Geostatistical modelling of cyclic and rhythmic facies architectures

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 covariance allowing a dampened hole-effect to capture rhythmicity in the vertical direction and a different covariance in the lateral plane along strata, as in space-time models. In addition, facies ordering is created by using a spatial shift between two latent Gaussian functions in the Pluri-Gaussian approach. Rapid conditioning to data is performed via Gibbs sampling and kriging using the screening properties of separable covariances. The resulting facies transiograms can show complex patterns of cyclicity and rhythmicity. Finally, a three dimensional case study of shallow-marine carbonate deposits at outcrop shows the applicability of the modelling method.

Versatile Parametric Classes of Covariance Functions that Interlace Anisotropies and Hole Effects

“…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.…”