A study is made of the possibility of calculating electric potentials, and therefore of interpreting apparent resistivity measurements, when the ground presents structural conditions more complicated than plane, parallel stratification.
For this work a schematic type of structure has been chosen, in which the discontinuity planes for electric resistivity are both parallel and perpendicular to the level of the ground.
The problem has been examinated in its general aspect, and then some criteria for the numerical calculation have been indicated.
Some calculated examples are presented, relevant to vertical electric soundings accomplished by conventional technique, for particular types of structure.
Dipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar‐dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field.
A special measurement technique is required since the dipole‐dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.
ALFANO L. 1980, Dipole-Dipole Deep Geodectric Soundings over Geological Structures, Geophysical Prospecting 28,283-296.The dipole-dipole array is used for deep vertical gsoelectric soundings for practical reasons. However, the data obtained are often too scattered and the quality is lower than that of a Schlumberger sounding. The mathematical transform from these fields data to the corresponding Schlumberger ones is needed. It is demonstrated that for more general underground structures different from plane parallel stratifications, only the continuous polar dipole-dipole array permits a general and reliable transform of this type. It follows that any other dipoledipole array, (for instance the azimuthal, equatorial, parallel, perpendicular, etc.), are useless over complex structures, or in the presence of irregularities on the ground surface.
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