity) and is defined by [Formula: see text], where [Formula: see text] and L are the Schlumberger apparent resistivity and electrode spacing, respectively. A collinear symmetric system (B′AMNBA′) consisting of two pairs of current electrodes and one pair of potential electrodes is used for measuring the value of [Formula: see text] directly in the field. For the interpretation of TDS curves obtained in the field, theoretical sets of master curves are computed either directly from the formal expression for [Formula: see text] in terms of Stefanesco’s kernel function and Bessel functions or by transformation of Schlumberger (VES) and/or dipole‐dipole sounding curves. Conversely, TDS and VES curves computed for the same horizontally stratified earth models and for corresponding electrode spacings are easily transformed, by means of simple relations, into radial, perpendicular, and parallel dipole‐dipole, or LDS (longitudinal differential sounding) curves. It is mathematically established that TDS curves, for horizontally stratified laterally homogeneous media, are identical to sounding curves obtained with a parallel dipole‐dipole array at an azimuth angle of 60 degrees, and that negative values of apparent resistivity [Formula: see text] are measured for certain geoelectric sections. Examples of theoretical TDS and LDS curves for two‐, three‐, and four‐layer earth models compared with corresponding VES curves illustrate the higher resolving power and greater probing depth of differential soundings. The field procedures and electric current requirements described for TDS and other types of soundings show that seven apparent resistivity values, corresponding to four electrode arrays, can be measured at each electrode setup.
Published Version
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