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Addressing Conditioning Data in Multiple-Point Statistics Simulation Algorithms Based on a Multiple Grid Approach

Straubhaar, Julien ; Malinverni, Duccio

In: Mathematical Geosciences, 2014, vol. 46, no. 2, p. 187-204

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    Titre
    • Addressing Conditioning Data in Multiple-Point Statistics Simulation Algorithms Based on a Multiple Grid Approach
    Auteur
    • Straubhaar, Julien. The Centre for Hydrogeology and Geothermics (CHYN), University of Neuchâtel, Rue Emile-Argand 11, 2000, Neuchâtel, Switzerland
    • Malinverni, Duccio. École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Mathematical Geosciences, 2014, vol. 46, no. 2, p. 187-204. Springer Berlin Heidelberg
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:325289
    Summary
    Multiple-point statistics (MPS) allows simulations reproducing structures of a conceptual model given by a training image (TI) to be generated within a stochastic framework. In classical implementations, fixed search templates are used to retrieve the patterns from the TI. A multiple grid approach allows the large-scale structures present in the TI to be captured, while keeping the search template small. The technique consists in decomposing the simulation grid into several grid levels: One grid level is composed of each second node of the grid level one rank finer. Then each grid level is successively simulated by using the corresponding rescaled search template from the coarse level to the fine level (the simulation grid itself). For a conditional simulation, a basic method (as in snesim) to honor the hard data consists in assigning the data to the closest nodes of the current grid level before simulating it. In this paper, another method (implemented in impala) that consists in assigning the hard data to the closest nodes of the simulation grid (fine level), and then in spreading them up to the coarse grid by using simulations based on the MPS inferred from the TI is presented in detail. We study the effect of conditioning and show that the first method leads to systematic biases depending on the location of the conditioning data relative to the grid levels, whereas the second method allows for properly dealing with conditional simulations and a multiple grid approach.