Smoothing noise-degraded electrical soundings in shallow and deep investigation studies

A method of smoothing noise-degraded Schlumberger and axial dipole-dipole electrical founding curves is developed. It is based on two expressions relating the Schlumberger and the dipole-dipole apparent resistivity to the pole-pole apparent resistivity. The analysis in the frequency-domain reveals that the pole-pole spectrum is related both to the Schlumberger and to the dipole-dipole spectrum as in linear systems, with transfer functions typical of low-pass filters (smoothers). The calculation of the impulse responses allows to obtain in the spacing-domain relationships that are used to transform original Schlumberger and dipole-dipole curves into equivalent pole-pole curves. Smoothing is therefore an intrinsic property of the transformation. The goodness of the filtering process is demonstrated also by examples.