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2126RE: [ai-geostats] Irf-k theory...

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  • Gregoire Dubois
    Jun 30, 2005
      Ciao Simone,

      I'm not sure I fully understand your question. Are you referring to the
      monomials used to define the stationary trend model of the IRF-k?
      What are these coefficients of 1 and -1 ?? I must admit I am very lazy
      tonight !

      The fundamental differences between IRF-k and UK can be found in part 6
      of a paper by Arianna Orasia

      Some readings are:

      1) the paper of D. Marcotte, M. David (1988)

      Trend surface analysis as a special case of IRF-k kriging,
      Mathematical Geology, 20(7): 821 - 824

      2) the papers of van den Boogaart (hard reading !!!), e.g.


      Why Universal Kriging is better than IRFk-Kriging: Estimation of
      Variograms in the Presence of Trend
      Karl Gerald van den Boogaart& Alexander Brenning
      June 30, 2001

      3) If you survived the reading above, then you can always go for a paper
      from Alexander Brenning:


      4) This one should saves your day (in Italian and easy reading) but it
      is probably impossible to find today:

      Bruno R. & Raspa G. (1994). La pratica della geostatistica lineare. Il
      dei dati spaziali. Guerini Studio. 170 p

      The book is all about FAIK (Italian equivalent to IRFk) and has (had?)
      an MS DOS software for FAIK, FAIPACK, that was not bad at all.

      There was also a wonderful text from Chauvet that I could try to find
      again if needed but it is in French (try to contact Fontainebleau).
      Chiles and Delfiner probably discuss this as well in their book but I
      don't have it here.

      For what concerns the previous mail regarding trend modelling, IRF-k can
      be nicely automated for detecting the optimal "k" but I would make the
      same critic as for the Neural Nets, you do not extract any useful
      information from the drift (although you could map the local values of
      k.. allowing you so to describe somehow the complexity of the underlying
      trend.. Don't know if this has been done or any useful).



      PS: there are some nice papers from Chauvet (Fontainebleau) that I could
      try to find again if needed but there are in French.
      Chiles and Delfiner probably discuss this in their book but I don't have
      it here.

      -----Original Message-----
      From: Simone Sammartino [mailto:marenostrum@...]
      Sent: 29 June 2005 17:49
      To: Geostat newsgroup
      Subject: [ai-geostats] Irf-k theory...

      Dear all
      about Irf-k...
      I can't understand the link between the two approach explaining the
      Irf-k theory... 1st approach: The Irf-k approach is based on a
      generalization of the intrinsic model, in which the coefficients of the
      combination of the variables in the X points are such that the
      combination of monomials of the variables (computed with such
      coefficients) is zero mean and second order stationary. In the intrinsic
      model the coefficients are 1 and -1 and the linear combination of the
      variables with such coefficients (the increment) is second order
      stationary. Now...how to insert the generalized covariance in this
      speech?... 2nd approach:

      The non stationary random function is seen as the sum of a trend and a
      residual (as in UK?!)...such trend is the linear combination of
      monomials of the variables (as in UK?!) with the said coefficients. And
      the generalized covariance? Reassuming...I did not understand the Irf-K

      Someone can explain it to me? or suggest some clear refer? Thank you

      Dr. Simone Sammartino
      PhD student
      - Geostatistical analyst
      - G.I.S. mapping
      I.A.M.C. - C.N.R.
      Geomare-Sud section
      Port of Naples - Naples

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