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RE: [ai-geostats] variograms of interpolated data

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  • Colin Daly
    RE: [ai-geostats] variograms of interpolated data Drink the beer Lise... the shape of the variogram will generally change. kriging is z^ = sum (lamdba_i * z_i)
    Message 1 of 5 , Sep 21, 2005
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      RE: [ai-geostats] variograms of interpolated data

      Drink the beer Lise...

      the shape of the variogram will generally change.

      kriging  is z^ = sum (lamdba_i * z_i)

      with, in simple kriging case, lambda_i = [C_ij]**(-1) * C_ix

      with C_ix being the covariance between i and x. So the weights, and hence the estimate
      itself z^ is a (fairly) simple function of the covariance C_ix. Most of the covariance functions that
      are used (spherical, exponential etc) are differentiable at almost all points (except the origin and possibly the sill) -
      so the kriging estimate is differentiable almost everywhere (except at the data points and possibly at some other points
      about a range away from other data). The variogram of any differentiable random function has got quadratic behavior
      (or maybe even higher, quartic etc.) at the origin.

      So the variogram of the kriged surface even when using the spherical, exponential etc will look more like a Gaussian variogram 
      (i'm not saying that it will be a gaussian - just that it will qualitatively look like one)

      That is my second answer today - so I really do deserve some of that beer!

      colin

      -----Original Message-----
      From: Nicolas Gilardi [mailto:ngilardi@...]
      Sent: Wed 9/21/2005 10:57 AM
      To: Lise Mentos
      Cc: ai-geostats@...
      Subject: Re: [ai-geostats] variograms of interpolated data

      Hi Lise,

      The best way to sort this out is to try it :-)

      However, the nugget effect will certainly disappear from a variogram
      constructed on krigged data (simulated data are supposed to keep it
      though). Sill, range and anisotropy should remain, as well as, I think,
      the general shape of the variogram model (i.e. spherical, exponential,
      etc.).

      As a conclusion, you can't retrieve the _exact_ variogram model only by
      doing variography on krigged data, but you can retrieve something very
      very close.

      IMHO, you should give it a try and share the beer ;-)

      Cheers

      Nicolas

      Lise Mentos wrote:

      > Hello,
      > Could someone please settle a beer-bet with a
      > classmate. He says that I should be able to reproduce
      > the variogram model used for kriging a dataset by
      > running a variogram analysis on the interpolated data.
      > I say he's all wet. Who wins the beer?  Thanks and I'm
      > sorry I can't award the judges a free one (especially
      > if you find in my favor!). Merci!
      > Lise
      >
      >
      >
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      --
      Nicolas Gilardi

      Particle Physics Experiment group
      University of Edinburgh, JCMB
      Edinburgh EH9 3JZ, United Kingdoms

      tel: +44 (0)131 650 5300     ; fax: +44 (0)131 650 7189
      e-mail: ngilardi@... ; web: http://baikal-bangkok.org/~nicolas


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