Semivariogramas médios para krigagem de blocos

Abstract

In several areas of science, such as biological, environmental, epidemiological, agricultural sciences, among others, data often exhibit spatial variations. In most studies, only the variations are measured using statistical methods that do not take into account the existing interactions between the dimensions of space. When addressing spatiality in continuous data, geostatistics emerges, which, through the use of the semivariogram, is capable of detecting spatial dependence. Commonly, geostatistics is used with a point predictor, which is the typical case of its application. This work addresses a prediction system for the mean of the random variable of the phenomenon over a rectangular region in a two-dimensional system, known as block kriging. The main complexity of this technique lies in modeling the average semivariance between the points and the rectangular block under analysis. Currently, there are only numerical methods available to obtain this value, and they are limited to phenomena following the spherical model. Thus, they present approximation errors and limitations for various types of phenomena. This study presents the analytical construction of the average semivariograms used for block kriging in rectangular regions, considering commonly used semivariogram models. This enables the application of the technique to various practical situations that were previously not possible. The entire method for analytically constructing the average semivariograms is presented and subsequently implemented in a Shiny App, aiming to facilitate the application of the technique by end users. The advancement of block kriging may solve problems related to mean prediction for various phenomena, such as agricultural production, mining block estimation, or any other need to obtain average values of a random variable while considering the spatiality of the phenomenon.