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. But, SAGE2001 can be downloaded at www.isaaks.com for free and is fully functional with no restrictions for 20 days. So if you have a difficult modeling problem - feel free to use it. Edward Isaaks
* By using the ai-geostats mailing list you agree to follow its rules ( see http://www.ai-geostats.org/help_ai-geostats.htm ) * To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to [EMAIL PROTECTED] Signoff ai-geostats
