The application of the jackknife in geostatistical resource estimation: Robust estimator and its measure of uncertainty.

Abstract

The application of the jackknife in geostatistical resource estimation (in conjunction with kriging) is shown to yield two significant contributions. The first one is a robust new estimator, called jackknife kriging, which retains ordinary kriging's simplicity and global unbiasedness while at the same time reduces its local bias and oversmoothing tendency. The second contribution is the ability, through the jackknife standard deviation, to set a confidence limit for a reserve estimate of a general shape. Jackknifing the ordinary kriging estimate maximizes sample utilization, as well as information of sample spatial correlation. The jackknife kriging estimator handles the high grade smearing problem typical in ordinary kriging by assigning more weight to the closest sample(s). The result is a reduction in the local bias without sacrificing global unbiasedness. When data distribution is skewed, log transformation of the data prior to jackknifing is shown to improve the estimate by making the data behave better under jackknifing. The technique of block kriging short-cut, combined with jackknifing, are shown as an easy-to-use solution to the problem of grade estimation of a general three-dimensional digitized shape and the uncertainty associated with the estimate. The results are a single jackknife kriging estimate for the shape and its corresponding jackknife variance. This approach solves the problem of combining independent block estimation variances, and provides a simple way to set confidence levels for global estimates. Unlike the ordinary kriging variance, which is a measure of data configuration and is independent of data values, the jackknife kriging variance reflects the variability of the values being inferred, both on an individual block level and on the global level. Case studies involving two exhaustive (symmetric and highly skewed) data sets indicates the superiority of the jackknife kriging estimator over the original (ordinary kriging) estimator. Some instability of the log-transformed jackknife estimate is noted in the highly skewed situation, where the data do not generally behave well under standard jackknifing. A promising solution for future investigations seems to lie in the use of weighted jackknife formulation, which should better handle a wider spectrum of data distribution.