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Re: AI-GEOSTATS: Ore Reserves Classification

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  • Turkan Kaynak
    Dear Jose, I m a mining engineer and I think I can answer your question. We use kriging variance for reserve classification. I think you know, the reserves are
    Message 1 of 5 , Mar 23, 2002
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      Dear Jose,
      I'm a mining engineer and I think I can answer your question. We use kriging variance for reserve classification. I think you know, the reserves are classified depend on their error quantity and this quantity can be represented using variance. If we use kriging for reserve estimation you can use kriging variance and classified reserves as possible, probable or proved reserves.
      ----- Original Message -----
      From: José Quintín Cuador Gil
      To: ai-geostats@...
      Sent: Tuesday, March 26, 2002 8:27 PM
      Subject: AI-GEOSTATS: Ore Reserves Classification


      Dear list members

      The Kriging variance has some uses. In mining, it can be used in the Ore Reserves Classification.
      What is the opinion about this in the Geostatistical community?
      It is possible to use the Kriging variance for ores reserves classification?, (Yes or No).
      Thanks in advances for any opinion.

      José Quintín Cuador Gil
      Department of Informática
      University of Pinar del Río
      Cuba
      <cuador@...>


      [Non-text portions of this message have been removed]
    • Richard Hague
      List Members, The use of the kriging variance to categorise/classify Mineral (Ore) Resources and/or Ore Reserves is an old chestnut that periodically raises
      Message 2 of 5 , Apr 2 8:47 PM
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        List Members,

        The use of the kriging variance to categorise/classify Mineral (Ore) Resources and/or Ore Reserves is an old chestnut that periodically raises it's ugly head. The kriging variance is related, pure and simply, to the data configuration and has nothing to do with the sample grades/variables being used for interpolation. As an example say a grade was being interpolated into a block which has been sampled on each corner, regardless of what the individual sample grades are, the kriging variance for that block is going to be the same. Example: if all four samples have the same grade of (say) 2.35g/t Au you will get the same kriging variance as the case where the four samples grades are (say) 0.01, 102.9, 0.88 and 3.60 g/t Au. Naturally I would have more confidence in the interpolated grade in the former scenario than the latter; thus the use of the kriging variance to determine confidence (or classification) of an estimate is misleading.

        One method of obtaining some feel for the possible error range would be to run a large number of grade simulations into the block, the variance of all simulated grades would give an indication of error - again in the example given above, the variance of the simulated grades using the former case would be much smaller than in the latter case.

        Of course classification of Mineral (Ore) Resources and/or Ore Reserves needs to take into account a lot more items (as expounded by the JORC (1999) code) - than just some objective measure of estimation error, it needs to take into consideration, amongst other things, data quality - if you have poor quality data (eg biased/inaccurate), regardless of how good any statistical measure of the estimation error is, you will always have poor estimate.

        REFERENCES
        JORC; 1999: Australasian code for reporting of mineral resources and ore reserves (the JORC Code). Prepared by the Joint Ore Reserves Committee of the Australasian Institute of Mining and Metallurgy, Australian Institute of Geoscientists and Minerals Council of Australia (JORC).

        Richard Hague
        Hellman & Schofield Pty Ltd
        Brisbane Office
        p&f: +61 (0)7 3217 7355
        e: richardh@...
        w: http://www.hellscho.com.au


        ----- Original Message -----
        From: José Quintín Cuador Gil
        To: ai-geostats@...
        Sent: Wednesday, March 27, 2002 4:27 AM
        Subject: AI-GEOSTATS: Ore Reserves Classification


        Dear list members

        The Kriging variance has some uses. In mining, it can be used in the Ore Reserves Classification.
        What is the opinion about this in the Geostatistical community?
        It is possible to use the Kriging variance for ores reserves classification?, (Yes or No).
        Thanks in advances for any opinion.

        José Quintín Cuador Gil
        Department of Informática
        University of Pinar del Río
        Cuba
        <cuador@...>


        [Non-text portions of this message have been removed]
      • Isobel Clark
        Richard Thanks for the clear exposition on the limitation of the kriging variance as a measure of reliability for block estimation. It should, perhaps, be
        Message 3 of 5 , Apr 3 1:09 AM
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          Richard

          Thanks for the clear exposition on the limitation of
          the kriging variance as a measure of reliability for
          block estimation.

          It should, perhaps, be pointed out that the kriging
          variance is what we minimise and hence, surely, some
          measure of reliability? The whole geometry versus
          variability thing has been at issue since Philips and
          Watson provided their seminal (sic) paper in 1986.
          Given consistent data quality and a Normal (gaussian)
          distribution, geometry is what determines likely
          error. Under those circumstances, 1000 simulations
          will yield an average of the kriged value and a
          standard deviation equal to the kriging standard
          deviation.

          If the data quality is not consistent and the
          distribution of values is not Gaussian, then your
          comments hold particular force. Since these are the
          circumstances under which I labour daily, I would
          appreciate any and all suggestions as to what we use
          instead. Simulation is not an option when you have
          hundreds of thousands of blocks and a limited time to
          produce a reserve.

          Isobel Clark
          http://www.stokos.demon.co.uk

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        • Stelpstra, David
          Dear list members, I wish to make a remark on the discussion started on the kriging variance. In my opinion the SD of the solution obtained by kriging is
          Message 4 of 5 , Apr 3 2:15 AM
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            Dear list members,

            I wish to make a remark on the discussion started on the kriging variance.
            In my opinion the SD of the solution obtained by kriging is determined by
            two effects. One is the (geometrical) distribution of the data, the other
            one is the (a priori) standard deviation of the data. Richards remark is
            right if the data has equal weights or standard deviations (SD). However if
            the data is all weighted equally (by say 1.0) we will get a scaled 'SD'. If
            you like studentized statistics, you can get a estimate for the SD of the
            solution by multiplying with the a posteriori variance factor.

            In our problems (cross validation of bathymetry data) we have a estimate for
            the SD, which we use in the covariance function for the kriging problem. The
            resulting SD of the solution will depend on the chosen a priori SD for the
            samples.

            Just my 2 cents,
            David.



            Quality Positioning Services bv, Huis ter Heideweg 16, 3705 LZ
            Zeist, the Netherlands
            Tel +31 (0)30 6925825, Fax +31 (0)30 6923663, Web http://www.qps.nl
            <http://www.qps.nl/>


            -----Original Message-----
            From: Richard Hague [mailto:richardh@...]
            Sent: woensdag 3 april 2002 6:48
            To: ai-geostats@...
            Subject: Re: AI-GEOSTATS: Ore Reserves Classification



            List Members,

            The use of the kriging variance to categorise/classify Mineral (Ore)
            Resources and/or Ore Reserves is an old chestnut that periodically raises
            it's ugly head. The kriging variance is related, pure and simply, to the
            data configuration and has nothing to do with the sample grades/variables
            being used for interpolation. As an example say a grade was being
            interpolated into a block which has been sampled on each corner, regardless
            of what the individual sample grades are, the kriging variance for that
            block is going to be the same. Example: if all four samples have the same
            grade of (say) 2.35g/t Au you will get the same kriging variance as the case
            where the four samples grades are (say) 0.01, 102.9, 0.88 and 3.60 g/t Au.
            Naturally I would have more confidence in the interpolated grade in the
            former scenario than the latter; thus the use of the kriging variance to
            determine confidence (or classification) of an estimate is misleading.

            One method of obtaining some feel for the possible error range would be to
            run a large number of grade simulations into the block, the variance of all
            simulated grades would give an indication of error - again in the example
            given above, the variance of the simulated grades using the former case
            would be much smaller than in the latter case.

            Of course classification of Mineral (Ore) Resources and/or Ore Reserves
            needs to take into account a lot more items (as expounded by the JORC
            (1999) code) - than just some objective measure of estimation error, it
            needs to take into consideration, amongst other things, data quality - if
            you have poor quality data (eg biased/inaccurate), regardless of how good
            any statistical measure of the estimation error is, you will always have
            poor estimate.

            REFERENCES
            JORC; 1999: Australasian code for reporting of mineral resources and ore
            reserves (the JORC Code). Prepared by the Joint Ore Reserves Committee of
            the Australasian Institute of Mining and Metallurgy, Australian Institute of
            Geoscientists and Minerals Council of Australia (JORC).

            Richard Hague
            Hellman & Schofield Pty Ltd
            Brisbane Office
            p&f: +61 (0)7 3217 7355
            e: richardh@... <mailto:richardh@...>
            w: http://www.hellscho.com.au <http://www.hellscho.com.au>



            ----- Original Message -----
            From: José <mailto:cuador@...> Quintín Cuador Gil
            To: ai-geostats@... <mailto:ai-geostats@...>
            Sent: Wednesday, March 27, 2002 4:27 AM
            Subject: AI-GEOSTATS: Ore Reserves Classification

            Dear list members

            The Kriging variance has some uses. In mining, it can be used in the Ore
            Reserves Classification.
            What is the opinion about this in the Geostatistical community?
            It is possible to use the Kriging variance for ores reserves
            classification?, (Yes or No).
            Thanks in advances for any opinion.

            José Quintín Cuador Gil
            Department of Informática
            University of Pinar del Río
            Cuba
            < cuador@... <mailto:cuador@...> >



            [Non-text portions of this message have been removed]
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