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Re: [ai-geostats] Sill not reaching 1

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  • Dan Bebber
    nugget + sill = sample variance unless you have normalized the data prior to analysis. So you could get any value from raw data. Dan Bebber ... From: Colin
    Message 1 of 6 , Feb 7, 2006
      nugget + sill = sample variance
      unless you have normalized the data prior to analysis.
      So you could get any value from raw data.
       
      Dan Bebber
      ----- Original Message -----
      Sent: Tuesday, February 07, 2006 9:17 AM
      Subject: [ai-geostats] Sill not reaching 1

      Hi All,

       

      I am performing estimation for Ni as a penalty element to our main ore, using nested spherical correlogram models. One of these shows abundant and robust experimental data reaching a plateau at gamma = 0.90, and is thus modelled in such a way that the sill of this spherical model is at 0.9, instead of at 1.00.

       

      I’m not sure of this, but is there a strict requirement that the sill differentials and nugget need to sum to 1.00 for estimation purposes. I use Vulcan (effectively GSLIB) for estimation. If it is a requirement that they add to 1.00, it has been suggested that I could scale the nugget and sill to a value of 1, but I’m not sure exactly how to do this.

       

      Does anyone have any comments and/or suggestions?

       

      Regards,

      Colin



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    • Dan Bebber
      yes- but shouldn t use gamma to mean correlation, it confuses me. rho is the usual symbol. In which case, the correlogram shouldn t reach a plateau at
      Message 2 of 6 , Feb 7, 2006
        yes- but shouldn't use 'gamma' to mean correlation, it confuses me.
        'rho' is the usual symbol.
        In which case, the correlogram shouldn't 'reach a plateau at gamma = 0.9'
        Would expect correlation (and covariance) to decrease with lag.
        Colin- we need a clearer description of your problem!
         
        Dan
        ----- Original Message -----
        Sent: Tuesday, February 07, 2006 10:05 AM
        Subject: Re: [ai-geostats] Sill not reaching 1

        When working with correlograms the maximum theoretical sill is 1 with no need of previously normalizing data.
         
        Maria
        ----- Original Message -----
        Sent: Tuesday, February 07, 2006 7:34 AM
        Subject: Re: [ai-geostats] Sill not reaching 1

        nugget + sill = sample variance
        unless you have normalized the data prior to analysis.
        So you could get any value from raw data.
         
        Dan Bebber
        ----- Original Message -----
        Sent: Tuesday, February 07, 2006 9:17 AM
        Subject: [ai-geostats] Sill not reaching 1

        Hi All,

         

        I am performing estimation for Ni as a penalty element to our main ore, using nested spherical correlogram models. One of these shows abundant and robust experimental data reaching a plateau at gamma = 0.90, and is thus modelled in such a way that the sill of this spherical model is at 0.9, instead of at 1.00.

         

        I’m not sure of this, but is there a strict requirement that the sill differentials and nugget need to sum to 1.00 for estimation purposes. I use Vulcan (effectively GSLIB) for estimation. If it is a requirement that they add to 1.00, it has been suggested that I could scale the nugget and sill to a value of 1, but I’m not sure exactly how to do this.

         

        Does anyone have any comments and/or suggestions?

         

        Regards,

        Colin



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      • Marco Alfaro S.
        Hello Colin. The experimental correlogram in geostatistics is an artifact. To see that, we can examine an example: Let a line sampled at equal intervals. The
        Message 3 of 6 , Feb 8, 2006
          Hello Colin.
           
          The experimental correlogram in geostatistics is an artifact. 
           
          To see that, we can examine an example:
           
          Let a line sampled at equal intervals. The grades are (N=10 samples):
           
          1  2  3  3  4  4  4  6  8  8  10  10
           
          We can see a drift in the data.
           
          If we calculate the correlogram and the variogram we have:
           
          Lag        correlogram        variogram
          1                0.046                    0.682
          2                0.071                    1.950
          3                0.097                    3.667
          4                0.135                    6.688
          5                0.093                    9.643
          6                0                          12.250
          7                0.109                  17.100
          8                0.095                  22.875      
           
          The graphics show that:
           
          a) The correlogram has a nugget effect at the origin.
          b) The correlogram is linear near the origin.
          c) The correlogram never reaches the sill
          d) The correlogram show a periodicity at lag 6
          e) The variogram is parabolic at the origin.
          f) The variogram shows the drift.  
           
          Why the correlogram is 0 at lag 6?. In the table, we have the head grades and the tail grades for h=6:
           
          Head        Tail
              1            4
              2            6
              3            8
              3            8
              4          10
              4          10
           
          We see that a linear relationship exists between the head and the tail (tail = 2* head + 2) => The correlation coefficient between the head end the tail is 1 and the correlogram is 0!
          This example was taken from a real case: a hole in the Alemao deposit in Brazil.
           
           
          Regards,
           
          Marco.
           
           
           
           
          -------Mensaje original-------
           
          Fecha: 02/07/06 06:20:19
          Asunto: [ai-geostats] Sill not reaching 1
           

          Hi All,

           

          I am performing estimation for Ni as a penalty element to our main ore, using nested spherical correlogram models. One of these shows abundant and robust experimental data reaching a plateau at gamma = 0.90, and is thus modelled in such a way that the sill of this spherical model is at 0.9, instead of at 1.00.

           

          I’m not sure of this, but is there a strict requirement that the sill differentials and nugget need to sum to 1.00 for estimation purposes. I use Vulcan (effectively GSLIB) for estimation. If it is a requirement that they add to 1.00, it has been suggested that I could scale the nugget and sill to a value of 1, but I’m not sure exactly how to do this.

           

          Does anyone have any comments and/or suggestions?

           

          Regards,

          Colin



          ****************************************************************************************************************

          This e-mail and its attachments, is confidential and is intended for the addressee(s) only. If you are not the intended recipient, disclosure, distribution or any action taken in reliance on it is prohibited and may be unlawful. Please note that any information expressed in this message or its attachments is not given or endorsed by Lisheen Mine unless otherwise indicated by an authorised representative independently of this message. Lisheen Mine does not accept responsibility for the contents of this message and although it has been scanned for viruses Lisheen Mine will not accept responsibility for any damage caused as a result of a virus being passed on.


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