Statistical modelling exploits the properties of random variables that can be used to emulate the spatial variation of geological observations.
The selection of an appropriate random variable is important, and we put a lot of effort into testing that a particular random variable is appropriate for our geological data — more about distinguishing spatially correlated random variation; linear mixed model with non-stationary mean and covariance.
Often the normal random variable, the well-known bell curve, is appropriate; but it is not suitable for all geological phenomena, particularly for those influenced by deposits with complex geometry.
We have initiated research into random variables that arise in an area of mathematics called stochastic geometry. We are trying to discover whether stochastic geometry allows us to use geological knowledge to develop random variables that are suitable for our purposes — more about stochastic geometric model for continuous local trends in soil variation.
In collaboration with colleagues at Ghent University we have shown that a stochastic geometric model of soil formed in Pleistocene cover sands in a part of Belgium describes the spatial variation better than the standard normal model.
The picture below shows an example of the random variation generated by the fitted model. The yellow areas correspond to the network of ice-wedges that formed in the soil during the last glaciation.
Contact Dr Murray Lark for more information