Mathematical modeling of electrometric diagrams in fissured media. Part 2: Synthesized well-loggins curves for four-electrode sounding

Abstract

1. It has been proved that the distance between cracks can be determined by the distance between the principal maxima of electrical well logging diagrams. 2. Coordinates of the measured electric resistivity should be tied to the center of the receiving dipole of the electrometric sounding probe. There is a direct correlation between the location of cracks and the extrema on geophysical well logging curves. 3. The correlation between the position of the principal bendpoints on geophysical well logging diagrams and the location of cracks (according to conclusion 2 above) is especially stable for a symmetric four-electrode setup. 4. With decreasing length of the receiving dipole the absolute maximum of\(\hat \rho _a \) from the crack grows while its width decreases. The width of the principal maximum is practically equal to the length of the measurement dipole. 5. With a lateral setup (small MN) the position of the cracks should be determined by the position of the principal minima on\(\hat \rho _a \). 6) When the minimal distance between emitter and receiver electrodes is larger than the distances between long cracks (in areas of fractured beds), an effect may appear where the intensely fissured areas exhibit abnormally low effective electric resistivity. 7. A theoretical substantiation is given to the hypothesis at the basis of the phenomenological theory of geophysical bore hole defectoscopy described in [3] as it applies to the electrometric method: a) there is a correlation between the positions of extrema on geophysical well logging curves and the cracks in the bed; and b) perturbations of a parameter being measured from the cracks of a given level can be approximated by the sinusoid or cosinusoid curve of appropriate amplitude and period.