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2411Re: [ai-geostats] spherical model

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  • M. Nur Heriawan
    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.


      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

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