Construção analítica de semivariogramas médios para krigagem de blocos

Abstract

Several areas of science, such as environmental, biological, epidemiological, agricultural, among others, have data with variations in space. In most studies, one only measures variations using statistical procedures that do not take into account the interactions between the dimensions of space. In order to address spatiality, there is Geostatistics, which uses the semivariogram to detect the spatial dependence of a phenomenon. Normally, Geostatistics uses a point predictor; this work deals with a prediction system for an entire region, called block kriging, which aims to predict the average value of the phenomenon at the study site. The main complexity of this technique is the modeling of the average semivariograms, since it is currently addressed only numerically, thus containing approximation errors. In this study, we analytically present the construction of the average semivariograms, and, with the results obtained, it is possible to work in any dimension of the region without producing numerical errors, with the total precision of an analytical solution that had not yet been presented in the recurrent literature on block kriging. The entire technique for constructing the average semivariograms in an analytical manner is presented, with focus on modeling the average semivariograms for the linear, spherical and pentaspherical models. For the three results obtained, the spherical and pentaspherical average semivariograms do not yet have analytical results in the usual literature, as well as the pentaspherical model. The advancement of kriging blocks can solve problems of average prediction for several phenomena, such as agricultural production, quantitative of mining blocks or any other need to obtain average values of the random variable, considering the spatiality of the phenomenon.