Here are some points on the hole effect variogram model in GSLIB.
o. The cosine hole effect applied in GSLIB is only positive definite
(permissible) in ID. Therefore it is required that the ranges in all
other directions be set as very large - this results in zonal anisotropy
in the other directions.
o. The sum or product of positive definite models is positive definite.
The dampened hole effect variogram model is the product of the hole
effect and exponential covariance models. There is flexibility in the
choice of the dampening range,'d'. The assignment of 'd' based on the
range in the GSLIB code may have been in an effort to avoid the addition
of another parameter, which would have required a fair bit of coding.
o. The range is the distance to the first peak in the hole effect
variogram model. Dampening will attenuate the amplitude (with respect
to lag distance) but will not affect the wave length.
I have written a paper on the hole effect. If you are interested
contact me at the address below.
Hope this helps,
Department of Civil & Environmental Engineering
University of Alberta
Behalf Of Noemi Barabas
Sent: Sunday, December 01, 2002 7:55 PM
Subject: AI-GEOSTATS: hole effect modeling in 3D
Dear list members,
I hope to get some insight into modeling and kriging with 3-D variograms
where all 3 directions display a pronounced hole-effect/oscillations. (I
am using GSLIB)
First of all, are there any permissibility issues regarding a hole
effect model? I am thinking in particular of the dampening factor,
which is an additional parameter that is not accounted for in the
kriging parameter files. I know that kt3d has a built-in relationship
of d to the range, and I wonder if that is just for simplification or
because of permissibility contraints.
Second, what does the range mean for a hole effect model in terms of the
maximum distance between the estimation location and a contributing data
location. Does the dampening affect this distance in kt3d and would
there be permissibility issues if I were to modify the program?
Third, what if the dampening parameter is different in all 3 directins?
And finally, my grid will be discretized such that in one direction I
will only estimate at three different distances, and I assume that the
semivariogram model needs a good fit only at those lags. Is this a
I much appreciate any insights into these questions!!
The University of Michigan
Dept. Civil and Environmental Engineering
1351 Beal Avenue (13 EWRE)
Ann Arbor, MI 48109-2125
Phone: (734) 615-5905
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