Ruben (et al) It is true that Matheron's theory is based on no distributional assumptions. In fact, there is no requirement for the distribution to be the same at every location in the study area.
The necessity for using traditional geostatistical theory is that the 'difference between two values' should have a common distribution for a specified distance (and possibly direction). The form of this distribution is irrelevant but it needs to possess a mean and variance. The problem lies not with the theory but with the practice. If you have the whole 'realisation' you can calculate the true average and variance and the shape of each distribution is irrelevant. If you have only a few samples, then you can only find estimates for the means and variances at each distance. If the underlying distribution is highly skewed then, unless you have ideal conditions (large number of samples, regular sampling locations), your estimate of the variance will be unstable -- influenced by the average of the samples included in the particular estimate. There was a huge amount of debate about this "proportional effect" back in the 70s [search for 'relative semi-variogram']. So, you have two potential problems: (1) you may not get any true picture of the semi-variogram due to the uncertainty associated with each point exacerbated by the proportional effect; (2) you may not wish to use an averaging technique such as kriging on skewed samples. All of Sichel's (mining) and much of Krige's work was motivated by the fact that local averaging is not sensible when your data has a coefficient of variation greater than around 1. The theory is terrific, witness its survival for over 40 years and its proliferation over many fields of application. However, real life isn't so tidy at the sharp end ;-) Isobel http://geoecosse.bizland.com/whatsnew.htm
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