Geostatistics with locally varying anisotropy

• Author / Creator

  Boisvert, Jeff

• Many geological deposits contain nonlinear anisotropic features such as veins, channels, folds or local changes in orientation; numerical property modeling must account for these features to be reliable and predictive. This work incorporates locally varying anisotropy into inverse distance estimation, kriging and sequential Gaussian simulation. The methodology is applicable to a range of fields including (1) mining-mineral grade modeling (2) petroleum-porosity, permeability, saturation and facies modeling (3) environmental-contaminate concentration modeling. An exhaustive vector field defines the direction and magnitude of anisotropy and must be specified prior to modeling. Techniques explored for obtaining this field include: manual; moment of inertia of local covariance maps; direct estimation and; automatic feature interpolation.

  The methodology for integrating locally varying anisotropy into numerical modeling is based on modifying the distance/covariance between locations in space. Normally, the straight line path determines distance but in the presence of nonlinear features the appropriate path between locations traces along the features. These paths are calculated with the Dijkstra algorithm and may be nonlinear in the presence of locally varying anisotropy. Nonlinear paths do not ensure positive definiteness of the required system of equations when used with kriging or sequential Gaussian simulation. Classical multidimensional scaling is applied to ensure positive definiteness but is found to be computationally infeasible for large models, thus, landmark points are used for efficiency with acceptable losses in precision. The methodology is demonstrated on two data sets (1) net thickness of the McMurray formation in northern Alberta and (2) gold grade in a porphyry copper deposit. Integrating LVA into numerical modeling increases local accuracy and improves leave-one-out cross validation analysis results in both case studies.

• Subjects / Keywords

  • Krige
  • Geostatistics
  • Models
  • Dijkstra
  • MDS
  • Anisotropy
  • Resources
  • Multidimensional
  • ISOMAP
  • Estimation
  • Stationarity
  • Simulations

• Graduation date

  Spring 2010

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R31X5C

• 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.