Automatic Variogram Modeling

• Author / Creator

  Davila Saavedra, Luis A

• The variogram characterizes the spatial variability of a regionalized variable. Variogram calculation and modeling require a significant amount of professional time. The variogram has a significant impact on estimation and simulation, and it has a considerable impact in the mining industry since ordinary kriging is one of the most used tools for resource estimation. This thesis proposes novel tools and techniques related to automatic variogram calculation.
  The first contribution of this thesis is implementing a GSLIB-like program: autovar. This program calculates the variograms for disseminated and tabular deposits. Autovar prompts the user for some basic parameters only. Autovar implements all necessary steps to get the experimental variogram points and its model directly from the data. The program infers the principal directions of continuity by eigendecomposition of the inertia tensor, followed by an order of the vectors. Then, the program calculates the experimental variogram points and models them. This thesis considers standard guidelines for variogram calculation and modeling. Different search parameters are implemented based on the deposit type. An important functionality of the program is the geolocated option, which allows the identification of variability centred at points (anchor locations) selected by the practitioner.
  The second contribution is a novel technique to estimate a block model using a mix of ordinary kriging models. This mixed estimation technique considers several block kriging models and mixes them at each node of the block model. Each estimated model has a different variogram as input, reflecting different continuity characteristics. The variograms used in the kriging estimations are outputs from the autovar program: a general variogram and geolocated variograms centred at each selected anchor location. The weights are calculated based on the distance from each node to the anchor points. The postprocessing step standardizes the weights to add up to one, ensuring that kriging is exact. Generally, this technique recognizes local variability better than a regular technique.
  This thesis presents different examples to show the potential and limitations of the proposed methodologies. This research presents a comparison of the proposed workflows with regular methodologies. Finally, a summary of tests is shown at the end to compare the results of the mixed estimation methodology with a regular estimation workflow.

• Subjects / Keywords

  • Automatic variogram modeling
  • Variogram
  • Geostatistics
  • Local variability
  • Estimation

• Graduation date

  Spring 2024

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-kj2a-bj79

• License

  This thesis is made available by the University of Alberta Libraries 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.