GEOSTATS: so-called kriging paradox
- 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,
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
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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