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455RE: AI-GEOSTATS: Kriging with External Drift

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  • Michael Dennis
    Dec 6, 2001
    • 0 Attachment
      So are you saying that the external drift variable in the matrix is just the
      magnitude of the the drift variable at that point?

      ie :

      3 point kriging

      s = drift variable

      [ k11 k12 k13 1 s1 ] [ l1 ] [ k01 ]
      [ k21 k22 k23 1 s2 ] [ l2 ] [ k02 ]
      [ k31 k32 k33 1 s3 ] [ l3 ] = [ k03 ]
      [ 1 1 1 0 0 ] [ u0 ] [ 1 ]
      [ s1 s2 s3 0 0 ] [ u1 ] [ s0 ]


      So in this 3 point Kriging case I just plug in the magnitude of my drift
      variable in for s0, s1, s2,and s3?

      And if you substituted a drift with a magnitude which was computed based
      upon 1st order polynomial you would get the same results from this matrix as
      you would by removing the 1st order polynomial trend and kriging the
      residuals and adding the 1st order polynomial trend back in?

      It is all starting to make sense now (if I'm correct in what I'm saying
      above). Thanks so much for your help!

      Mike

      -----Original Message-----
      From: ai-geostats-list@... [mailto:ai-geostats-list@...]On
      Behalf Of sshibli@...
      Sent: Thursday, December 06, 2001 11:59 AM
      To: Michael Dennis
      Cc: AI-Geostats Mailing List
      Subject: Re: AI-GEOSTATS: Kriging with External Drift



      On Thursday, December 6, 2001, at 04:12 AM, Michael Dennis wrote:
      >
      > I don't think this is right but if you can explain to me how the Drift
      > is
      > actually applied in laymans terms it would be greatly appreciated. Also
      > when you do kriging with external drift do you have to model a
      > variogram or
      > can a reasonable one be computed automatically, if so how would you
      > compute
      > it?

      Kriging with an external drift is just an extension of universal kriging.
      UK assumes that one knows the shape of the trend but not its
      magnitude (or coefficients). For example a linear drift could be modeled
      by Mean = a + bX + cY where X and Y are the coordinates of the data.
      And so on and so forth for higher order polynomial trends.

      In KED, the trend shape is not defined analytically; rather, it is
      assumed that
      it is defined explicitly at all locations based on some densely sampled
      secondary variable. However, such a secondary variable must be
      smoothly varying in space, and also it must be available at all locations
      of the primary data and the locations being estimated.

      As in UK, the magnitude of the trend is unimportant, it is the shape
      that we're interested in. An external drift that varies linearly with X
      and
      Y would be equivalent to UK with an analytical trend of the same
      order polynomial, i.e. 1.

      Regards,

      Syed
      Maersk Copenhagen


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