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GEOSTATS: Back Transform

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  • Ian Hunt
    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
    Message 1 of 2 , Jun 24, 1998
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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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    • 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 2 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
        >
        > --
        > *To post a message to the list, send it to ai-geostats@....
        > *As a general service to list users, please remember to post a summary
        > of any useful responses to your questions.
        > *To unsubscribe, send email to majordomo@... with no subject and
        > "unsubscribe ai-geostats" in the message body.
        > DO NOT SEND Subscribe/Unsubscribe requests to the list!

        --
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