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Re: AI-GEOSTATS: Noemi Barabas' Questions on the Hole Effect Variogram Model

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  • Michael Pyrcz
    Good Day, 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)
    Message 1 of 1 , Dec 2, 2002
      Good Day,

      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,

      Michael Pyrcz
      Ph.D. Candidate
      Department of Civil & Environmental Engineering
      University of Alberta
      (780) 492-3153

      -----Original Message-----
      From: ai-geostats-list@... [mailto:ai-geostats-list@...]On
      Behalf Of Noemi Barabas
      Sent: Sunday, December 01, 2002 7:55 PM
      To: ai-geostats@...
      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
      workable assumption?

      I much appreciate any insights into these questions!!


      Noemi Barabas

      PhD Candidate
      The University of Michigan
      Dept. Civil and Environmental Engineering
      1351 Beal Avenue (13 EWRE)
      Ann Arbor, MI 48109-2125
      Phone: (734) 615-5905

      [Non-text portions of this message have been removed]
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