2020/03/25 by Denis Allard, Allard, Denis, Paolo Fabbri +3
Earth and Planetary Sciences · Engineering · Environmental Science · Mathematics · #Algorithm #Applications (stat.AP) #Artificial intelligence #Bayesian probability #Borehole #Computer science #FOS: Computer and information sciences #Gaussian #Gaussian process #Gaussian random field #Geological Modeling and Analysis #Geology #Geomorphology #Geostatistics #Geotechnical engineering #Hydrogeology #Machine learning #Markov chain Monte Carlo #Mathematics #Random field #Reservoir Engineering and Simulation Methods #Sedimentary depositional environment #Sequence (biology) #Soil Geostatistics and Mapping #Statistics #Truncation (statistics) #math.ST #stat.AP
paper · pdf · doi:10.48550/arxiv.2003.11383
arxiv created 2020/03/25 · openalex publication_date 2020/03/25 · arxiv updated 2020/03/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Simulating a depositional (or stratigraphic) sequence conditionally on\nborehole data is a long-standing problem in hydrogeology and in petroleum\ngeostatistics. This paper presents a new rule-based approach for simulating\ndepositional sequences of surfaces conditionally on lithofacies thickness data.\nThe thickness of each layer is modeled by a transformed latent Gaussian random\nfield allowing for null thickness thanks to a truncation process. Layers are\nsequentially stacked above each other following the regional stratigraphic\nsequence. By choosing adequately the variograms of these random fields, the\nsimulated surfaces separating two layers can be continuous and smooth. Borehole\ninformation is often incomplete in the sense that it does not provide direct\ninformation as to the exact layer some observed thickness belongs to. The\nlatent Gaussian model proposed in this paper offers a natural solution to this\nproblem by means of a Bayesian setting with a Markov Chain Monte Carlo (MCMC)\nalgorithm that can explore all possible configurations compatible with the\ndata. The model and the associated MCMC algorithm are validated on synthetic\ndata and then applied to a subsoil in the Venetian Plain with a moderately\ndense network of cored boreholes.\n