New kriging method for estimation from strings of data in a finite domain - SME Transactions 2009

A longstanding problem in geostatistics is that kriging usually assigns significantly greater weights to end samples in strings of data than it does to central samples. These weights are theoretically valid, but suboptimal estimates may result when there are geological trends in the variable near contacts, that is, large weights may be applied to samples that are systematically lower or higher than average. A number of ad-hoc corrections exist, each with pros and cons; none are fully automatic with a well-defined measure of optimality. A new method for estimation in a finite domain is proposed. This method is referred to as finite domain kriging. The method is based on kriging with a successively larger number of data. The total number of relevant data (n) is established, and then n kriging matrices are solved. The first matrix has the closest single data value (n-1 weights are set to zero); the second has the two closest data (n-2 weights are set to zero) and so on. The final matrix has all n data. The kriging weights used for estimation are the average of the weights from the n successive kriging runs. Each kriging run is optimal, yet with different smoothing and a different treatment of data at the end of the strings. The result is a set of weights that does not give undue influence to data values at the end of strings. The methodology is developed with examples. Cross validation shows that finite domain kriging outperforms conventional kriging.