Statistical process control in the evaluation of geostatistical simulations

Geiger, János (2018) Statistical process control in the evaluation of geostatistical simulations. Central European Geology, 61 (1). pp. 50-72. ISSN 1788-2281

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Abstract

This paper deals with a question: how many stochastic realizations of sequential Gaussian and indicator simulations should be generated to obtain a fairly stable description of the studied spatial process? The grids of E-type estimations and conditional variances were calculated from pooled sets of 100 realizations (the cardinality of the subsets increases by one in the consecutive steps). At each pooling step, a grid average was derived from the corresponding E-type grid, and the variance (calculated for all the simulated values of the pooling set) was decomposed into within-group variance (WGV) and between-group variance (BGV). The former was used as a measurement of numerical uncertainty at grid points, while the between-group variance was regarded as a tool to characterize the geologic heterogeneity between grid nodes. By plotting these three values (grid average, WGV, and BGV) against the number of pooling steps, three equidistant series could be defined. The ergodic fluctuations of the stochastic realizations may result in some “outliers” in these series. From a particular lag, beyond which no “outlier” occurs, the series can be regarded as being fully controlled by a background statistical process. The number of pooled realizations belonging to this step/lag can be regarded as the sufficient number of realizations to generate. In this paper, autoregressive integrated moving average processes were used to describe the statistical process control. The paper also studies how the sufficient number of realizations depends on grid resolutions. The method is illustrated on a computed tomography slice of a sandstone core sample.

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