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[ai-geostats] Standardised semivariograms

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  • Gregoire Dubois
    Dear list. a bit late but worth to be kept in the archives of the ai-geostats mailing list, here under is a reply from Henri Sanguinetti to my question on
    Message 1 of 1 , Apr 20, 2005
      Standardised semivariograms

      Dear list.
      a bit late but worth to be kept in the archives of the ai-geostats mailing list, here under is a reply from Henri Sanguinetti to my question on standardised semivariograms.

      Sorry for being so late with this posting and thanks very much again to Henri for your reply !
      Best regards,
      Gregoire
      ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

      >>There are various reasons why one might "standardize" the sample variogram but mostly they are not related to theory.

      Exactly.
      Among them is a very important one for plain users: to obtain interpretable variograms. For many years we have used two methods as follows:

      1/. Gaussian anamorphosis. The model fitted on the "experimental" variogram of the "gaussian transformed data" is backtransformed to obtain the model of the "raw data". The backtransformed model respects the experimental total sill and nugget. The objective is here to find "masked" structures and does not imply any particular hypothesis on the distribution of the data. It has a big advantage on using logarithms: it works better, and the back transformation to obtain an "usable" variogram is easy. It also authorises the weighing of data in the transformation process (number of data falling in a given block, or kriging weights derived from a first rough calculation). The method can be used on any type of variable (grade, indicators etc..).

      2/. "Relative pair wise " variograms. Two types of strandardization:
      a/ Dividing the variogram of each lag (z,z') by the product of the means: m*m',
      or
      b/ by the product of the std deviations: s*s'.
      By far the second one (b) is the most efficient. It works in many situations, giving often results very comparable to method 1/, but one should always be critical. There is no recipe!

      The model obtain on the "normated" variogram cannot be used directly for kriging. Sills have to be corrected. We kept the different "ranges" and their sill ratios, at the exception of the nugget, which has of course to be added.


      __________________________________________
      Gregoire Dubois (Ph.D.)
      JRC - European Commission
      IES - Emissions and Health Unit
      Radioactivity Environmental Monitoring group
      TP 441, Via Fermi 1
      21020 Ispra (VA)
      ITALY
       
      Tel. +39 (0)332 78 6360
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      Email: gregoire.dubois@...
      WWW: http://www.ai-geostats.org
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      "The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission."

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