Smoothing Filter and Correction Factor for Two-Dimensional Electrical Resistivity Tomography and Time Domain-Induced Polarization Data Collected in Difficult Terrains to Improve Inversion Models

When collecting data using ERT2D (2D electrical resistivity tomography) and TDIPT2D (2D time domain-induced polarization), different phenomena can occur, which can cause natural or anthropogenic noise, contaminating the data and making its processing, analysis, and interpretation difficult. Different techniques have been developed to eliminate or reduce these effects on the data, such as noise filtering or the development of new techniques to improve data collection in the field. In the present work, an iterative, weighted, least-squares filter was employed after voltage normalization using current and geometrical factor correction on data collected in rough topographic terrains. The selected filter basis function should be able to represent the natural behavior of the function to be filtered. Stationary or variable voltages in electrical prospecting decay with the inverse of the distance, which can be represented by an expansion in Legendre polynomials. On the other hand, uneven spacing of the electrodes leads to using the incorrect geometric factor, resulting in an error in the calculation of the electrical anomaly. The efficiency of the proposed technique was analyzed and tested with field examples using different filters and by comparing applying and not applying the proposed correction factor. The results indicated low RMS and L2-Norm errors, and better definition of the inverted resistivity image was obtained. For the TDIP data, a better correspondence between the inverted images of resistivity and chargeability was obtained.