###### Abstract
However, for the design of grounding systems in electrical engineering, a horizontal layer model to perform the necessary calculations is more than suitable. Among other reasons, for layered models, semi-analytical expressions can be found for the potential created by a current element at any point on the ground, allowing for the evaluation of the effect produced by the current leaked into the ground by a finite electrode. The most commonly used soil resistivity model is the Horizontal Constant Multi-Layered model (HCMS) [17], which, in its simplest version, involves dividing the ground into horizontal layers of constant resistivity. The soil parameters are the constant resistivities of the different layers and their thicknesses, with the exception of the deepest layer, which extends to infinity. It is a semi-analytical model in the sense that it provides calculable expressions that can be mathematically implemented numerically in the equations that determine the electrical potential in the soil, leading to more acceptable results the more closely the actual soil matches the proposed model. The HCMS is not the only possible model. For us, it is clear that, unless we are dealing with soils composed of perfectly horizontal layers with constant resistivity throughout their thickness, the resistivity will not be a piecewise constant function, but rather a magnitude that will vary within each layer with depth. Recently, a multilayer model has been proposed that allows the resistivity in each layer to vary with depth according to specific functions. This is the Functionally Graded Multilayered Soil model (FGMS) [18]. This model is also semi-analytical, in the same sense as the HCMS mentioned earlier, although it is mathematically much more complex. Itoffers three possible modes of resistivity variation with depth: exponential, parabolic, and trigonometric, with the first being the functional mode used in this paper--the Exponentially Graded Multilayered Soil model (EGMS) [18]. Additionally, the model can be adjusted so that the resistivity is continuous at the layer interfaces, although this does not always yield suitable final results in the inversion process. With this new model for soil resistivity, it is possible to provide an alternative interpretation of apparent resistivity profiles, as was already highlighted in [18], but it also offers an interpretation of BRL profiles, which is the main contribution of the present work. For the authors, it is clear that not all soils can be satisfactorily modeled using HCMS models, so alternative models should be welcomed. In summary, this work focuses on applying an inversion algorithm to the results of BRL measurements using an EGMS-type soil resistivity model and comparing the final results with a conventional HCMS model by directly simulating BRL with both models. While, in the field of geophysics, the inversion of an BRL is not a primary concern, the inversion of an BRL or an apparent resistivity pattern using a layered model, whether HCMS or EGMS, plays an important role in the design and calculation of protection systems for electrical installations. The application of the EGMS model to the calculation of relevant quantities in grounding systems is straightforward. Quantities such as resistance, as well as step and touch potentials, can be evaluated through implementation in numerical schemes similar to those already operating with the HCMS model. Having alternative models to compare results is, therefore, highly convenient. To this end, after this introduction, the paper continues with a description of the mathematical foundations of the calculations to be performed. The calculation scheme is then applied to several examples to highlight the differences between the models. The paper concludes with the findings derived from the previous applications.