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AI-GEOSTATS: Samples in a block

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  • Mark Burnett Deelkraal
    Hi all I have a number of questions to all out there..any help/ pointers would be appreciated. 1. What is the optimum number of samples in a block of any
    Message 1 of 3 , Aug 27 11:41 PM
      Hi all

      I have a number of questions to all out there..any help/ pointers would be
      appreciated.

      1. What is the optimum number of samples in a block of any particular size?

      What I have been able to track down so far has not really been helpful, this
      includes comments like:

      Samples should be spaced at half the first range...of the semivariogram

      samples should be spaced in such a way as to reduce the Krige variance

      etc.

      All of these appear to pre-suppose that you already have sampling.

      Is there any way that I can work out the theoretical number of samples in an
      e.g. 30x30m block assuming some a priori information (gold deposit, high
      nugget of e.g. 1.2 e6, pop.var having the same type of magnitude etc) ?

      2. Does anyone know of a good "idiots guide" to GSLIB? I have bought the
      manual, however I have not found it particularly helpful for a first time
      user of the software (I want to start simulations of the ore body that I
      work on, prior to us commencing a capital intensive exploration programme).

      3. Is there a good declustering programme out there? (This gets back to
      question 1), when developing the ore body the sample spacing is approx.
      2.5m, when production commences the sample spacing changes to a 5x5 grid
      (ideally, this never really happens in actuality). What I want to do is to
      try and overcome the change of support issue, declustering is the only way
      that I can think of at the moment.

      4. Does anyone know where I can get hold of a good ( preferably
      introductory) text on Probability Kriging? and is there any software that
      has been designed to run this?


      Thanks to all

      Yours

      Mark Burnett

      Ore Reserve Manager

      Deelkraal Gold Mine


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    • Isobel Clark
      ... This part I can answer on the general mailing list (I think). Use the free unlimited use downloadable Kriging Game to be found on my pages at
      Message 2 of 3 , Aug 28 5:30 AM
        > 1. What is the optimum number of samples in a block
        > of any particular size?
        >
        > Is there any way that I can work out the theoretical
        > number of samples in an
        > e.g. 30x30m block assuming some a priori information
        > (gold deposit, high
        > nugget of e.g. 1.2 e6, pop.var having the same type
        > of magnitude etc) ?
        This part I can answer on the general mailing list (I
        think).

        Use the free unlimited use downloadable Kriging Game
        to be found on my pages at
        http://uk.geocities.com/drisobelclark/briefcase.html

        This package reads Geostokos type files, Geo-EAS type
        files, CSVs dumped from spreadsheets or you can type
        in data from the keyboard.

        Comments and queries to me please.
        Isobel Clark

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      • Jan-Willem van Groenigen
        Hi Mark, it seems you have already realized the paradox of sampling in geostatistics: the more you know about the variable in question, the better you can
        Message 3 of 3 , Aug 28 8:53 AM
          Hi Mark,

          it seems you have already realized the paradox of sampling in
          geostatistics: the more you know about the variable in question, the better
          you can optimize a sampling scheme for it. It isn't easy to break out of
          this paradox, and that's probably the reason that sampling has received
          relatively little attention in the geostatistical literature. You will not
          find much about it in most textbooks.

          You have probably already found a number of papers by Webster and McBratney
          from the beginning of the 80's (mainly in the Journal of Soil Science, I
          think). They described an algorithm for calculating the optimum grid
          spacing for a sampling scheme, given the maximum allowed kriging variance
          and a variogram. These papers, although relatively old, are still often
          quoted. Another paper from those days dealing with the optimal type of grid
          is Yfantis, E.A., Flatman, G.T. and Behar, J.V., 1987. Efficiency of
          kriging estimation for square, triangular and hexagonal grids. Mathematical
          Geology, 19(3): 183-205.

          I normally don't like to advertize my own work this much, but hey.... this
          was my Ph.D. thesis. I developed a simulated annealing - based algorithm
          that (among other things) optimizes for the same criterion as the
          Webster/McBratney papers, but that optimizes the optimal location of
          individual points, rather than optimal grid spacing. Although this might
          not be very useful in large, contiguous sampling areas, it considerably
          improves your sampling efficiency when you already have preliminary samples
          and/or many sampling constraints. Again, you need (to assume) a variogram.

          A couple of references to my work:

          -Van Groenigen, J.W. and Stein, A., 1998. Constrained optimization of
          spatial sampling using continuous simulated annealing. Journal of
          Environmental Quality, 27(5): 1078-1086.
          -Van Groenigen, J.W., Siderius, W. and Stein, A., 1999. Constrained
          optimisation of soil sampling for minimisation of the kriging variance.
          Geoderma, 87: 239-259.
          -Van Groenigen, J.W., Pieters, G. and Stein, A., 2000. Optimizing spatial
          sampling for multivariate contamination in urban areas. Environmetrics, 11:
          227-244.

          Also, you can download a preliminary software implementation of this
          algorithm from my website (see below).

          Of course, there is a lot a controversy in the geostatistical community
          about the use of kriging variance as a measure for interpolation error,
          since it does not take into account the actual values of the measured
          variable, which can give you problems when the intrinsic hypothesis doesn't
          hold (and it often doesn't). Although this has some truth to it, my
          philosophy is that that is exactly what makes it interesting for sampling
          optimization, since you don't have those values before sampling anyway....
          However, the last of my references used an optimization criterion that
          doesn't involve kriging variance.

          Cheers,

          Jan Willem.



          ******************************************
          Jan Willem van Groenigen
          University of California - Davis
          Dept. of Agronomy and Range Science
          1 Shield Avenue
          Davis, CA 95616 - 8515, U.S.A.
          ------------------------------
          e-mail: groenigen@...
          http://agronomy.ucdavis.edu/groenigen
          tel. (530) 752-3457
          fax. (530) 752-4361
          *****************************************


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