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RE: [ai-geostats] Definition of standardized variograms

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  • Pierre Goovaerts
    Hi Gregoire, I agree with you regarding the merits of the standardized semivariogram as implemented in variowin software. In one of my last studies, the
    Message 1 of 3 , Apr 5, 2005
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      Hi Gregoire,

      I agree with you regarding the merits of the standardized semivariogram as implemented
      in variowin software. In one of my last studies, the rescaling by the lag variance helped
      correcting the preferential sampling of wells with high arsenic levels, leading to a
      susbtantial decrease in random fluctuations of the experimental semivariograms.
      While the general relative semivariogram approximates the lag variance by the square
      of the lag mean, the standardized semivariogram uses the actual lag variance, hence
      makes less assumptions.
      Regarding the terminology, I guess we should used a term like "lag-standardized"
      to distinguish the global and lag-specific standardization or rescaling of semivariogram



      -----Original Message-----
      From: Gregoire Dubois [mailto:gregoire.dubois@...]
      Sent: Tue 4/5/2005 9:48 AM
      To: ai-geostats@...
      Cc: mueller@...
      Subject: [ai-geostats] Definition of standardize variograms

      Dear list,

      While playing around with different software, I encounter different definitions for standardized variograms.

      Surfer (which is using the terminology of Variowin), uses the term "standardized semivariogram" for variograms obtained by dividing the semivariance by the lag variance, while GS+ uses the total variance. While the function obtained in GS+ is only a matter of rescaling variograms, allowing so various variograms to be compared, those proposed in Surfer have the same pupose as the local, pairwise and/or general relative variograms (see Isaaks & Srivastava, page 163-170), that is to reduce the influence of local means. Interestingly enough, one may note that very few software propose relative variograms while I, very personally, consider these functions as essential for detecting spatial structures of many environmental variables.

      I have thus here two questions about the use of standardized/relative variogram:

      1) What is the correct terminology or definition for standardized variograms? (I personally do not like very much the use of "standardized" when the standardisation is only applied to each lag...)

      2) The general relative variogram (lag divided by the mean of the lag) has properties that are very similar to the "standardized" variogram (lag divided by the variance of the lag) but both functions differ. How shall one decide what to use and what are the relative properties of these functions?

      Thank you in advance for any feedback.


      PS: a few points here good be added to Tom Mueller's FAQ on Geostatistical Software Conventions.

      Gregoire Dubois (Ph.D.)
      JRC - European Commission
      IES - Emissions and Health Unit
      Radioactivity Environmental Monitoring group
      TP 441, Via Fermi 1
      21020 Ispra (VA)

      Tel. +39 (0)332 78 6360
      Fax. +39 (0)332 78 5466
      Email: gregoire.dubois@... <mailto:gregoire.dubois@...>
      WWW: http://www.ai-geostats.org <http://www.ai-geostats.org>
      WWW: http://rem.jrc.cec.eu.int <http://rem.jrc.cec.eu.int>

      "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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