Statistical modeling of gas-permeability spatial variability along a limestone core

• Published in: Spatial statistics 2019-12, Vol.34, p.100249, Article 100249
• Main Authors: Siena, M., Riva, M., Giamberini, M., Gouze, P., Guadagnini, A.
• Format: Article
• Language: English
• Subjects: Earth Sciences; Generalized sub-Gaussian model; Geophysics; Geostatistical analysis; Heavy-tailed distributions; Model parameter estimation; Sciences of the Universe; Spatial heterogeneity
• ISSN: 2211-6753; 2211-6753
• DOI: 10.1016/j.spasta.2017.07.007

A set of more than 200 gas-permeability data is collected on centimeter-scale plugs drilled in a regular pattern along a core of Majorca limestone to test at the laboratory scale a recent model for the statistical characterization of spatial heterogeneity. Data are interpreted as samples of a generalized sub-Gaussian (GSG) random field. The latter results from the subordination of a spatially-correlated Gaussian field by a statistically-independent random field, which we take as log-normal in this application. The GSG model we analyze has been shown to be consistent with non-Gaussian and statistical scaling features that are frequently exhibited by several environmental variables, including hydrological properties. Key objectives of the current study are: (i) to provide a high-quality dataset from which one can assess statistical scaling features displayed by the data and their spatial increments; and (ii) to test the ability of the GSG model to characterize the observed behavior. We apply a statistical inference method to estimate the parameters of the GSG model on the basis of the available data. We then take advantage of formal model-identification criteria to consider the relative skills of diverse variogram models associated with the underlying Gaussian field to interpret the observed behavior of the dataset. Our results corroborate the effectiveness of the GSG modeling framework to characterize the documented aspects of statistical scaling.