Universal kriging with training images

In the past decade, the training image (TI) has received considerable attention as a source for modeling spatial continuity in geostatistics. In this paper, the use of TIs in the context of kriging is investigated, specifically universal kriging (UK). Traditionally, kriging relies on a random function model formulation whereby the target variable is decomposed into a trend and residual. While the theory is firm and elegant, the actual practice of UK remains challenging; in particular when data is sparse, and the modeler has to decide what to model as the trend and as the residual. This paper juxtaposes this variogram-based universal kriging (UK-v) with a TI-based approach (UK-TI). It is found that the latter need not rely on random function theory, but rather on the specification of a TI on which “universal” conditions are verified. Through illustrations with examples, it is seen that the modeling challenge in UK-TI is on the training image. Using a Monte Carlo study, the statistical performance of both methods is found to be comparable. Recommendations on which method to choose, based on practical criteria, are also formulated. Additionally, the study provides more insight into the use of the TI in general, including in multiple-point geostatistics.