Gocad implementation of a new space/time mathematical framework: The geochronological space

in: Proc. $22^{nd}$ Gocad Meeting, Nancy

Abstract

One of the most difficult and recurrent problem in petroleum geology is the modeling of subsurface petrophysical properties, such as porosity or permeability. Part of the difficulty comes from the sometimes complex structural geology underlying. This complexity forces the building of 3D meshes, and the use of geostatistical method to compensate. Property modeling thus often has to mix structural and petrophysical information. Since the geometry of the layers is generally much better known than the properties, it could be wise to “simplify the geology” by removing the influence of the geometry of layers, keeping then only the petrophysical data. Removing the influence of geometry not only means reducing the effects of post-depositionnal deformation, but also erasing the geometrical variation at time of deposition. The model used for geostatistics is thus one where all layers are horizontal, the general aspect being similar to the one of the Wheeler diagrams used in stratigraphy. In such a space, all the faults have disappeared, and the vertical axis is no more a geometrical coordinate z , but a geological time of deposition f . The purpose of this article is to describe a method to concretely build such a space, using a new 3D parameterization, in GOCAD. This new approach of the parameterization of space can also be used in many more applications, such as estimating the tensor of deformation applied in each point of the studied volume during its history, or measuring the sedimentary deposition speed. These application will not be developed in this article, but are some of the goals for future improvements. We will focus on the mathematical principles necessary to build such a parameterization, then we will look at the way it is implemented in GOCAD. Finally, some tests and functionalities allowing to concretely use the new parameterization will be shown.

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    BibTeX Reference

    @INPROCEEDINGS{Moyen02GM,
        author = { Moyen, Rémi and Mallet, Jean-Laurent },
         title = { Gocad implementation of a new space/time mathematical framework: The geochronological space },
     booktitle = { Proc. $22^{nd}$ Gocad Meeting, Nancy },
          year = { 2002 },
      abstract = { One of the most difficult and recurrent problem in petroleum geology is the modeling of subsurface petrophysical
    properties, such as porosity or permeability. Part of the difficulty comes from the sometimes
    complex structural geology underlying. This complexity forces the building of 3D meshes, and the use of
    geostatistical method to compensate. Property modeling thus often has to mix structural and petrophysical
    information. Since the geometry of the layers is generally much better known than the properties,
    it could be wise to “simplify the geology” by removing the influence of the geometry of layers, keeping
    then only the petrophysical data.
    Removing the influence of geometry not only means reducing the effects of post-depositionnal deformation,
    but also erasing the geometrical variation at time of deposition. The model used for geostatistics
    is thus one where all layers are horizontal, the general aspect being similar to the one of the Wheeler
    diagrams used in stratigraphy. In such a space, all the faults have disappeared, and the vertical axis is no
    more a geometrical coordinate z , but a geological time of deposition f . The purpose of this article is to
    describe a method to concretely build such a space, using a new 3D parameterization, in GOCAD.
    This new approach of the parameterization of space can also be used in many more applications, such
    as estimating the tensor of deformation applied in each point of the studied volume during its history, or
    measuring the sedimentary deposition speed. These application will not be developed in this article, but
    are some of the goals for future improvements. We will focus on the mathematical principles necessary
    to build such a parameterization, then we will look at the way it is implemented in GOCAD. Finally,
    some tests and functionalities allowing to concretely use the new parameterization will be shown. }
    }