Enhanced Geologic Modeling of Multiple Categorical Variables

  • Author / Creator
    Silva, Diogo
  • Widely spaced data sets from drilling are used in the mining and petroleum industries to model subsurface resources. These data sets have high associated economic and environmental costs. Maximizing the use of information contained in data while minimizing the amount of data required to achieve acceptable understanding of risk and uncertainty is critical in this context. These data sets usually consists of spatially correlated categorical and continuous variables that are modeled using geostatistics, which is a branch of statistics particularly applicable to spatiotemporal variables. Categorical variables are usually modeled first and utilized to define stationary domains for the modeling of the continuous variables. As a result, the categorical variables are key for the accurate modeling of attributes such as ore concentrations, metallurgical recoveries and structural stability. Each one of these variables are affected in different ways by different combinations of categorical variables. Limitations of existing techniques force the merging of multiple categorical variables into a single variable causing the loss of information and deteriorating the quality of predictions. Amongst the existing techniques for categorical modeling, TPGS is one of the most flexible. The utilization of underlying Gaussian latent variables for the simulation of categories allows for the use of the well established techniques for the simulation of GRF. The truncation rules utilized to map the continuous variables to the categorical variable allow the introduction of geological constraints. These geological constraints assist the generation of models that are more realistic and accurate. The practical application of TPGS is often limited to the utilization of no more than three Gaussian latent variables. This is mostly attributed to the current practice on the definition of truncation rules using truncation masks. This limitation is addressed in this thesis with the development the HTPG. HTPG utilizes a tree structure for the truncation of the Gaussian latent variables facilitating its definition based on geological expertise. The developed methodology allows for the utilization of an arbitrary number of latent variables to model an arbitrary number of categories. As a result, the developed method better explores the potential of the truncated Gaussian method. The HTPG framework developed in this thesis is extended to the modeling of multiple categorical variables. The extension is achieved by allowing correlation between the latent Gaussian variables defining each categorical variable. This improves the utilization of the information available by preventing the merging of multiple categorical variables into a single set. It is demonstrated that the developed technique leads to significant improvement of the prediction of attributes that depends on the multivariate relationship between the categorical variables. The research work of this thesis also led to significant contributions in other aspects of the truncated Gaussian methods, such as the numerical derivation of the latent variables variograms and the imputation of the latent variables. Significant contributions are also made on the multiple data imputation for application with multivariate transformations in advanced geostatistical methods.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
  • Degree
    Doctor of Philosophy
  • DOI
  • License
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