## [ai-geostats] Automatic variogram modeling software

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• Re automatic semi variogram modeling. Here are a few things to be aware of when looking for automatic semi variogram modeling software. 1. Generally, one is
Message 1 of 1 , Mar 1, 2006
Re automatic semi variogram modeling.

Here are a few things to be aware of when looking for automatic semi
variogram modeling software.

1. Generally, one is faced with the problem of modeling several directional
sample variograms calculated from a particular data set.
2. However, modeling the directional sample variograms from a two
dimensional data set is relatively simple. If a 2D anisotropy is suspected,
one should calculate multiple directional sample variogram on azimuths of at
least 30 degree intervals. Four directional sample variograms at 90 degree
intervals are generally insufficient for accurately modeling an anisotropy.
The task at hand is to "fit" a model to all of the directional sample
variograms. Thus, any automatic fitting software that only models one
directional sample variogram at a time is likely not very useful.
3. The problem is considerably more difficult when working with 3
dimensional data. For example, experience suggests that in general, one
cannot obtain a reasonable sample of the inherent 3 dimensional anisotropic
spatial continuity with less than 19 directional sample variograms, e.g. 30
degree increments on the azimuth combined with 30 degree increments on dip.
(Recall, that the turning bands algorithm is based on the "icosahedron
approximation" which requires a minimum of 15 lines to simulate an isotropic
covariance in 3D space). The task at hand is to "fit" a model to all 19
directional sample variograms. To appreciate the difficulty, consider
fitting a simple variogram model with two structures to the 19 directional
sample variograms. One must determine values for 15 parameters, e.g.,
1. The nugget.
2. The coefficient for the first structure.
3. The coefficient for the second structure.
4. The range along the major axis of the anisotropy model associated with
the first structure.
5. The range along the semi-major axis of the anisotropy model associated
with the first structure.
6. The range along the minor axis of the anisotropy model associated with
first structure.
7. The range along the major axis of the anisotropy model associated with
the second structure.
8. The range along the semi-major axis of the anisotropy model associated
with the second structure.
9. The range along the minor axis of the anisotropy model associated with
second structure.
10. The rotation angle around the Z axis of the anisotropy model for the
first structure.
11. The rotation angle around the rotated X axis of the anisotropy model for
the first structure.
12. The rotation angle around the rotated Y axis of the anisotropy model for
the first structure.
13. The rotation angle around the Z axis of the anisotropy model for the
second structure.
14. The rotation angle around the rotated X axis of the anisotropy model for
the second structure.
15. The rotation angle around the rotated Y axis of the anisotropy model for
the second structure.

Thus, although the problem can be stated quite simply in terms of least
squares, e.g.;

Find the set of 15 parameters that;

Minimize [ Sum_i w_i * (VariogramModel(15 parameters, lag_i) -
sample_variogram_point_i)^2 ] where "Sum_i" is the sum over all sample
variogram points from all 19 directional sample variograms. Note that w_i
may be a set of weights such as "number of pairs" etc.

The solution is not straightforward. However, the software product
"SAGE2001" solves the problem above quite quickly by determining the optimum
set of 15 parameters. The result is a weighted least squares fit to all
directional sample variogram points simultaneously.

SAGE2001 is used throughout the mining industry by many companies including
Newmont, Barrick, Placer, AMEC, and so on.

Unfortunately, SAGE2001 development costs were steep. Thus, it is not
freeware or shareware.