Publications

There are many approaches to geostatistical simulation that can be used to generate realizations of random fields. These approaches differ fundamentally in a number of ways. First, each approach is inherently different and will produce fields with different statistical and geostatistical properties. Second, the approaches differ with respect to the choice of the features of the region that are to be modeled, and how closely the generated realizations reproduce these features. Some fluctuation in the statistical and geostatistical properties of different realizations of the same random field are natural and desirable, but the proper amount of deviation is an open question. Finally the approaches differ in how the conditioning information is incorporated. Depending on the source of randomness and the uncertainty in the given data, direct conditioning of realizations is not always desirable. In this paper, we discuss and illustrate these differences in order to emphasize the importance of these components in geostatistical simulation.

An assessment of the long term containment capabilities of a possible nuclear waste disposal site requires both an understanding of the hydrogeology of the region under consideration and an assessment of the uncertainties associated with this understanding. Stochastic simulation - the generation of random {open_quotes}realizations{close_quotes} of the regions hydrogeology, consistent with the available information, provides a way to incorporate various types of uncertainty into a prediction of a complex system response such as site containment capability. One statistical problem in stochastic simulation is: What features of the data should be {open_quotes}mimicked{close_quotes} in the realizations? The answer can depend on the application. A discussion is provided of some of the more common data features used in recent applications. These features include spatial covariance functions and measures of the connectivity of extreme values, as examples. Trends and new directions in this area are summarized including a brief description of some statistics (the features) presently in experimental stages.