Multi-Gaussian kriging and simulation in the presence of an uncertain mean value

The multi-Gaussian model is used in geostatistical applications to predict functions of a regionalized variable and to assess uncertainty by determining local (conditional to neighboring data) distributions. The model relies on the assumption that the regionalized variable can be represented by a transform of a Gaussian random field with a known mean value, which is often a strong requirement. This article presents two variations of the model to account for an uncertain mean value. In the first one, the mean of the Gaussian random field is regarded as an unknown non-random parameter. In the second model, the mean of the Gaussian field is regarded as a random variable with a very large prior variance. The properties of the proposed models are compared in the context of non-linear spatial prediction and uncertainty assessment problems. Algorithms for the conditional simulation of Gaussian random fields with an uncertain mean are also examined, and problems associated with the selection of data in a moving neighborhood are discussed.