Automatic approximate mapping of the subsurface resistivity from apparent resistivity data using geostatistics

Abstract

We have developed a new method for the approximate mapping of subsurface resistivity based on a geostatistical approach. We have used the characteristic points (CPs) of a resistivity sounding, which are their inflection and extreme (maximum and minimum) points. The methodology consists of five stages: (1) smoothing the geoelectric soundings to assure stability in the presence of measurement errors, (2) identifying the CPs in the smoothed versions of the geoelectric soundings, (3) obtaining subsurface sparse point resistivity estimates for the subsurface resistivity from the CPs, using empirical relationships between electrode spacing and penetration depth, (4) calculating semivariograms using the subsurface sparse point resistivity estimates, and fitting them with semivariogram models, and, finally, (5) estimating the subsurface resistivity distribution by kriging interpolation of the sparse point estimates. No explicit assumption is made about the true subsurface resistivity and, as result, the method can be applied to models of any dimension, given that the empirical rule for the penetration depth is approximately valid. Computationally, the method is very fast because no numerical modeling (either direct or inverse) is demanded and the most intensive computer operation is just a kriging interpolation. Given its independence of the model dimension and stability in the presence of measurement errors, the method can be readily implemented as a fast automatic method of interpretation. As result, the best scenario to apply the method is the initial treatment of large data sets. The methodology was developed, with synthetic and field data, using direct current (DC) resistivity soundings obtained with the Schlumberger array. The proposed method might be generalized for other DC-resistivity arrays and electromagnetic techniques based on resistivity soundings.