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GEOSTATS: Robust Variogram Estimators

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  • Simon Brewer
    Here is a summary of the responses I received to my question. Thank you to Donald Myers, Evan Englund, Murray Lark, Ulrich Leopold and Pierre Goovaerts for
    Message 1 of 1 , Dec 10, 1999
      Here is a summary of the responses I received to my question. Thank you
      to Donald Myers, Evan Englund, Murray Lark, Ulrich Leopold and Pierre
      Goovaerts for replies.

      First two corrections:
      As the change in the title of this email suggest - I was asking for
      information on variogram estimators, not the variograms. Second, the
      alternative variogram estimator in Variowin is the standardized
      semivariogram, and not the generalized variogram.

      My question was:
      I am trying to model the spatial structure of several data-sets using
      Variowin. Using the generalised variogram gives a clear variogram
      structure, with a range parameter which compares well with the
      distribution of the data points. The experimental variogram gives no
      clear spatial structure. Can I use the parameters (with some form of
      conversion) from a model fitted to the generalised variogram for
      interpolation? Also, could someone suggest references for the use of the
      relative variogram?

      As any valid model can be used in the kriging system, a model derived
      from a robust variogram estimator is therefore equally valid. The
      problem is to relate the model to the spatial structure of the data. It
      was suggested that checks should be made for outliers or non-normal
      distribution of the data. If these exist, data transformations may allow
      the spatial structure to be seen more clearly with the traditional
      estimator.

      Alternatively, two approaches were suggested for the use of the relative
      variogram estimator:
      First, the model parameters can be used directly in the kriging system.
      in this case the kiriging standard deviations are relative standard
      deviations and not absolute.
      Second, the relative variogram estimator is used to estimate the range
      and anisotrophy directions, and the sills are estimated from the
      traditional semivariogram.

      The following references were suggested:
      Genton (1998) Mathematical Geology 30, 213-221

      Goovaerts, P. 1997: Geostatistics for natural resources evaluation.
      New York

      Isaaks, E.H. and Srivastava, R.M. 1989: Applied geostatistics. An
      introduction. New York

      Srivastava, R.M. and Parker, H.M. 1989: Robust measueres of spatial
      continuity. In: Armstrong, M. (ed.) 1989: Geostatistics. Vol.1, pp.
      295-308.

      Thanks again for your help. If anything is unclear, please let me know.

      Cheers
      Simon
      --

      -------------------------------------------------------
      Simon Brewer email: simon.brewer@...

      European Pollen Database
      (Laboratoire de Botanique Historique et Palynologie)
      (IMEP CNRS URA 1152)
      (Faculte St Jerome - Aix Marseille III)

      Centre Universitaire d'Arles
      Place de la Republique
      13200 Arles - France
      Tel: (33)-(0)4 90 96 18 18 Fax: (33)-(0)4 90 93 98 03
      -------------------------------------------------------

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