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. They can span multiple lines, as shown by the following example. 5 Defining a 3D ellipsoid Many algorithms in SGeMS require the user to specify a 3D ellipsoid, for example to represent a search volume through three anisotropy directions and affinity coefficients. In SGeMS, a 3D ellipsoid is represented by six parameters: the three radii of the ellipsoid rmax , rmed , rmin , and three angles, α, β, θ positioning the ellipsoid in space (see Figs.

The second approach avoids such extreme division of the conditioning data event. Instead it consists of using an explicit multiple-point (mp) model, which allows considering the (n) data altogether, or a set n(u) of neighbor data. , 2006). 3 Conditional distributions and simulations 43 prior model implicit to the Ti used. The consideration of training images, if available, allows making use of mp structural information much beyond the variograms of these Tis. A training image is a representation of how z values are jointly distributed in space (Farmer, 1992; Strebelle, 2002; Journel, 2002; Zhang, 2006).

How many realizations? 133)? Since there is no reference model to approach, the number L should be chosen large enough to ensure stability of the results and small enough to allow the intended processing of the L simulated realizations. Consider as “result” a specific function ϕ z (l) (u), u ∈ S built from any one simulated realization. 2 Random function 37 statistics such as the variance of the L values ϕ z (l) (u), u ∈ S , l = 1, . . , L stabilizes as L increases towards L. 2 Estimated maps There can be applications where values z(u) are dealt with one at a time independently of the next one z(u ), no matter how close the locations u and u are.

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