Interpretation of apparent soil resistivity and stratification with schlumberger arrangement
The paper proposes a methodology for interpretation results of apparent resistivity obtained with collinear arrangements of four electrodes (Wenner and Schlumberger). Also proposes equations for soil stratification using apparent resistivity measured from collinear arrangements of four electrodes (Wenner and Schlumberger). It is usual that, since soil resistivity measurements are made using the Wenner method (which consists of four rods arranged in a line and equally spaced), the results are presented graphically in which the y-axis is the apparent resistivity, and spacings are marked on the x-axis. Eventually, the spacings between electrodes are correlated with the depth of measurement or investigation. However, in Schlumberger's arrangement, the graphical representation is not so obvious, because the spacing is not the same as in the Wenner method. Differently from the methodologies found in the literature, this paper proposes, in an innovative way, a comparative study between the results obtained using the arrangements of Wenner and Schlumberger and presents the mathematical equations necessary to the stratification of soils from measurements of resistivities obtained using these two arrangements. In terms of the first objective, a hypothetical soil, for which the configuration of four collinear electrodes, Wenner's arrangement (aj = bj) and Schlumberger's (bj = 1m) was simulated. The effective depth of investigation (EDI), so called to distinguish the depth characteristic of investigation (DCI), is an appropriate parameter to compare the apparent resistivity curves, regardless of the arrangement that was used to obtain them. For the second objective, we propose an algorithm that allows to stratify soils from measurements made with both methods. The equations were compatibilized, making it generic for any spacings, aj and bj. The proposed algorithm solves in a satisfactory and innovative way the soil stratification from apparent resistivity obtained with collinear arrangements of four electrodes. In this paper, the proposed methodology is applied to the Wenner and Schlumberger arrangements, where the Wenner method is considered as a particular case of the generic equation developed. The apparent resistivity calculated can be determined according with the proposed equation, which represents a generalization of apparent resistivity calculated for multilayer soils (N layers). The objective function to be minimized in the stratification algorithm corresponds to the sum of the relative quadratic deviations between the apparent resistivity measured and apparent resistivity calculated. Tests are presented for three-layer soil in order to demonstrate the application of the proposed methodology.
File Size: 331,8 KB
Pages NB: 6