Bounding the required sample size for geologic site characterization

The proposed objective of limited sample geologic site characterization is to minimize the chance of unknown and unexpected extremes. This problem proves to be extremely difficult when the data are spatially correlated. A generalization of the classical one-sided nonparametric tolerance interval, based upon the statistical concept of associated random variables, establishes a rigorous, almost distribution-free, tool for computing the minimum required sample size for site characterization. An upper bound on the required number of samples follows from a heuristic measure for the quantity of information in a spatially dependent sample; the measure presented is the equivalent number of uncorrelated samples and is calculated using an estimated variogram. An empirical check of the upper and lower bounds, using more than 2 million simulations and seven real data sets produces a heuristic rule for quantifying the required number of samples.