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GEOSTATS: Summary: Interpolation of data with line collection error

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  • Marco Albani
    Thank you to all that have answerd my query. ... Dr. James G. Wendelberger suggested to use multidimensional smoothing ... Gilles Bourgault suggested to use
    Message 1 of 1 , Aug 26, 1999
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      Thank you to all that have answerd my query.

      These are the suggestions I received:

      -----------------------------
      Dr. James G. Wendelberger suggested to use multidimensional smoothing
      splines:

      > The method of multidimensional smoothing splines may be used
      > with the type of data you describe. An example of the method may be
      > found in:
      >
      > ftp://ftp.geog.uwo.ca/SIC97/Wendelberger/Wendelberger.htm
      >
      > The incorporation of a correlation between measurement errors may
      > be included in the model description. See my thesis for the general
      > formulae. I am not aware of any computer code which allows for the
      > automatic selection of the correlation parameter. However,
      > generalized cross validation (GCV) could be used to estimate the
      > correlation parameter.
      > By the way, multidimensional smoothing splines can be used quite
      > effectively to estimate derivatives. See my thesis.
      >
      > Wendelberger, J. G. (1982a) Smoothing Noisy Data with Multidimensional
      > Splines and Generalized Cross-Validation, Ph.D. Thesis, University of
      > Wisconsin - Madison.

      -----------------------------------------------------

      Gilles Bourgault suggested to use Factorial Kriging

      > An idea will be the filtering of those errors on each line. Factorial kriging can be used
      > to filter out correlated errors. You will need to model a variogram for each line. Then,
      > you will have to identify the variogram's component that represents the correlated
      > noise and filter out that component from your data.
      >
      > You may find a bit more information on factorial kriging in GSLIB book. You will have to
      > adapt GSLIB FORTRAN programs to do factorial kriging.

      ------------------------------------------------------------

      David Garner suggested to grid with an angular sectors moving
      neighborhood:

      > My solution is to grid with an angular sectors moving neighborhood.
      > Often I will use between 25 and 50 sectors. In each sector one can
      > use as few as 2 or 3 points per sector. The neighborhood is large,
      > yet each grid node is limited to being estimated by 50-100 points.
      > The sectors force the estimation to use data from nearby lines and
      > thereby describe the trend adequately for my purposes as the target
      > grid nodes fall at any location between lines. Before running, I test
      > the estimation results at selected grid nodes to see the influence of
      > the parameter choices before running the entire dataset.

      ----------------------------------------------

      I received other suggestions from colleagues here at UBC, and they
      include:

      Interpolate using a trend surface over a moving neighbourhood. Play with
      parameters until the directional variograms look the same.

      Use a Fourier Transformation and extract the high-frequency variations
      as noise. This soulition is the same used for de-striping in remote
      sensing.

      --
      Marco Albani - PhD Candidate, Quantitative Landscape Ecology
      Department of Forest Sciences, University of British Columbia
      3041 - 2424 Main Mall - Vancouver, BC V6T 1Z4 Canada
      Phone: (604) 822 8295 Fax: (604) 822 9102
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