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Re: GEOSTATS: Back Transform

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  • Tony Lolomari
    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:
    Message 1 of 2 , Jun 24, 1998
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      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


      > From: "Ian Hunt" <ianh@...>
      > To: <ai-geostats@...>
      > Subject: GEOSTATS: Back Transform
      > Date: Wed, 24 Jun 1998 15:12:57 +0200
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      > Hello,
      >
      > I need to do grade calculations [ for a mining operation ] on assay values,
      > which has a lognormal distribution. The samples are de-surveyed drillhole
      > chemical assays.
      >
      > I have fitted very nice spherical models on the semi-variograms of the
      > lognormal values.
      > This produced a very good nugget effect and a sill, as well as some ranges
      > for kriging purposes.
      >
      > I foresee two scenarios for solving this:
      > a) Calculate the log grades with the log semi-variogram parameters and then
      > back transform the log grades to raw values. But how do I know what the
      > estimation errors for each grade block is? What is the correct way of back
      > transformation?
      > b) Some people suggest that one must try to fit the raw semi-variogram as
      > best as possible with the log semi-variogram parameters and proportions.
      > The raw semi-variogram must look almost the same in a graphical way, just
      > with the raw nugget and sill. Then the raw grades should be calculated and
      > reported as is. Does this make sense?
      >
      > Please feel free to make any suggestions, as I have to report the grades
      > for an official feasibility document.
      >
      > Ian Hunt
      >
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