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.

Lateral facies variations in the Triassic Dachstein platform: A challenge for cyclostratigraphy

“…This study emphasizes the importance of quantifying lateral persistence in the analysis of sedimentary cycles and provides quantitative data for carbonate depositional models (cf. Burgess, 2016;Burgess & Wright, 2003; Burgess, Wright, & Emery, 2001;Le Blévec, Dubrule, John, & Hampson, 2018).…”

Geostatistical Earth modeling of cyclic depositional facies and diagenesis

“…A geostatistical method has been developed recently to model simultaneously facies cyclicity and rhythmicity (Le Blévec et al, 2018), thus improving the realism of facies Earth models. The method is based on Pluri-Gaussian Simulations (Armstrong et al, 2011), constrained by facies transiograms.…”

“…The method is based on Pluri-Gaussian Simulations (Armstrong et al, 2011), constrained by facies transiograms. The facies asymmetric ordering (or cyclicity) is defined by two Gaussian random functions spatially shifted from each other, and rhythmicity of the facies succession is modeled by defining new hole-effect covariance models (Le Blévec et al, 2018). However, the method has only be tested so far for a model with three facies and it might be more difficult to model cyclicity with more facies, which is investigated here.…”

“…Stratigraphic forward models can produce asymmetry between facies in lateral directions (Burgess et al, 2001), and such lateral facies asymmetry is also explicit within Walther's Law (e.g., Middleton, 1973). This could possibly be modeled with the shifted Pluri-Gaussian method (Le Blévec et al, 2018) by defining a spatial shift with a lateral component.…”

“…The algorithm of Renard et al (2008) to model diagenesis is thus extended here by including a shift between depositional and diagenetic facies fields, which allows diagenetic facies to overprint depositional facies preferentially at their top or at their base. These relationships are constrained by cross-transiograms between the two facies fields, and the method is also combined with the advancements of Le Blévec et al (2018), so that diagenesis is modeled in the context of depositional facies cyclicity and rhythmicity.…”