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Modeling and Simulating Depositional Sequences Using Latent Gaussian Random Fields

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Abstract

Simulating a depositional (or stratigraphic) sequence conditionally on borehole data is a long-standing problem in hydrogeology and in petroleum geostatistics. This paper presents a new rule-based approach for simulating depositional sequences of surfaces conditionally on lithofacies thickness data. The thickness of each layer is modeled by a transformed latent Gaussian random field allowing for null thickness thanks to a truncation process. Layers are sequentially stacked above each other following the regional stratigraphic sequence. By choosing adequately the variograms of these random fields, the simulated surfaces separating two layers can be continuous and smooth. Borehole information is often incomplete in the sense that it does not provide direct information about the exact layer that some observed thickness belongs to. The latent Gaussian model proposed in this paper offers a natural solution to this problem by means of a Bayesian setting with a Markov chain Monte Carlo (MCMC) algorithm that can explore all possible configurations that are compatible with the data. The model and the associated MCMC algorithm are validated on synthetic data and then applied to a subsoil in the Venetian Plain with a moderately dense network of cored boreholes.

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Acknowledgements

This work was initiated during a visit of the first author to Ca’ Foscari University of Venice. He acknowledges the support of that institution. We wish to thank two anonymous reviewers for their in-depth and detailed reading of the first version of the manuscript. Their many valuable comments helped us to improve the manuscript.

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Authors and Affiliations

  1. BioSP, INRAE, 84914, Avignon, France

    Denis Allard

  2. Department of Geosciences, University of Padua, Padua, Italy

    Paolo Fabbri

  3. Department of Environmental Sciences, Informatics and Statistics, Ca’ Foscari University of Venice, Venice, Italy

    Carlo Gaetan

Authors
  1. Denis Allard
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  2. Paolo Fabbri
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  3. Carlo Gaetan
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Corresponding author

Correspondence to Denis Allard.

Appendix A: A Longer Example of Incomplete Sequence

Appendix A: A Longer Example of Incomplete Sequence

See Table 5.

Table 5 A longer and more complex example of a parent sequence \(\mathbf {C}\) = [Blue-Red, Blue-Green-Blue-Red-Green-Blue] with respect to a recorded sequence \(\mathbf {C}^o\) and \(\mathbf {T}^o\)
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Allard, D., Fabbri, P. & Gaetan, C. Modeling and Simulating Depositional Sequences Using Latent Gaussian Random Fields. Math Geosci 53, 469–497 (2021). https://doi.org/10.1007/s11004-020-09875-0

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