An Extension of the Data-Adaptive Probability-Based Electrical Resistivity Tomography Inversion Method (E-PERTI)

Abstract

About a decade ago, the PERTI algorithm was launched as a tool for a data-adaptive probability-based analysis of electrical resistivity tomography datasets. It proved to be an easy and versatile inversion method providing estimates of the resistivity values within a surveyed volume as weighted averages of the whole apparent resistivity dataset. In this paper, with the aim of improving the interpretative process, the PERTI method is extended by exploiting some peculiar aspects of the general theory of probability. Bernoulli’s conceptual scheme is assumed to comply with any resistivity dataset, which allows a multiplicity of mutually independent subsets to be extracted and analysed singularly. A standard least squares procedure is at last adopted for the statistical determination of the model resistivity at each point of the surveyed volume as the slope of a linear equation that relates the multiplicity of the resistivity estimates from the extracted data subsets. A 2D synthetic test and a field apparent resistivity dataset collected for archaeological purposes are discussed using the new extended PERTI (E-PERTI) approach. The comparison with the results from the original PERTI shows that by the E-PERTI approach a significantly greater robustness against noise can be achieved, besides a general optimisation of the estimates of the most probable resistivity values.

Keywords

• resistivity tomopraphy
• probability approach
• a data-adaptive probability-based ERT inversion (PERTI) method
• extension to the PERTI method (E-PERTI)