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[ai-geostats] error knowledge

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  • Gali
    Dear list members, Question: At each observation point we do know an error of measurement. How can we incorporate this knowledge when krigging sparce
    Message 1 of 2 , Sep 17, 2005
      Dear list members,

      Question: At each observation point we do know an
      error of measurement. How can we incorporate this
      knowledge when krigging sparce observation values?

      The specific example: You create depth markers by
      puting mark over the zone of transition between
      different lithologies on the lithology log. You can be
      wrong as much as the thickness of transition zone, so
      you can calculate your observation error quite
      precisely. As you can understand, those errors are not
      spatially correlated, neither they are correlated with
      marker value.

      Many thanks in advance,

      Gali Sirkis.



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    • Gerald van den Boogaart
      Dear Gali Sirkis, If you know the variogram 2gamma of the values without error and the variance of the observation errors sigma^2_x, this can be used fairly
      Message 2 of 2 , Sep 19, 2005
        Dear Gali Sirkis,

        If you know the variogram 2gamma of the values without error and the variance
        of the observation errors sigma^2_x, this can be used fairly easy by setting

        2gamma_new(x-y) = 2gamma(x-y)+sigma^2_x+sigma^2_y

        if x and y are to observation locations and

        2gamma_new(x-y) = 2gamma(x-y)+sigma^2_x
        if y is the prediction location (since you want to predict the correct value
        and not the one with error)
        and then build the kriging system with the gamma_new instead of gamma. However
        that only modifies the kriging error and not the weights.

        This theory is more or less discribed in the books e.g. Cressie.

        For your practical applications three problems:

        --> How to estimate the 2gamma without error?
        You could in principle use the same formula to correct the observed squared
        increments by substracting the sgima^2_x.

        --> You don't really have error variances.
        You more or less have error bounds. You could consider Bayesian Maximum
        Entropy here, but that would increase complexity of your work dramatically.

        --> How to do the computation?
        Thats a problem if you favourit software doesn't do it.

        However If you would assume that sigma^2_x is a constant and accept the
        kriging error to be for the observation and not for the true mean value, you
        could also compute your variogram based on the observations with measurement
        error directly estimating 2gamma_new and do you kriging in the usual way.

        So in conclusion: If your situation is nice there is nothing to do. If your
        situation is not such nice there is plenty of work.

        Best regards,
        Gerald v.d. Boogaart


        Am Sonntag, 18. September 2005 02:58 schrieb Gali:
        > Dear list members,
        >
        > Question: At each observation point we do know an
        > error of measurement. How can we incorporate this
        > knowledge when krigging sparce observation values?
        >
        > The specific example: You create depth markers by
        > puting mark over the zone of transition between
        > different lithologies on the lithology log. You can be
        > wrong as much as the thickness of transition zone, so
        > you can calculate your observation error quite
        > precisely. As you can understand, those errors are not
        > spatially correlated, neither they are correlated with
        > marker value.
        >
        > Many thanks in advance,
        >
        > Gali Sirkis.
        >
        >
        >
        > __________________________________
        > Yahoo! Mail - PC Magazine Editors' Choice 2005
        > http://mail.yahoo.com
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