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Re: AI-GEOSTATS: Ore Reserves Classification

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  • 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 1 of 5 , Apr 3, 2002
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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 2 of 5 , Apr 3, 2002
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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@...> >



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