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Re: AI-GEOSTATS:

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  • Heinz Burger
    Ian Hunt [KLP BUSINESS DEVELOPMENT] schrieb: Hello Ian, for classification reports on ore reserves you may refer to the jorc guidelines, which are very
    Message 1 of 6 , May 7 7:31 AM
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      "Ian Hunt [KLP BUSINESS DEVELOPMENT]" schrieb:

      Hello Ian,

      for classification reports on ore reserves you may refer to the
      jorc guidelines, which are very similar to the European
      standard.

      http://www.jorc.org

      Regards,

      Heinz Burger

      > Hello List Members,
      >
      > I am trying to use Kriging Efficiency and Regression Slope on a grade
      > model to draw the boundaries between Inferred/Indicated on an orebody.
      > Any experience or "gutfeel" values would be appreciated. I have heard
      > that a regression slope value of 0.9 is good for a measured status but
      > we do not have that high level of drilling yet. The average regression
      > slope is 0.39 with very few values above 0.9.
      >
      > We do not have extensive drilling as the project is in the early stages
      > of exploration with the drilling grid on 100m X 100m and the
      > semi-variogram ranges on 180 meters.
      >
      > The problem is that we (geology team) knows that the drilling is
      > inadequate but the powers that be must be convinced for budgetry
      > purposes and a documented scientific method would be nice.
      >
      > Regards
      >
      > Ian Hunt
      >
      >
      >
      >
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      --
      *****************************************************
      Visit IAMG2002: http://www.fu-berlin.de/iamg2002
      *****************************************************
      Dr. Heinz Burger
      Freie Universitaet Berlin
      - Geoinformatik -
      Malteserstr. 74-100
      12249 BERLIN, Germany
      Tel. (49) 30-838-70561 Fax: (49) 30-775-2075
      mailto: hburger@...-berlin.de
      Web-Seite: http://userpage.fu-berlin.de/~hburger/hb
      ****************************************************



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    • Isobel Clark
      Thank you, Marco! My point exactly. Isobel ____________________________________________________________ Do You Yahoo!? Get your free @yahoo.co.uk address at
      Message 2 of 6 , May 23 11:41 AM
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        Thank you, Marco!

        My point exactly.
        Isobel

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      • Isobel Clark
        Dear All I have received a couple of emails about difficulties with accessing the stuff in my Yahoo briefcase . Please accept my apologies for not reading the
        Message 3 of 6 , Mar 29, 2002
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          Dear All

          I have received a couple of emails about difficulties
          with accessing the stuff in my Yahoo "briefcase".
          Please accept my apologies for not reading the small
          print.

          Apparently Yahoo has ceased allowing public access to
          briefcase files as of 25th March 2002. I am working
          hard to move and update all of the files and links and
          hope you will bear with me in the meantime.

          They should be working by Monday 1st April. If you
          find any false or broken links after that please
          please let me know.

          Isobel Clark
          http://uk.geocities.com/drisobelclark/briefcase.html

          __________________________________________________
          Do You Yahoo!?
          Everything you'll ever need on one web page
          from News and Sport to Email and Music Charts
          http://uk.my.yahoo.com

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        • Marco Alfaro S.
          Dear Isobel: In the case of intrinsic random functions the covariance (non ergodic covariance) and the correlogram are artifacts (see my example in
          Message 4 of 6 , May 23 12:10 PM
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            Dear Isobel:

            In the case of intrinsic random functions the covariance (non ergodic covariance) and the
            correlogram are artifacts (see my example in ai-geostats).

            I prefer to use the variogram. If you whish to have a symetric system, with no problems of pivoting,
            use the "Matheron System", and your program runs faster!

            Proof:

            The kriging system is (take a as lambda, g as gamma):

            a1g(1,1)+a2g(1,2)+...+aNg(1,N)+mu=g(1,0)............(1)
            a1g(2,1)+a2g(2,2)+...+aNg(2,N)+mu=g(2,0)............(2)
            ........................................
            a1g(N,1)+a2g(N,2)+...+aNg(N,N)+mu=g(N,0).........(N)
            a1+a2+...+aN=1.......................................................(N+1)
            ______________________________________________________

            Now I sustract the equation (N) from the others (mu vanishes):

            a1(g(1,1)-g(N,1))+a2(g(1,2)-g(N,2))+...+aN(g(1,N)-g(N,N))=g(1,0)-g(N,0)
            a1(g(2,1)-g(N,1))+a2(g(2,2)-g(N,2))+...+aN(g(2,N)-g(N,N))=g(2,0)-g(N,0)
            ......................................................................
            a1(g(N,1)-g(N,1))+a2(g(N,2)-g(N,2))+...+aN(g(N,N)-g(N,N))=g(N,0)-g(N,0)
            _______________________________________________________________________

            The last equation is an identity, then you have only N-1 equations. Now
            I take (to eliminate the weight aN):

            aN=1-a1-a2-...-aN-1 and replace in the others equations to get the
            "Matheron System":

            a1R(1,1)+a2R(1,2)+...+aN-1R(1,N-1)=B(1)...........................(1)
            a1R(2,1)+a2R(2,2)+...+aN-1R(2,N-1)=B(2)...........................(2)
            .......................................
            a1R(N-1,1)+a2R(N-1,2)+...+aN-1R(N-1,N-1)=B(N-1).........(N-1)
            _________________________________________________________

            with: R(i,j)=g(N,j)-g(i,j)+g(i,N)-g(N,N)
            B(i)=g(N,0)-g(i,0)-g(N,N)+g(i,N)

            (for the kriging variance you have a very nice formula, cf. (2))

            The system is symetric R(i,j)=R(j,i), and the diagonal term
            R(i,i) is never 0.

            This is a system with only N-1 equations!! (not with N+1 equations).
            If you use this system, your kriging program runs faster!(I remember
            that the time to solve a linear system of n equations is exponential
            with n, cf (1)).

            References:

            1. M. Alfaro: Nouveaux Résultats sur la vitesse des calculs
            géostatistiques. Journées de Géostatistique, Fontainebleau, 1991.
            2. G. Matheron. Cours de Géostatistique. Fascicule 1. Ecole des
            Mines de París, 1965.
            3. A. Maréchal: El sistema de Matheron en Krigeage Universal.
            Boletín de Geoestadística, Chile, 1972.


            Best regards

            Marco






            Isobel Clark wrote:

            > > It is well known that when inverting a
            > > matrix it is much better (for numerical reasons)
            > > that the higher values
            > > are on the diagonal and the lower values far off the
            > > diagonal.
            > Have you not heard of "pivoting"?
            >
            > The computational "problems" of using a matrix based
            > on the semi-variogram rather than the covariance are
            > removed totally by putting the last equation first in
            > the matrix. Of course, this means you cannot use a
            > computational algorithm which demands a symmetric
            > matrix, but so what?
            >
            > Alternatively, you pivot on the largest term in the
            > first equation, then the second etc. I did a lot of
            > experimentation with this around 15 years ago and
            > found that the two (covariance and semi-variogram)
            > sets of equations become identical after around the
            > second or third 'pivot'.
            >
            > Please let us not confuse programming problems with
            > geostatistical problems.
            >
            > There are a lot of packages out there which ask you to
            > model the semi-variogram and then use a covariance for
            > kriging. There are a lot of packages out there which
            > model the semi-variogram and krige with the
            > semi-variogram. Are there main stream geostatistical
            > (as opposed to statistical or strict GIS) packages
            > which model the covariance?
            >
            > Isobel Clark
            > http://geoecosse.bizland.com
            >
            > ____________________________________________________________
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            > Get your free @... address at http://mail.yahoo.co.uk
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            >
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          • Julian Ortiz
            Hi Dean, Average over a moving window can help you show how the mean (and variance) changes with location... This may indicate that a stationary random
            Message 5 of 6 , Sep 10, 2003
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              Hi Dean,

              Average over a moving window can help you show how the mean (and variance)
              changes with location... This may indicate that a stationary random function
              model will not be appropriate for your data. You can also use indicator maps.

              An approach to handle the "trend" is to use an estimation or simulation method
              with locally varying mean, or to use a secondary variable as external drift.
              IRF-k methods are also an alternative. Removing the trend and working with the
              residuals carries some problems: you may end up overfitting the trend and
              loosing all the correlation in your residuals.

              You can look at almost any book in Geostatistics to find more details:

              GSLIB: Geostatistical Software Library and User's Guide, by Deutsch and
              Journel (1997)

              Geostatistics for Natural Resources Evaluation, by Goovaerts (1997)

              Geostatistics: Modeling Spatial Uncertainty, by Chiles and Delfiner (1999)

              Hope this helps,

              Julian.
              -------------------------
              Julian Ortiz C., Ph.D.
              jmo1@...
              www.ualberta.ca/~jmo1
              -------------------------

              >===== Original Message From Dean Monroe <monroea@...> =====
              >Group:
              >
              > How is the best to graphically show non-stationarity in spatial data with
              say one variable of interest and two dimensions? In time series, one can plot
              realizations over time, what is the spatial analog?
              > Second, what may a person do to correct non-stationarity? Again, in time
              series a common practice is to use first, second, etc differences.
              >
              >Best,
              >Dean Monroe
              >Oklahoma State University
              >Environmental Sciences


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            • Ines
              dear elisa I think it is possible to check the relation between your data and these are outside the study are. you can investigate all the data using
              Message 6 of 6 , Jan 15, 2004
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                dear elisa
                I think it is possible to check the relation between your data and these are outside the study are.
                you can investigate all the data using geostatistical analyst (semivariogram - covariance cloud), selecting after only the new data you can see if they are located in this diagramm (near the other point or father by them) and then you can decide if they are connected with your data or not.



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