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Re: [ai-geostats] spherical model

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  • Rajni Gaur
    I am happy to know about such querry from you also, Few days back i also posted the same question but somehow i was not satisfied. If you get the satisfactory
    Message 1 of 4 , Feb 16, 2006
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      I am happy to know about such querry from you also, Few days back i
      also posted the same question but somehow i was not satisfied.
      If you get the satisfactory answer then please let me know



      On 2/14/06, M. Nur Heriawan <mn_heriawan@...> wrote:
      > Dear list,
      >
      > I have small query. Why almost all kind of spatial
      > data set (ore grade data, sea surface temperature
      > data, soil thickness, etc.) is fitted to the spherical
      > (variogram) model? May anyone explain the origin of
      > this spherical model?
      >
      > Thank you for your help.
      >
      > Regards,
      >
      > M. Nur Heriawan
      > ---------------
      > Graduate School of Science and Technology
      > Kumamoto University
      > Kurokami 2-39-1, Kumamoto 860-8555, JAPAN
      >
      >
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    • Isobel Clark
      Hi, I do not know whether you received any answers off-list, so here goes. The spherical model of geostatistics was so-named by Matheron and is sometimes
      Message 2 of 4 , Feb 20, 2006
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        Hi, I do not know whether you received any answers off-list, so here goes.
         
        The "spherical" model of geostatistics was so-named by Matheron and is sometimes also known as the Matheron model. His idea was that a sample has a 'sphere of influence' around it. Potential (or actual) samples within this sphere have values which are 'related' to the value at the central point. Imagine, now, a second such point with its own sphere of influence. If the spheres do not touch, there is no relationship between the values at the two central points. If the spheres overlap, there will be a relationship. The more the spheres overlap, the stronger the relationship.
         
        The spherical semi-variogram is the simple geometric calculation for the volume of NON-overlap of the two spheres, given the distance between their centres.
         
        There is no real reason why it should work in so many cases -- any more than there is for the Normal (Gaussian) distribution being found so often in nature. In fact, there is often a possibility to fit several of the semi-variogram models in practice. You could decide which is most appropriate using something like Cressie's goodness of fit test (analagous to a sort of chi-squared statistic).
         
        Isobel
        http://uk.geocities.com/drisobelclark

        "M. Nur Heriawan" <mn_heriawan@...> wrote:
        Dear list,

        I have small query. Why almost all kind of spatial
        data set (ore grade data, sea surface temperature
        data, soil thickness, etc.) is fitted to the spherical
        (variogram) model? May anyone explain the origin of
        this spherical model?

        Thank you for your help.

        Regards,

        M. Nur Heriawan
        ---------------
        Graduate School of Science and Technology
        Kumamoto University
        Kurokami 2-39-1, Kumamoto 860-8555, JAPAN
      • M. Nur Heriawan
        Dear Isobel, Thanks for your reply. It is the first reply regarding this subject. Beforehand, I got one information mentioned that spherical model corresponds
        Message 3 of 4 , Feb 20, 2006
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          Dear Isobel,

          Thanks for your reply. It is the first reply regarding
          this subject. Beforehand, I got one information
          mentioned that spherical model corresponds to a Random
          Function resulting of the summation of 3D spheres
          random in space, each sphere being given a value.

          Moreover, it is mentioned that there is no particular
          reason why this model should be used rather than
          another (positive definite) equation. But historically
          people have given preference to this model, and most
          (but not all) experimental semivariograms can be
          modeled by a combination of spherical.

          The information I got above is exactly matching with
          yours. Again thank you.

          Cheers,

          Nur H.

          --- Isobel Clark <drisobelclark@...> wrote:

          > Hi, I do not know whether you received any answers
          > off-list, so here goes.
          >
          > The "spherical" model of geostatistics was
          > so-named by Matheron and is sometimes also known as
          > the Matheron model. His idea was that a sample has a
          > 'sphere of influence' around it. Potential (or
          > actual) samples within this sphere have values which
          > are 'related' to the value at the central point.
          > Imagine, now, a second such point with its own
          > sphere of influence. If the spheres do not touch,
          > there is no relationship between the values at the
          > two central points. If the spheres overlap, there
          > will be a relationship. The more the spheres
          > overlap, the stronger the relationship.
          >
          > The spherical semi-variogram is the simple
          > geometric calculation for the volume of NON-overlap
          > of the two spheres, given the distance between their
          > centres.
          >
          > There is no real reason why it should work in so
          > many cases -- any more than there is for the Normal
          > (Gaussian) distribution being found so often in
          > nature. In fact, there is often a possibility to fit
          > several of the semi-variogram models in practice.
          > You could decide which is most appropriate using
          > something like Cressie's goodness of fit test
          > (analagous to a sort of chi-squared statistic).


          M. Nur Heriawan
          http://www.mining.itb.ac.id/heriawan

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