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445GEOSTATS: so-called kriging paradox

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  • Donald Myers
    Aug 21 9:49 AM
      Don't assume that the monograph by R. shurtz resolves or
      answers the question, it does not.

      Part of the problem with the so-called paradox is using
      data locations that are all in a 1- dimensional space to
      estimate values at locations not in that one-dimensional
      space. No interpolation method is going to produce good
      results unless additional model characteristics are
      assumed to provide for a relationship between the one
      dimensional space and higher dimensional space. This
      is particularly true if an isotropic variogram/covariance
      model is used. With this mis-match in dimensions the
      problem is ill-posed.

      One way to see the ambiguity is to consider locations on
      circles in a plane perpendicular to the the drill
      hole axis. Using a an isotropic variogram will result
      in the same estimated values at all points on such a
      circle. This implies a rather weird physical phenomenon,
      i.e., unrealistic.

      The flaw is not in geostatistical theory but rather in
      the application, simplistic use of black boxes without
      consideration of the underlying phenomenon can lead to
      strange results.

      It is necessary to incorporate some "expert" knowledge
      and/or soft data in such cases.

      Donald E. Myers
      Department of Mathematics
      University of Arizona
      Tucson, AZ 85721
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