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AI-GEOSTATS: Re: setting up cokriging equations

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  • Isobel Clark
    Bettina I can t do math over the email but there are some papers Bill Harper and I wrote back in the mid-late 80s which you might find useful. Download from
    Message 1 of 4 , Apr 19, 2004
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      Bettina

      I can't do math over the email but there are some
      papers Bill Harper and I wrote back in the mid-late
      80s which you might find useful. Download from
      http://uk.geocities.com/drisobelclark/resume
      (click on Publications).

      Basically, the principle is simple:

      Consider each variable on each sample to be a
      different 'data point'

      Left hand side matrix is all semi-variograms between
      each data point and each data point. Only, this time,
      you have to remember which 'variable' is measured on
      that datum and identify which semi-variogram model is
      relevant.

      Right hand side 'vector' is similar in that the
      semi-variograms are between your estimated variable at
      specified point and each data point. Again, you just
      need to track which semi-variogram is relevant
      (ordinary or cross).

      The only real practical difference between co-kriging
      and kriging is that the weights on your primary
      variable (the one you are estimating) must sum to 1,
      while the weights one each co-variable (individually)
      must sum to zero to ensure unbiassedness. So, if, you
      are using one co-variable you will have two extra
      columns (and rows) on your left hand side matrix
      ensuring that the weights on your co-variable add up
      to zero. If you have two co-variables, you will get
      yet another row and column ensuring the weights on the
      second co-variable add up to zero.

      Does this help?
      Isobel
      http://geoecosse.bizland.com/whatsnew.htm





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    • Edward Isaaks
      Hi Bettina I suggest the book An Introduction to Applied Geostatistics by Isaaks and Srivastava. Chapter 17 is devoted soley to cokriging. And as a bonus,
      Message 2 of 4 , Apr 19, 2004
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        Hi Bettina
        I suggest the book "An Introduction to Applied Geostatistics" by Isaaks and
        Srivastava. Chapter 17 is devoted soley to cokriging. And as a bonus,
        Chapter 16 explains how to construct the linear model of coregionalization
        for co-kriging.
        Cheers, Ed


        ----- Original Message -----
        From: "Bettina Berger" <Bettina_Berger@...>
        To: <ai-geostats@...>
        Sent: Monday, April 19, 2004 1:03 AM
        Subject: AI-GEOSTATS: setting up cokriging equations


        > Hello!
        > Can anybody help me to set up the cokriging equations? I found the
        > theoretical equations in various books (Cressie, Chiles, Wackernagel), but
        I
        > have a hard time to really understand them and to implement them into
        > MATLAB. To be honest: I´m lost.
        > I´m "only" a MechEng student, so it seems that my mathematical
        possibilities
        > are at its limits with kriging generally and furthermore with cokriging.
        >
        > What I would need are not only the general theoretical equations for
        > Cokriging but also a practical example with real "numbers", which is
        > calculated from beginning to the end, including finding the C-Matrix, D
        > Matrix and the Kriging Weights.
        > And: what exactly is the difference between kriging and co-kriging at all?
        >
        > Is there any article or book I can find that? Or is anyone of you able to
        > write it down for me?
        > Thank you so much,
        > Cheers, Bettina
        >
        >
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