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Abstract

So far, we have presented approaches for generating conditional simulations of the distribution of geological or petrophysical parameters in one, two and three dimensions. The goal of these approaches is to generate representations of the variable of interest that mimic the unknown spatial distribution of this variable: object-based models honour width-thickness distributions, variogram-based models honour the input variogram model, etc… We have seen that, for each set of wells and input statistical relationships, a large number of representations could be generated, all matching the wells and the statistical parameters. This is simply a consequence of the non-uniqueness of the problem. The wells and the statistical parameters are not sufficient to uniquely constrain the model between the wells. Variability between different realisations is simply a measure of the uncertainty affecting the knowledge of the parameter at any given location. The standard deviation of all values of the realisations at a fixed location is a quantification of this uncertainty.

In many instances, geostatistical realisations offer an interesting solution to the problem of generating realistic images of the variability in the inter-well volume, and of quantifying the associated uncertainty. In some situations, the large number of realisations may overwhelm the user of geostatistical techniques, who may just need a simple map of the variable of interest in the inter-well volume.

Consider the average of several geostatistical realisations at the same location. A 1D example (Fig. 55) shows that the average of all conditional simulations is a smooth function, far smoother than any of the realisations.

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