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GEOSTATS: Summary - Back Transform

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  • Ian Hunt
    Here is a summary of the anwers about back transformation. Thanks for all the reply s Ian Hunt 1) A (there are others) correct way to perform the back
    Message 1 of 1 , Jun 29, 1998
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      Here is a summary of the anwers about back transformation.

      Thanks for all the reply's

      Ian Hunt

      1)
      A (there are others) correct way to perform the back transform is:

      z*(u) = exp{y*(u) + [(sigma)^2(u)/2]}

      where (sigma)^2(u) = Simple Kriging variance

      Note: this back-transform is delicate since any error in the estimation
      process
      is exponentiated too. Consider kriging with the multi-Gaussian approach
      (i.e
      normal score transform the data and perform either simple or ordinary
      kriging
      with the normal score covariance).

      If you need to get a feel for uncertainty, then it's better to use a
      simulation-type algorithm e.g. sequential gaussian or indicator simulation.

      It's impossible to know what the estimation error is since the true value
      is
      unknown.

      A good reference for lognormal kriging is:
      A.Journel: The lognormal approach to predicting local distributions of
      selective
      mining grades. (Math Geology, 12(4):285-303, 1980).


      Cheers,

      -------
      Tony Lolomari
      GeoFrame Modeling Commercialization
      Schlumberger GeoQuest
      5599 San Felipe, Suite 1700; Phone: +1 (713) 513 2478
      Houston Texas 77056-2722 Fax: +1 (713) 513 2039

      2)
      Interpolating grades as suggested in option a will underestimate the
      grades.
      Taking the log of the grades, interpolating, and then back transforming
      the resulting
      grades will give you the Geometric Mean or the median value.

      If you want to do kriging better approach would be to use indicator
      kriging.

      Most of our reserves are actually prepared using inverse distance
      squared
      and this has proved to be very adequate.

      regards

      alan

      3)
      To give you a better answer, we need to know the following:

      What kind of deposit are you working on and what metals are you
      interpolating? Why do you transform the data? Is the metal "spikey" and
      discontinuous or is it continuous. Is there a known trend?

      There are those who still use lognormal variography and kriging, but it is
      not popular as it used to be... (see Snowden, Clark etc.)

      Variograms of the log transformed data tend to show longer ranges and lower
      nuggets than the untransfomed data, and this carries on through the the
      kriging weights etc... ie. the back-transformed block grades will show more
      continuiity than actually exists in the data. (Try some correlograms of
      relative-by-pair variograms...the transformed variograms will give you the
      relative shapes and anisotropism however.)

      good luck,

      keith

      4)
      A small reminder, the sferical model and the lognormal are theoretically
      incompatable under certain conditions, I believe a small note on this was
      published by M. Armstrong in the early nineties or late eighties, in Math
      Geol. I would also recommend to read the paper by Andre Journel on
      lognormal kriging published in 1984 in Math. Geol. However at Stanford we
      recommend caution when using this technique as it is not very robust
      (exploding variance).


      regards,

      Jef

      _______________________________________________________
      Jef Caers

      (work)
      Stanford University
      School of Earth Sciences
      Department of Geological and Environmental Sciences
      Green Earth Sciences Building, Rm 337,
      Stanford, CA 94305-2220, USA

      tel (1) 650 723 8064
      fax (1) 650 725 2099
      e-mail jef@...

      (home)
      160, Clarendon Rd, #E
      Pacifica, CA 94044-2727, USA
      tel (1) 650 738 3056
      _______________________________________________________

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