Optimized spatial sampling of soil for estimation of the variogram by maximum likelihood

Recent studies have attempted to optimize the configuration of sample sites for estimation of the variogram by the usual method-of-moments. This paper shows that objective functions can readily be defined for estimation by the method of maximum likelihood. In both cases an objective function can only be defined for a specified variogram so some prior knowledge about the spatial variation of the property of interest is necessary. This paper describes the principles of the method, using Spatial Simulated Annealing for optimization, and applies optimized sample designs to simulated data. For practical applications it seems that the most fruitful way of using the technique is for supplementing simple systematic designs that provide an initial estimate of the variogram.