Mineral Resource Estimates with Machine Learning and Geostatistics

• Author / Creator

  Samson, Matthew

• Mineral resource estimation is an integral part of making informed decisions while evaluating the
  feasibility of a mining operation. Geostatistical tools estimate geological and spatial features with
  the assumptions of first and second‑order stationarity. In the modelling process, Geostatisticians
  make subjective decisions regarding stationarity, potentially introducing bias into the estimates.
  Kriging is considered the best unbiased linear estimation technique for modelling geological and
  spatial features; however, in domains where data is non‑Gaussian, and features are complex, the
  assumption of stationarity can cause difficulties in the modelling process. The purpose of this thesis
  is to present two new estimation techniques. The first estimation technique uses machine learning
  for geological and spatial estimations without assuming first and second‑order stationarity, minimizing
  human interaction and potentially reducing estimation bias. The second technique is a
  hybrid method that consists of using geostatistical methods combined with the machine learning
  method. Integrating geostatistics and machine learning improves geological and spatial estimation
  in situations that have complex features, poorly defined domains, or non‑Gaussian data.
  Elliptical radial basis function networks (ERBFN) and k‑means clustering are used for estimation.
  An ERBFN machine learning method takes advantage of a Gaussian function to generate
  geological estimates similar to kriging. An ERBFN does not require the assumption of stationarity
  and the only input features required are the spatial coordinates of the known data. The parameter
  required for the ERBFN is the number of nodes to model the estimations domain. Each node learns
  a unique anisotropy allowing for complex features to be modelled.
  The hybrid estimation takes advantage of the machine learning estimation from the ERBFN
  and uses it as an exhaustive secondary data in ordinary intrinsic collocated cokriging. The hybrid
  estimation requires the assumption of stationarity and variograms must be modelled. Combining
  machine learning and geostatistics takes advantage of the unbiasedness of kriging while including
  the non‑stationary features modelled in the ERBFN.
  To validate the estimation techniques, examples are simulated and sampled. Machine learning,
  hybrid, and kriging estimates are made using the sampled dataset and compared to the exact
  truth. Multiple validation checks are used to compare the different estimates. The coefficient of
  determination and root mean squared error are used to assess model performance.Plots of the estimates
  and error maps are used for visual inspection to determine if modelling artifacts are present.
  Histograms determine if the mean and data distribution reproduction are reasonable.
  The machine learning estimation method developed in this thesis is shown to produce similar
  results to simple kriging without requiring the assumption of first and second‑order stationary.
  The hybrid estimation technique developed in this thesis appears to outperform simple kriging
  in scenarios that demonstrate non‑stationary features, poorly defined domains, and non‑Gaussian
  data. The research work of the thesis has led to a significant contribution in making spatial and
  geological predictions.

• Subjects / Keywords

  • Mining
  • Geostatistics
  • Machine Learning
  • Resource Estimation
  • Neural Networks
  • Engineering

• Graduation date

  Spring 2020

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-xxxz-5z86

• License

  Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.