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