Advances in Geostatistical Modeling of Categorical Variables

• Author / Creator

  Barros Ortiz, Rafael

• In the mining and petroleum industries, subsurface resources are modeled using data sets obtained
  from widely spaced drilling. It is crucial to optimize the use of available information from
  these data sets while reducing the amount required to adequately assess risks and uncertainties. Typically,
  these data sets include spatially correlated categorical and continuous variables. Geostatistics
  is commonly applied to model these types of spatial variables.
  Categorical variables are modeled first to establish stationary domains for continuous variables
  like ore grades and, therefore, are essential for the accurate modeling of continuous variables. Techniques
  such as object-based models (Lantuéjoul, 2002), sequential indicator simulation (A. G. Journel
  & Alabert, 1990), multiple-point statistics (S. Strebelle, 2002), truncated Gaussian and pluri-
  Gaussian simulation (Armstrong et al., 2011; Matheron et al., 1987), and hierarchical truncated
  pluri-Gaussian simulation (D. Silva, 2018) have been developed to model and characterize geological
  uncertainties. Modern approaches in multivariate modeling of continuous variables include principal
  component analysis (PCA) for dimension reduction and decorrelation. Suro (1988) applied PCA to
  decorrelate indicators and used kriging, followed by a back transformation, to derive the conditional
  cumulative distribution function.
  This research aims to obtain a greater understanding of the characteristics of categorical indicator
  variables. Studying the characteristics of categorical indicator variograms led to the demonstration
  that the nugget effect must be zero. Additionally, correlograms are shown to be a robust alternative
  in the presence of clustered data. This work also compares multiple-point statistics-based (MPS)
  conditional probabilities to variogram-based simple kriging (SK), ordinary kriging (OK), simple
  cokriging (SCK), and standardized ordinary cokriging (SOCK) estimates to evaluate which kriging
  variant comes closest to the benchmark MPS probabilities. SOCK stands out among the kriging
  variants when compared to the MPS probabilities. Subsequently, SOCK and OK estimates are
  compared to reference (training images) for several different cases. The difference in the root mean
  squared error (RMSE) gives a very small advantage to the SOCK method.
  The research work of this thesis also led to the implementation of a method to mitigate extreme
  weights that result from indefinite or ill-conditioned matrices in linear systems of equations. The
  method consists of inflating the diagonal of the left-hand side covariance matrix by a small constant.
  As the constant increases, all weights converge to 1
  n, where n is the number of weights. This
  technique shows that the extreme weights are mitigated but does not significantly alter the overall
  estimation across an entire grid.

• Subjects / Keywords

  • Geostatistics
  • Categorical

• Graduation date

  Fall 2024

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-9953-ne44

• License

  This thesis is made available by the University of Alberta Library with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.