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Re: GEOSTATS:cross variogram

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  • Pierre Goovaerts
    I am not sure that I have fully understood your question but I would recommend performing an indicator transform of your data before starting the (cross)
    Message 1 of 2 , May 5, 1999
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      I am not sure that I have fully understood your question
      but I would recommend performing an indicator transform of
      your data before starting the (cross) variogram analysis.
      For each class, you can define an indicator of occurrence
      of that class at any location u; e.g. for your classes
      1 (0-10) and 2 (10-20):
      I(u;c_1)=1 if 0 < z(u) <= 10, and I(u;c_1)=0 otherwise
      I(u;c_2)=1 if 10 < z(u) <= 20, and I(u;c_2)=0 otherwise

      Then, you compute a semivariogram of these indicators:
      g(h,c_1) = (1/2N(h)) sum_alpha=1^N(h) [i(u_alpha;c_1)-i(u_alpha+h;c_1)]^2
      or cross semivariogram
      g(h,c_1,c_2) = (1/2N(h)) sum_alpha=1^N(h)
      [i(u_alpha;c_1)-i(u_alpha+h;c_1)] x
      [i(u_alpha;c_2)-i(u_alpha+h;c_2)]

      The indicator variogram (=twice the value of the semivariogram 2g(h,c_1))
      measures how often two locations a vector h apart belong to c_1
      and another category. The smaller 2g(h,c_1), the better the spatial
      connectivity of the class c_1. The cross variogram (2g(h,c_1,c_2))
      measures the transition frequency between c_1 and c_2.

      Cross indicator semivariograms can be computed using the public-domain
      gslib programs that can be downloaded from
      http://www.ualberta.ca/~smpe/people/clayton/software.html
      Examples of class indicator variograms can be found in the paper:
      Goovaerts, P. 1996.
      Stochastic simulation of categorical variables using a classification
      algorithm and simulated annealing.
      Mathematical Geology, 28(7):909--921.

      There is also a research report (SCRF 94 paper) that you can download
      from my webpage.

      If you want to invest more time in the use of
      indicator variograms to detect different types
      of processes (e.g. mosaic, diffusion-type..), two
      references are:
      Rivoirard (1993). Relations between the indicators related to a
      regionalized variable. In: Soares, A. (Ed.), Geostatistics Tr\'oia '92,
      Kluwer Academic Publishers, Dordrecht, pp. 273--284.

      Webster R, Boag B (1992) Geostatistical analysis of cyst nematodes
      in soil. J. Soil Sci. 43: 583--595

      Regards,

      Pierre


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      ________ ________
      | \ / | Pierre Goovaerts
      |_ \ / _| Assistant professor
      __|________\/________|__ Dept of Civil & Environmental Engineering
      | | The University of Michigan
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      On Wed, 5 May 1999, nowook park wrote:

      > Dear all..
      >
      > I have some question about cross variogram analysis..
      >
      > in geoscience data integration scheme,
      > for the purpose of the evaluation of quantitative spatial influences of
      > each data layer to integrated layer.
      > if I perform cross variogram analysis with respect to
      > classified data, not continous data,
      > (ex) class 1 : 0 ~ 10 , class 2 : 10 ~ 11 etc..
      > control variable : integrated layer , target variable : each input
      > layer)
      > is it reasonable ? or is it useless ?
      > I wonder whether application to the classified data of cross variogram
      > is valid, or not..
      > also,if the grid cell size is 30m * 30m,
      > what is the reasonable unit lag interval w.r.t. sampling space?
      >
      > If anyone has cross variogram fortran codes,
      > please let me know..
      >
      > Thank you..
      >
      > best regards,
      >
      > nowook..
      >
      >
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