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[ai-geostats] regularization

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  • samuel verstraete
    Hi, I have a 3D data set that has been sampled by a private company. They lacked a complete knowledge of geostatistics so there is no sampling strategy
    Message 1 of 3 , Oct 26, 2004
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      Hi,

      I have a 3D data set that has been sampled by a private company. They
      lacked a complete knowledge of geostatistics so there is no sampling
      "strategy" involved. Another thing is that the support of the samples is
      strongly fluctuating. Horizontally the sampling support is constant and
      can be considered as a point (about 70cm^2 compared to a few hectares)
      Vertically the sampling support is not stable and rather "huge" in
      comparison with the vertical scale... (sampling can be 0.10 to 1 meter
      and maximum depth would be 5 to 6 meter or even less)

      I've read in the literature that there is a possibility to correct for
      such a things, through regularization. But none of the literature seems
      to discuss the possibility that the samples themself do not always have
      the same support, as stated before samples can have a support that is 10
      times bigger than the smallest sample.

      Question is... Is there any other literature that discusses this matter
      and even more importantly is there any software out there that can take
      this sampling support into consideration when I'm calculating the
      variogram or when I start with estimation/simulation of the field.


      Thanks in advance,

      --
      Samuel Verstraete
      Ghent University
      Faculty of Bioscience Engineering
      Dept. of Soil Management and Soil Care
      Coupure Links 653, B-9000 Gent, Belgium
    • Edzer J. Pebesma
      Two relevant publications mentioned by Carol Gotway during her geoENV keynote (I happen to have them both on my desk right now, but haven t read them yet):
      Message 2 of 3 , Oct 26, 2004
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        Two relevant publications mentioned by Carol Gotway during her
        geoENV keynote (I happen to have them both on my desk right
        now, but haven't read them yet):

        Gotway & Young, 2002, Combining incompatible spatial data,
        JASA (I don't have the issue and page numbers) -- this paper
        deals with block kriging when the data are observed on blocks
        with varying size

        A Mockus, 1998, Estimating dependencies from spatial averages.
        Journal of computational and graphical statistics 7:4, 501-513. --
        this paper explains how to estimate the point support variogram
        (probably up to the nugget) from blocks of varying size.

        If you find software for either of the issues in these papers, please let
        the list know.
        --
        Edzer


        samuel verstraete wrote:

        >Hi,
        >
        >I have a 3D data set that has been sampled by a private company. They
        >lacked a complete knowledge of geostatistics so there is no sampling
        >"strategy" involved. Another thing is that the support of the samples is
        >strongly fluctuating. Horizontally the sampling support is constant and
        >can be considered as a point (about 70cm^2 compared to a few hectares)
        >Vertically the sampling support is not stable and rather "huge" in
        >comparison with the vertical scale... (sampling can be 0.10 to 1 meter
        >and maximum depth would be 5 to 6 meter or even less)
        >
        >I've read in the literature that there is a possibility to correct for
        >such a things, through regularization. But none of the literature seems
        >to discuss the possibility that the samples themself do not always have
        >the same support, as stated before samples can have a support that is 10
        >times bigger than the smallest sample.
        >
        >Question is... Is there any other literature that discusses this matter
        >and even more importantly is there any software out there that can take
        >this sampling support into consideration when I'm calculating the
        >variogram or when I start with estimation/simulation of the field.
        >
        >
        >Thanks in advance,
        >
        >
        >
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