Nonparametric Geostatistical Simulation of Subsurface Facies: Tools for Validating the Reproduction of, and Uncertainty in, Facies Geometry

  • Nasser MadaniEmail author
  • Mohammad Maleki
  • Xavier Emery
Original Paper


Delineation of facies in the subsurface and quantification of uncertainty in their boundaries are significant steps in mineral resource evaluation and reservoir modeling, which impact downstream analyses of a mining or petroleum project. This paper investigates the ability of nonparametric geostatistical simulation algorithms (sequential indicator, single normal equation and filter-based simulation) to construct realizations that reproduce some expected statistical and spatial features, namely facies proportions, boundary regularity, contact relationships and spatial correlation structure, as well as the expected fluctuations of these features across the realizations. The investigation is held through a synthetic case study and a real case study, in which a pluri-Gaussian model is considered as the reference for comparing the simulation results. Sequential indicator simulation and single normal equation simulation based on over-restricted neighborhood implementations yield the poorest results, followed by filter-based simulation, whereas single normal equation simulation with a large neighborhood implementation provides results that are closest to the reference pluri-Gaussian model. However, some biases and inaccurate fluctuations in the realization statistics (facies proportions, indicator direct and cross-variograms) still arise, which can be explained by the use of a single finite-size training image to construct the realizations.


Geological uncertainty Pluri-Gaussian model Sequential indicator simulation Single normal equation simulation Filter-based simulation Statistical fluctuations 



The first author acknowledges the Nazarbayev University for financial supporting. The second and third authors acknowledge the support of the Chilean Commission for Scientific and Technological Research (CONICYT), through projects CONICYT/FONDECYT/POSTDOCTORADO/N°3180655 and CONICYT PIA Anillo ACT1407, respectively. The examples presented in “Essential Statistical and Geometrical Characteristics of Facies” section were provided by Dr. Bijan Biranvand from the Department of Petroleum Geology, Research Institute of Petroleum Industry, Tehran, Iran. The data for the case study were provided by CODELCO—Chile. Constructive comments by two anonymous reviewers are gratefully acknowledged. Also, we deeply thank Dr. Carranza for the valuable comments on the final version of manuscript.


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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  • Nasser Madani
    • 1
    Email author
  • Mohammad Maleki
    • 2
    • 3
  • Xavier Emery
    • 2
    • 3
  1. 1.Department of Mining Engineering, School of Mining and GeosciencesNazarbayev UniversityAstanaKazakhstan
  2. 2.Department of Mining EngineeringUniversity of ChileSantiagoChile
  3. 3.Advanced Mining Technology CenterUniversity of ChileSantiagoChile

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