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 characterised by shallowing-upward or deepening-upward sequences and rhythmicity by the repetition of facies at constant interv...

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Bibliographic Details
Published inMathematical geosciences Vol. 50; no. 6; pp. 609 - 637
Main Authors Le Blévec, Thomas, Dubrule, Olivier, John, Cédric M., Hampson, Gary J.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018
Springer Nature B.V
Subjects
Carbonates
Case studies
Chemistry and Earth Sciences
Computer Science
Computer simulation
Covariance
Dimensions
Direction
Earth and Environmental Science
Earth Sciences
Geostatistics
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Kriging interpolation
Modelling
Outcrops
Physics
Rhythms
Statistical methods
Statistics for Engineering
Three dimensional models
Hole-effect
Transiogram
Asymmetric facies ordering
Carbonate
Separable
Pluri-Gaussian
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Summary: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.
ISSN:1874-8961
1874-8953
DOI:10.1007/s11004-018-9737-y