On the Reduction of Algorithmic Smoothing of Kriged Estimates

Utilizing a very large database from a mined-out area on a South African gold mine, the relative efficacy of a method to mitigate the smoothing effect introduced by the algorithmic constraints imposed by kriging was investigated. Smoothing effects arising from limited data availability are differentiated from the smoothing arising from the application of estimation algorithms. Very little can be done to ameliorate smoothing of estimates because of too little data, barring additional drilling or sampling. However, the smoothing effects resulting from the kriging process are shown to be mitigated by use of an alternative algorithm. The primary criterion in the development of the new algorithm was to avoid re-introducing conditional bias. This paper examines firstly the smoothing effects introduced into estimates via the kriging covariance matrix, secondly the process for ameliorating the smoothing effect, and finally it uses a case study to demonstrate the effectiveness of the new algorithm on a very large database. The database was used to introduce a 60 m by 60 m drilling pattern which in turn was used to model the semi-variogram and produce 30 m by 30 m kriged block estimates. The follow-up database was then re-introduced (roughly 5 m by 5 m grid spacing) and averaged into 30 m by 30 m blocks to provide a direct comparison with the initial estimates. In this way the extent of smoothing and accuracy of the estimates before and after the corrections was tested.