Geostatistics in GenStat-what would earth scientists like next?
by
Richard Webster
Rothamsted Experimental Station

GenStat contains facilities for standard analyses of linear geostatistics. It computes sample (experimental) variograms from data by the method of moments, it fits the most commonly used models to the results, and it combines the fitted models with the data to estimate (predict) at points and over larger blocks by ordinary kriging. These facilities have probably served adequately in 90% of applications to date.

Earth scientists are becoming more demanding, and geostatisticians are becoming more adventurous in trying meet those demands. What seemed enough ten years ago is no longer so. The following is a list of techniques that we should to consider in the future and the reasons for them.

Coregionalization and cokriging.  These are to improve prediction of a primary variable by taking into account one or more subsidiary variables with which it is correlated. They can also ensure `coherence' when all variables are predicted.

Kriging with drift.  When the `drift' is local trend in the primary variable we have universal kriging. It is little used because of the difficulty in estimating the variogram. Estimating the drift in a subsidiary variable that is densely sampled is much easier, and this can be taken into account when predicting the primary variable.

Disjunctive kriging.  This technique enables one to estimate the probabilities that thresholds are exceeded at target sites in addition to predicting the variables themselves.

Indicator and Bayesian kriging.  These are valuable because they enable us to incorporate `soft' and prior information into our predictions.

Geostatistical simulation.  We now often want to produce fields of values that have the same geostatistical characteristics as a set of data. The fields may be `conditioned' in the sense that they contain the data or unconditional in that only the variogram is the same.

Wavelets.  Standard geostatistics is based on the assumption of stationary variances. Increasingly we see that this is violated, and we want to describe the way that the variance changes. Wavelets appear to offer a way forward.

I summarize each technique and illustrate it with an example from soil science.

Date received: October 14, 2002