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Abstract

Actually, some of the earlier applications of geostatistical simulations were twodimensional. In their simpler form, these applications used as input the layer-averaged values of petrophysical properties at wells. For instance, Fig. 80 shows four realisations of a continuous parameter map generated by conditional simulation. The values at the three control points are the same in each realisation. These four realisations share the following properties: an identical (spherical) variogram, a similar histogram, and they all honour the wells. The realisations are often called “equiprobable” in the sense that they all share the statistical properties believed to be those of the actual (unknown) map. The use of such straightforward 2D conditional simulations has decreased. They can prove useful for mapping permeability in the case of high net/gross layers (as encountered for instance with braided-streams deposits ) where lateral variations are more important than vertical ones.

For training purposes, Fig. 81 shows four other realisations of the parameter of Fig. 80, obtained this time with a gaussian variogram, the practical range of which was chosen to be equal to that of the spherical model used in Fig. 80. The realisations are smoother with the gaussian than with the spherical model. This is because a gaussian variogram implies that the modelled variable is very smooth (indefinitely differentiable, in mathematical terms). In spite of this somewhat unrealistic assumption, the gaussian model often proves useful in applications, because the models produced are smooth and easy to interpret.

More important is the use of 2D conditional simulation for the evaluation of structural uncertainties.

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