Analysis of direct current resistivity data using continuous wavelet transform

We have developed a new method for the direct current resistivity interpretation, based on the continuous wavelet transform (CWT) of electric potential-difference data. It exploits the main properties of the CWT, such as stability versus noise, and does not require a starting model or other a priori information such as a model weighting function or constraints. Because the approximate integral equation of the resistivity problem has the same form as the forward problem for potential fields, the authors analyze geoelectric data (with dipole-dipole configuration) using the wavelets belonging to the Poisson kernel semigroup. They find that the CWT analysis of the measured electric potential difference is able to identify buried bodies, defining their depth, position, and extent. Such parameters are estimated with no prior knowledge of the resistivity contrast between the bodies and the background. We consider several synthetic models, such as dikes, compact bodies, and contacts. In general, the depth and the lateral thickness of the buried bodies are estimated with good accuracy, using a diagram relating the singular point estimations to the different values of the dipole separation factor n. Thanks to the good results obtained from synthetic data, we test the method with data generated during laboratory experiments. In two laboratory-scale models, our method displays a better precision compared with smoothness-constrained least-squares inversion in identifying the exact position of the edges of a buried body. Finally, we find that combining CWT and inversion is advantageous: after constraining the inverse problem with a priori information from the CWT analysis, we obtain an improved inverse model.