Mathematical Geosciences

, Volume 45, Issue 2, pp 131–147 | Cite as

Parallel Multiple-Point Statistics Algorithm Based on List and Tree Structures

  • Julien StraubhaarEmail author
  • Alexandre Walgenwitz
  • Philippe Renard


Multiple-point statistics are widely used for the simulation of categorical variables because the method allows for integrating a conceptual model via a training image and then simulating complex heterogeneous fields. The multiple-point statistics inferred from the training image can be stored in several ways. The tree structure used in classical implementations has the advantage of being efficient in terms of CPU time, but is very RAM demanding and then implies limitations on the size of the template, which serves to make a proper reproduction of complex structures difficult. Another technique consists in storing the multiple-point statistics in lists. This alternative requires much less memory and allows for a straightforward parallel algorithm. Nevertheless, the list structure does not benefit from the shortcuts given by the branches of the tree for retrieving the multiple-point statistics. Hence, a serial algorithm based on list structure is generally slower than a tree-based algorithm. In this paper, a new approach using both list and tree structures is proposed. The idea is to index the lists by trees of reduced size: the leaves of the tree correspond to distinct sublists that constitute a partition of the entire list. The size of the indexing tree can be controlled, and then the resulting algorithm keeps memory requirements low while efficiency in terms of CPU time is significantly improved. Moreover, this new method benefits from the parallelization of the list approach.


Geostatistical simulation Multiple-point statistics Categorical variable List and tree structures Parallel computing 



We are grateful to Christian Höcker from Backer Hughes, to Pierre Biver from Total and to Jacques Rivoirard from Mines Paris Tech for providing us training images. We also thank the anonymous reviewers for their comments.


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Copyright information

© International Association for Mathematical Geosciences 2013

Authors and Affiliations

  • Julien Straubhaar
    • 1
    Email author
  • Alexandre Walgenwitz
    • 2
  • Philippe Renard
    • 1
  1. 1.The Centre for Hydrogeology and Geothermics (CHYN)University of NeuchâtelNeuchâtelSwitzerland
  2. 2.Ephesia Consult SAGenevaSwitzerland

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