The Piecewise Linear Model of Regionalization for Geostatistical Simulation

  • Author / Creator
  • Quantifying uncertainty is key to rational decision‐making in a geological context. Samples collected for Mineral Exploration are usually sparse and only represent a very small portion of the volume that might be mined in the future.
    To characterize and quantify geological uncertainty, it is commonplace to use Stochastic Simulation. Uncertainty is quantified and propagated in several steps when modeling geology. Samples are separated into different domains, uncertainty is quantified in the domain boundaries, parameters for modeling are established, and domain models are created. Afterward, inside each domain, continuous variables such as grades are modeled. This thesis proposes a novel method for continuous variable simulation.
    A common workflow to quantify uncertainty is to transform the data to a Gaussian distribution and use Sequential Gaussian Simulation (SGS) to generate realizations of the grades. However, this approach assumes that all spatial distributions have a Gaussian form, under the multivariate Gaussian assumption. Also, it is assumed that a single variogram model characterizes the spatial variability of the grade independent of the magnitude. High grades, however, are usually less continuous. Using SGS to model such variables, with a single variogram model will impose the same continuity for lows and high values which may be unrealistic.
    The main contribution of this thesis is to propose a novel simulation framework for grades that have different continuity for low and high values. The Piecewise Linear Model of Regionalization (PLMR) defines different bins to the data distribution and imposes different spatial model to each bin. By doing so, the model can capture different spatial continuity of highs and low values in a consistent mathematical manner. The proposed framework considers indicator variograms as well as traditional variograms, which brings more spatial information to the simulated realizations. When comparing the PLMR to modeling under the multivariate Gaussian assumption the former tends to be, on average, more conservative regarding the influence of high values in nearby locations.

  • Subjects / Keywords
  • Graduation date
    Fall 2022
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • 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.