Localized kriging parameters optimization using local uncertainty

ABSTRACT

Estimates of natural phenomena with spatial correlation, i.e. stationary domains, are more precise and accurate when performed using geostatistical techniques (e.g. kriging). The kriging estimates require the definition of the spatial continuity model and a search strategy. Many techniques, such as unfolding and dynamic anisotropy, try to give some improvement in the estimates, considering the variations of the distributions in the geological bodies, however, the definition of the search strategy in the other parameters is unique. This study presents an alternative to this, called Localized Kriging Parameters optimization (LKPO). LKPO considers the best local kriging parameters settings (block by block) through the local uncertainly (simulations). To illustrate this methodology, a synthetic dataset is presented, and the results are compared with the methodologies currently available in the geostatistical literature. Validation checks show a significant improvement in precision and accuracy on the estimates when using local kriging parameters.

KEYWORDS:

• Search neighbourhood
• Kriging parameters
• local uncertainty
• simulations
• optimization
• search parameters
• search strategy
• local optimisation
• neighbourhood parameters

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 The modeling of stationary domains is not part of the proposed methodology, and the reader is free to choose the best techniques (some references can be visited in Abzalov (2016), Abzalov and Humphreys (2002), Chanderman et al. (2017), Duke and Hanna (2014), Emery and Ortiz (2005), Romary et al. (2012), Rossi and Deutsch (2014) and Wilde and Deutsch (2012).

2 The variations of the SNs occurred in the number of samples included in the search ellipsoid and the number of angular sectors. In addition, at least 4 samples were used in the interpolation process.

3 Two curves are involved: one is a graph of tonnage above cut-off grade versus cut-off grade and the other is the average grade of tonnage above cut-off grade versus cut-off grade.

4 The errors were calculated as a per centage in relation to each per centile of the grade’s distribution.

5 This method consists of making local comparisons of the values between the interpolated block model and the reference model along bands in the main directions (X, Y and Z). The mean is calculated for each band and the result is plotted against its location along the main directions. The plots show the coherence between the local mean along each band in both estimates.

6 According to Emery (2008) a common practice in this check consists in estimating the point-support grade distribution at the center of the block, subsequently, a post-processing for each distribution is then performed by applying of change-of-support models: Affine, Indirect Lognormal or Discrete Gaussian corrections (Matheron 1976, 1984, 1985; Emery 2004, 2008; Lajaunie 2000; Isaaks and Srivastava 1989).

7 The kriging variance depends on the sampling layout and not on the grades, i.e. between more samples used, less kriging variance.