Designing robust covariance models for geostatistical applications

Abstract Conventional covariance models based on Euclidean distance measures often fail to deal with the complexities of geographical landscapes or geological discontinuities such as natural obstacles (e.g., physical barriers) that disturb simple spatial relationships. To address these difficulties and complexities, the incorporation of non-Euclidean distance metrics can provide the research field with a wider range of analytical tools adapted to complex geographic landscapes to facilitate more robust resource modeling and thus more effective resource management strategies. However, since traditional covariance models are based on Euclidean distances primarily, there is a possibility that they may fail to yield valid covariance matrices in non-Euclidean conditions. In this research, alternative distance metrics, such as Manhattan or Chebyshev, are considered, necessitating the development of new covariance models capable of supporting these standard metrics, thus ensuring the positive definiteness required for reliable covariance matrices.