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GEOSTATS: [Q]: 1) stationarity 2) anisothropy 3) neighb.search

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  • Konstantin Malakhanov
    Dear all, I have three questions, as follows (supposed I have non-evenly distributed point data) 1) is that true that stationarity of data is just a question
    Message 1 of 1 , Apr 21, 1997
      Dear all,

      I have three questions, as follows (supposed I have non-evenly
      distributed point data)

      1) is that true that stationarity of data is just a question of

      If I make a search window too small, a mean of the data in this
      window will be very different from global mean , so I have

      If I make a search window large enough, a mean of the data in the
      window will be close to the global mean, so I have stationarity.

      Usually stationarity will be also checked through the form of
      variogramm. Variogramms without sill are said to be from
      non-stationary random process. Typical such are power variograms,
      including a linear one. But if I take into account, that spherical
      and exponential variograms are linear and gaussian model is parabolic
      NEAR THE ORIGIN, it looks to me, as such variograms were just a part
      of transition variograms (with a sill) near origin, so my region is
      just not large enough to show stationarity of data. So should one use
      exponential and gaussian variograms with a large range (larger as
      size of the region) to fit experimental variogram without sill?

      2) the next question is about modelling an anisotropy for kriging. If
      I have very different variograms in different directions, I can
      transform coordinates and calculate equivalent models with reduced
      distances to deal with it.

      The question is: why just not use different theoretical variograms for
      different directions. If one builds an ordinary kriging system, one
      could just pick up different variograms depending on the angle
      between i-th and j-th point?

      3) and the last question: should one use all data points for kriging
      or restrict to the nearby of them? Isaaks&Srivastava vote for the
      neighbourhood searching, and Peter Kitanidis in "Introduction to
      Geostatistics" write:
      Another motivation has been the estimate at x0 dependent only on
      observations in its neighbourhoods, which is often a desirable
      characteristic. However, the same objective can be achieved by using
      all data with an appropriate variogram(such as the linear one) that
      assigns vary small weights to observations at distant points. If the
      weights corresponding to points near the border of the neighbourhood
      are not small and the moving neighborhood method is applied in
      contouring, the estimated surface will have discontinuities that are
      unsightly as well as unreasonable, if they are the artifact of the
      arbitrarily selection of a moving neighbourhood.

      So - moving neighbourhood - is it good or bad ( beside of the question of
      computational effectiveness)?


      Konstantin Malakhanov, wiss. Mitarbeiter/research engineer

      IWW, RWTH Aachen
      Tel. 0241-807343
      Fax. 0241-8888348
      E-Mail: kosta@...-aachen.de
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