Mathematical Geosciences

, Volume 48, Issue 4, pp 353–369

Change-of-Support Models on Irregular Grids for Geostatistical Simulation

  • Victor Zaytsev
  • Pierre Biver
  • Hans Wackernagel
  • Denis Allard
Article

DOI: 10.1007/s11004-015-9614-x

Cite this article as:
Zaytsev, V., Biver, P., Wackernagel, H. et al. Math Geosci (2016) 48: 353. doi:10.1007/s11004-015-9614-x
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Abstract

In many domains, numerical models are initialized with inputs defined on irregular grids. In petroleum reservoir engineering, they consist of a great variety of grid cells of different size and shape to enable fine-scale modeling in the vicinity of the wells and coarse modeling in less important regions. Geostatistical simulation algorithms, which are used to populate the cells of unstructured grids, often have to address the problem of transition from the small-scale statistical data stemming from laboratory cores analysis and seismic processing to the multiple larger scale geological supports. The reasonable generalization of the above-mentioned problem is integrating the point-support data to simulations on irregular supports. Classical geostatistical simulation methods for generating realizations of a stationary Gaussian random function cannot be applied to unstructured grids directly, because of the uneven supports. This article provides a critical review of existing geostatistical simulation methodologies for unstructured grids, including fine-scale simulations with upscaling and direct sequential simulation algorithms, and presents two different generalizations of the discrete Gaussian model for this purpose, thereby discussing the theoretical assumptions and the accuracy when implementing these models.

Keywords

Unstructured grids Geostatistics Direct sequential simulation Change of support Discrete Gaussian model 

Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  • Victor Zaytsev
    • 1
    • 2
  • Pierre Biver
    • 1
  • Hans Wackernagel
    • 2
  • Denis Allard
    • 3
  1. 1.Geostatistics and Uncertainties ServiceTotal S.A.Pau CedexFrance
  2. 2.Equipe de Géostatistique, Centre de Géosciences, MINES ParisTechPSL Research UniversityFontainebleauFrance
  3. 3.Biostatistics and Spatial Processes (BioSP)INRAAvignon Cedex 9France