A simple mathematical formula relating the maximun entropy spectral estimate to the amplitude of a noisy signal; application to geoelectrical recordings

In geoelectrical prospecting with commutated currents it is very important to correctly evaluate the amplitude of the useful voltage signal necessary to compute the apparent resistivity. This procedure presents serious difficulties, particularly in highly noise-degraded situations. Various methods of filtering and spectral analysis of voltage recordings have been used in the past. In this research the maximum entropy method (MEM) is used. First we do some computations that allow us to obtain a straightforward formula relating the maximum entropy spectral estimate to the amplitude of the useful signal. Then we apply this mathematical relationship to several theoretical and experimental cases. Comparison of the results with those obtained by other spectral analysis techniques and some practical considerations allow us to conclude that, in general, MEM gives the best mathematical solution to the problem.