Mapeamento aproximado da resistividade em subsuperfície usando dados de resistividade aparente e geoestatística

Abstract

It is presented a new method for the approximate mapping of the subsurface resistivity based on a geostatistical approach. It are used the characteristic points (CPs) of a resistivity sounding, which are their inflection and extreme (maximum and minimum) points. The methodology consists basically of four stages: i) smoothing the geoelectric soundings to assure robusteness to measurement errors, ii) determining the CPs from the smoothed versions of the geoelectric soundings, and obtaining from the CPs point estimates for the subsurface resistivity using empirical relations between electrode spacing and depth, iii) calculating semivariograms associated to the point estimates, and fitting them to a semivariogram model, and finally iv) estimating the subsurface resistivity distribution by kriging interpolation of the point estimates. No assumptions are made about the true subsurface resistivity and, as result, the method is robust to the model dimension and can be implemented for any dimension. Computationally, the method is very fast because no modeling (either direct or inverse) is demanded and the most intensive computer operation is just a kriging interpolation. Given its robustness to measurement errors and model dimension, it can be implemented as a fast automatic method of interpretation. The estimated resistivity distribution has value both as an object to interpret and as a better initial model for inversion algorithms. In the latter use, about 30%-40% of the iterations can be saved when compared with initializations with the homogeneous semispace, for 2D algorithms incorporating the classic smoothness constraint, for example. The method’s performance is demonstrated with applications with 2D Schlumberger array data both for synthetic and real cases. The proposed method might be generalized for other DC-resistivity arrays and electromagnetic techniques based on apparent resistivity soundings.