Métodos para seleção de modelos de semivariograma em campos aleatórios gaussianos

Abstract

There is a wide range of phenomena that present some level of structuring and spatial dependence in the variation between observations. Geostatistics include a set of tools that allow the study of spatial dependence. For example, the Semivariogram, which is considered one of the main tools, expresses the spatial dependence between two observations as a function of the distance between them. The adjustment of a model to the semivariogram is fundamental since all geostatistical prediction depends on this model. It is of great importance to adjust data to models that fit the data well so that the kriging map that is generated after the selection can present a great level of coherence with reality. As a method of selection for semivariogram models, researchers use different statistics by selecting different models for the same semivariogram. However, the selection of different models reflects on a subjective decision of the researchers, resulting in different information in the same experiment. Therefore, focusing on this research problem, this work seeks to recommend a method to better select a model that best fits the semivariogram. A total of eight usual methods of selection were found and seven were proposed using the R software environment for statistical computing and graphics. The methods were applied in thousands of simulated data in different scenarios, and it was possible to recommend one that presented the best behavior in relation to the correctness rate. Considering the classification of the usual and proposed methods in relation to the correctness rates, it is worth noting that the proposed method number 7 was in the first position in all scenarios adopted. This method is advantageous because it is composed by other methods that were also close to the first positions. Therefore, it is recommended to use it in selecting the model that best fits the semivariogram in Gaussian random fields. It is expected that this work will be fundamental for a more efficient and informative geostatistical analysis.