Abstract
Stochastic simulation has been suggested as a viable method for characterizing the uncertainty associated with the prediction of a nonlinear function of a spatially-varying parameter. Geostatistical simulation algorithms generate realizations of a random field with specified statistical and geostatistical properties. A nonlinear function (called a transfer function) is evaluated over each realization to obtain an uncertainty distribution of a system response that reflects the spatial variability and uncertainty in the parameter. Crucial management decisions, such as potential regulatory compliance of proposed nuclear waste facilities and optimal allocation of resources in environmental remediation, are based on the resulting system response uncertainty distribution.
Many geostatistical simulation algorithms have been developed to generate the random fields, and each algorithm will produce fields with different statistical properties. These different properties will result in different distributions for system response, and potentially, different managerial decisions. The statistical properties of the resulting system response distributions are not completely understood, nor is the ability of the various algorithms to generate response distributions that adequately reflect the associated uncertainty.
This paper reviews several of the algorithms available for generating random fields. Algorithms are compared in a designed experiment using seven exhaustive data sets with different statistical and geostatistical properties. For each exhaustive data set, a number of realizations (both unconditional and data-conditioned) are generated using each simulation algorithm. The realizations are used with each of several deterministic transfer functions to produce a cumulative uncertainty distribution function of a system response. The uncertainty distributions are then compared to the single value obtained from the corresponding exhaustive data set. The results of the study facilitate comparisons between the individual methods, allow an assessment of the consistency of the simulation algorithms, and indicate potential for bias or imprecision.
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Gotway, C.A., Rutherford, B.M. (1994). Stochastic Simultation for Imaging Spatial Uncertainty: Comparison and Evaluation of Available Algorithms. In: Armstrong, M., Dowd, P.A. (eds) Geostatistical Simulations. Quantitative Geology and Geostatistics, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8267-4_1
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DOI: https://doi.org/10.1007/978-94-015-8267-4_1
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