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.

The Extended Data-Adaptive Probability-Based Electrical Resistivity Tomography Inversion Method (E-PERTI) for the Characterization of the Buried Ditch of the Ancient Egnazia (Puglia, Italy)

“…The E-PERTI method [11] is an extension of the PERTI method [19] that in turn was directly derived from the resistivity probability tomography approach [13]. The latter consisted in the determination of the resistivity anomaly occurrence probability function η m calculated in the space below the surface composed of M contiguous cubic cells with equal volume ∆V, each identified by the location of its center (x m , y m , z m ) (m = 1, 2, .…”

“…Therefore, in order to improve the accuracy of the method, the extension of PERTI (E-PERTI) [11] was developed considering the Bernoulli conceptual scheme in probability theory [33]. According to this scheme, each single geoelectrical measurement is considered as a "test", that is, the realization of a specific set of conditions that can give rise to an elementary event of a space U of elementary events (test space).…”

“…Sci. 2022, 12, 2690 7 of 25 Some results are now worth being recalled from [11] about the main advantages of extending the PERTI method, that is, about the role of the E-PERTI linear least squares best fit expressed by Equation (8), which is directly based on the PERTI formula (4).…”

“…In this paper, the Extended data-adaptive Probability-based Electrical Resistivity Tomography Inversion (E-PERTI) [11] has been applied for imaging the buried features. E-PERTI is the latest development within the probability tomography imaging approach as adapted to geoelectrical methods [12][13][14][15].…”

“…The E-PERTI method has at last been developed in order to enhance robustness to noise with respect to the original PERTI, as well as to optimize resistivity estimates. It consists of processing, with the PERTI algorithm, many different subsets of data extracted from the apparent resistivity dataset both randomly and by sequential vertical scanning and horizontal windowing across the datum space [11]. The result is a more or less dense cluster of resistivity values in each point of the surveyed volume, used at last to predict the best estimation of the most probable resistivity in the same point by an intrinsic linear regression model with ordinary least squares techniques.…”