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Mariethoz, Grégoire

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Mariethoz, Grégoire
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https://libra.unine.ch/handle/123456789/941

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  • Publication
    Accès libre
    An Improved Parallel Multiple-Point Algorithm Using a List Approach
    (2011-4)
    Straubhaar, Julien 
    ;
    Renard, Philippe 
    ;
    Mariethoz, Grégoire 
    ;
    Froidevaux, Roland
    ;
    Besson, Olivier 
    Among the techniques used to simulate categorical variables, multiple-point statistics is becoming very popular because it allows the user to provide an explicit conceptual model via a training image. In classic implementations, the multiple-point statistics are inferred from the training image by storing all the observed patterns of a certain size in a tree structure. This type of algorithm has the advantage of being fast to apply, but it presents some critical limitations. In particular, a tree is extremely RAM demanding. For three-dimensional problems with numerous facies, large templates cannot be used. Complex structures are then difficult to simulate. In this paper, we propose to replace the tree by a list. This structure requires much less RAM. It has three main advantages. First, it allows for the use of larger templates. Second, the list structure being parsimonious, it can be extended to include additional information. Here, we show how this can be used to develop a new approach for dealing with non-stationary training images. Finally, an interesting aspect of the list is that it allows one to parallelize the part of the algorithm in which the conditional probability density function is computed. This is especially important for large problems that can be solved on clusters of PCs with distributed memory or on multicore machines with shared memory.
  • Publication
    Accès libre
    Integrating collocated auxiliary parameters in geostatistical simulations using joint probability distributions and probability aggregation
    (2009)
    Renard, Philippe 
    ;
    Mariethoz, Grégoire 
    ;
    Froidevaux, Roland
    We propose a new cosimulation algorithm for simulating a primary attribute using one or several secondary attributes known exhaustively on the domain. This problem is frequently encountered in surface and groundwater hydrology when a variable of interest is measured only at a discrete number of locations and when the secondary variable is mapped by indirect techniques such as geophysics or remote sensing. In the proposed approach, the correlation between the two variables is modeled by a joint probability distribution function. A technique to construct such relation using underlying variables and physical laws is proposed when field data are insufficient. The simulation algorithm proceeds sequentially. At each location of the domain, two conditional probability distribution functions (cpdf) are inferred. The cpdf of the main attribute is inferred in a classical way from the neighboring data and a model of spatial variability. The second cpdf is inferred directly from the joint probability distribution function of the two attributes and the value of the secondary attribute at the location to be simulated. The two distribution functions are combined by probability aggregation to obtain the local cpdf from which a value for the primary attribute is randomly drawn. Various examples using synthetic and remote sensing data demonstrate that the method is more accurate than the classical collocated cosimulation technique when a complex relation relates the two attributes.