###### Abstract  
In this paper, we present the application of a special soil resistivity model, the Exponentially Graded Multilayered Soil model, to the interpretation of Borehole Resistivity Logging surveys. The model, which was recently introduced by the authors, offers an alternative to the interpretation provided by constant resistivity layer models. The model is applied to synthetic soil surveys as well as to a real survey that is not satisfactorily interpreted using conventional models. This model aids in the design and calculation of grounding systems in electrical engineering, providing an alternative to calculations performed by traditional layered models. resistivity logging; inversion procedure; exponentially graded multilayered soils; soil modeling; grounding systems calculations +
Footnote †: journal: Applied sciences  
0000-0002-4000-0000-0000-0000-0000-0000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-00000-000000-000000-000000-000000-  
to as Electrical Resistivity Ground Imaging (ERGI) or Electrical Resistivity Tomography (ERT) [8]. The aim is to study the variability of resistivity both with depth and laterally by measuring magnitudes directly related to resistivity. Apparent resistivity is one of these magnitudes, which can be measured using a set of surface electrodes in various configurations, with Wenner and Schlumberger arrays being some of them. When only the variability of resistivity with depth at a specific location is investigated, the survey is referred to as Vertical Electrical Sounding (VES) [9], which is a restricted type of soil test from a geophysical perspective, although it is very useful, for example, for the design of grounding systems in electrical engineering. On the other hand, invasive methods involve drilling a narrow vertical hole or well through which a bare rod can be inserted to release current into the ground, known as the Driven-Rod method (DRM) [10; 11], or a device with two or three electrodes can be introduced into the well, one of which releases current into the soil while the others measure the electric potential, a method known as Borehole Resistivity Logging (BRL) [12]. In general, it can be said that non-invasive surface measurement methods provide information about resistivity in the vertical direction while also allowing for investigation of its lateral variability, although they lose resolution with depth. However, drilling methods such as BRL provide information in the vertical direction, with the possibility of obtaining a large amount of data, but offer little information in the horizontal directions unless many adjacent parallel boreholes are drilled and studied [13]. In an electrical survey using any of the methods described above, the electrical resistivity is not directly determined; instead, some other electrical quantity related to it is measured. In VES, the so-called apparent resistivity is measured [14]; in surveys using DRM, the electrical resistance of the rod is measured as a function of the length inserted into the ground [15], while in BRL, the electrical potential at various depths in the well or the potential difference between two nearby points is measured. Based on the information provided by the survey device, the soil resistivity as a function of depth must be determined, a procedure known in the literature as inversion. This is only possible if a soil resistivity model is available, which can be used to apply an inversion procedure to the measurement data and thus obtain the specific parameters of the model [16]. Due to the nature of the measuring device, BRL data provide an almost direct measurement of electrical resistivity as a function of the depth of the materials that make up the soil, making the inversion of BRL data less relevant for geophysical knowledge of the ground than the inversion of apparent resistivity measured with some non-invasive surface method.