Geostatistical modelling of cyclic and rhythmic facies architectures

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 characterized by shallowing or deepening-upward sequences and rhythmicity by a low range of variability in cycle thicknesses. 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 plan, 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 modeling method.