Abstract:A Pluri-Gaussian method is developed for facies variables in three dimensions to model vertical cyclicity related to facies ordering and rhythmicity. Cyclicity is generally characterised by shallowing-upward or deepening-upward sequences and rhythmicity by the repetition of facies at constant intervals along sequences. Both of these aspects are commonly observed in shallow-marine carbonate successions, especially in the vertical direction. A grid-free spectral simulation approach is developed, with a separable… Show more
“…The former are characterized by tight limestone and isolated vugs, whereas the latter are associated with interconnected matrix and vugs or with a combination of interconnected vugs surrounded by limestone (Parra et al, 2009). Cyclic behaviors in the vertical covariances or variograms of rock properties are often observed in carbonate sequences and can be explained by periodic processes of deposition due to eustatic sea level oscillations or to tectonic activities (Chilès and Delfiner, 2012;Le Blévec et al, 2020). The east and depth are shifted to a local coordinate system.…”
Covariance functions are a fundamental tool for modeling the dependence structure of spatial random fields. This work investigates novel constructions for covariance functions that enable the integration of anisotropies and hole effects in complex and versatile ways, having the potential to provide more accurate representations of dependence structures arising with real-world data.We show that these constructions extend widely used covariance models, including the Matérn, Cauchy, compactly-supported hypergeometric and cardinal sine models. We apply our results to a geophysical data set from a rock-carbonate aquifer and demonstrate that the proposed models yield more accurate predictions at unsampled locations compared to basic covariance models.
“…The former are characterized by tight limestone and isolated vugs, whereas the latter are associated with interconnected matrix and vugs or with a combination of interconnected vugs surrounded by limestone (Parra et al, 2009). Cyclic behaviors in the vertical covariances or variograms of rock properties are often observed in carbonate sequences and can be explained by periodic processes of deposition due to eustatic sea level oscillations or to tectonic activities (Chilès and Delfiner, 2012;Le Blévec et al, 2020). The east and depth are shifted to a local coordinate system.…”
Covariance functions are a fundamental tool for modeling the dependence structure of spatial random fields. This work investigates novel constructions for covariance functions that enable the integration of anisotropies and hole effects in complex and versatile ways, having the potential to provide more accurate representations of dependence structures arising with real-world data.We show that these constructions extend widely used covariance models, including the Matérn, Cauchy, compactly-supported hypergeometric and cardinal sine models. We apply our results to a geophysical data set from a rock-carbonate aquifer and demonstrate that the proposed models yield more accurate predictions at unsampled locations compared to basic covariance models.
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