On the reduction of algorithmic smoothing of kriged estimates
L Tolmay
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.
Keywords: kriging, smoothing, direct conditioning, kriging weights, algorithmic
smoothing.