Inversion of geoelectrical data constrained by CWT analysis

We introduce a new method for the inversion of DC resistivity data. The method is based on constructing constraints based on the analysis of the Continuous Wavelet Transform (CWT) of the measured potential differences. We analyze the dipole-dipole geoelectric data through the wavelets belonging to the Poisson kernel semigroup and show that the CWT analysis of the measured electric potential differences is able to identify the main parameters of the buried sources such as depth, position and extent. Such source parameters are estimated with no need to know the resistivity contrast between the sources and the background. In general, the depth and the lateral thickness of the sources are estimated with a good accuracy, thanks to a diagram relating the singular points estimations vs. the different values of the dipole separation factor n. We proved the method by application to synthetic data and real data acquired under controlled conditions. Coupling CWT and inversion revealed to be really advantageous: after constraining the inverse problem with the a priori information from our CWT analysis, we obtained an inverse resistivity model well consistent with the known source.