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Re: AI-GEOSTATS: semivariogram for binary data

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  • Pierre Goovaerts
    Hi Malin, In theory and under stationary of order 2, indicator semivariogram values should not exceed 0.25 which is the maximum variance that you could obtain
    Message 1 of 3 , Jan 16, 2001
      Hi Malin,

      In theory and under stationary of order 2,
      indicator semivariogram values should not exceed
      0.25 which is the maximum variance that you could obtain
      for indicator variables, for a proportion of 50%.
      I am wondering whether you have used the option
      "standardize sill" in gamv, which could explain
      these values larger than 1.

      Pierre
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      |________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
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      On Tue, 16 Jan 2001, Malin Fahller wrote:

      > Hi everybody,
      >
      > I feel confused and really need some help to straighten things out.
      >
      > I am currently working with geostatistical methods for marine geological mapping. My sourcedata consists of sediment samples, interpreted seismic profiles, bathymetric data and sonardata. In my first, and easiest, case I only use the sedimentsamples to get a rough picture of the sedimentary boundaries.
      >
      > So this question concerns the use of one single source of data, sedimentary samples. The source data is an ascii_file with three columns: (x_location, y_location, category (i.e soiltype)).
      >
      > What I have done so far is that for each category (i.e soiltype), I have done an indicator transform (for example: value 1 = sand, value 0 = not sand). Then I have used GSLIB, gamv, to make an omnidirectional semivariogram for my indicator transformed data. This has worked really nicely but I get semivariogram values that is larger than 1 and this troubles me. How can I possibly get semivariogram values that is outside the range 0 - 1 when I have indicator transformed data? Is there an error in the program or have I misunderstood the mathematics of semivariograms? Can someone PLEASE help me out.
      >
      > I reccon this is a basic question, but I just cant proceed if I dont get this straightened out.
      >
      > Many thanks in advance
      > Malin
      >


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    • Marco Alfaro
      Dear Malin: The semivariogram of an indicator variable is always less than 1. Proof: The experimental semivariogram is (1/2) of the mean of the squared
      Message 2 of 3 , Jan 16, 2001
        Dear Malin:

        The semivariogram of an indicator variable is always less than 1.

        Proof:
        The experimental semivariogram is (1/2) of the mean of the squared
        differences Z(xi+h)-Z(xi) but the values of Z are 0 or 1, then the
        semivariogram is (1/2) of the mean of the absolutes values of
        Z(xi+h)-Z(xi). Now you use the triangular inequality and you get that
        the semivariogram is less than 1.

        Regards
        Marco Alfaro



        Malin Fahller wrote:

        > Hi everybody, I feel confused and really need some help to straighten
        > things out. I am currently working with geostatistical methods for
        > marine geological mapping. My sourcedata consists of sediment samples,
        > interpreted seismic profiles, bathymetric data and sonardata. In my
        > first, and easiest, case I only use the sedimentsamples to get a rough
        > picture of the sedimentary boundaries. So this question concerns the
        > use of one single source of data, sedimentary samples. The source data
        > is an ascii_file with three columns: (x_location, y_location, category
        > (i.e soiltype)). What I have done so far is that for each category
        > (i.e soiltype), I have done an indicator transform (for example:
        > value 1 = sand, value 0 = not sand). Then I have used GSLIB, gamv, to
        > make an omnidirectional semivariogram for my indicator transformed
        > data. This has worked really nicely but I get semivariogram values
        > that is larger than 1 and this troubles me. How can I possibly get
        > semivariogram values that is outside the range 0 - 1 when I have
        > indicator transformed data? Is there an error in the program or have I
        > misunderstood the mathematics of semivariograms? Can someone PLEASE
        > help me out. I reccon this is a basic question, but I just cant
        > proceed if I dont get this straightened out. Many thanks in
        > advanceMalin


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