The Importance of the Model Choice for Experimental Semivariogram Modeling and Its Consequence in Evaluation Process

Geostatistics was created during the second half of 20th century by Georges Matheron, on the basis of Danie Krige’s and Herbert Sichel’s theories. The purpose of this new science was to achieve an optimal evaluation of mining ore bodies. The interest in geostatistical tools has grown, and nowadays its techniques are applied in many branches of engineering where data analysis, interpolation, and evaluation are necessary. This paper presents an overview of the geostatistics approach in data analysis and describes each operative step from experimental semivariogram calculation to kriging interpolation, focusing and underlining the experimental semivariogram modeling step. To help any data analysts during geostatistical analysis process, an innovative geostatistical software was created. This new software, named “Kriging Assistant” (KA) and developed within the Department of Geoengineering and Environmental Technologies University of Cagliari, is able, with a marginal support of the user, to produce 2D and 3D grids and contour maps of sampled data. A comparison between kriging results obtained by KA and two of the most common data analysis softwares (Golden Software Surfer and ESRI Geostatistical Analyst for ArcMap) is presented in this paper. Reported data showed that KA minimizes interpolation errors and, for this reason, provides better interpolation results. 1. Introduction Geostatistics was born during the last century in the mining field. Georges Matheron, on the basis of Danie Krige’s and Herbert Sichel’s theories [1–5], created new tools for the evaluation of mineral deposits; Bertil and Gandin provided the same tools in meteorological and forestal fields [6, 7]. This new approach was based on the “regionalized variables” theory [8]: a new type of variable influenced by its position within a mineralized “region.” According to this theory, a “regionalized variable,” schematically represented in Figure 1, could be defined by where is the regionalized component and represents the random component that explains the local effects. Figure 1: Regionalized variable schematic representation. Since then a lot of progress has been made in the development of geostatistics techniques of data analysis and interpolation. For this reason, geostatistics has become an extremely powerful tool for studying and evaluating space- and/or time-related phenomena, and in the present days, its own techniques are implemented in all of the most popular data analysis softwares. Presently, geostatistics supplies a collection of powerful techniques that address the study of