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[ai-geostats] Simulating an autocorrelated field

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  • Peter Bossew
    Hi list, I need to generate a field f(x,y) with given variogram. More precisely, I have N points (x,y) and I want to assign f(x,y) such that the variable f has
    Message 1 of 3 , Jun 13 4:16 AM
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      Hi list,

      I need to generate a field f(x,y) with given variogram. More precisely, I
      have N points (x,y) and I want to assign f(x,y) such that the variable f
      has a spatial autocorrelation structure according to a given variogram
      model.

      My impression is that the way to do it is simulated annealing, as
      described in chapter 11 of the GSLIB manual. Is that correct ? Any other
      methods ? Is there any easy-to-use & free software for this purpose ? Any
      recommended literature ?

      For time series (1-dim case with regular grid) there is the possibilty of
      random walk, or more generally Levy flights to produce autocorrelated
      series, or alternatively, define a Fourier spectrum with given slope of
      the continous log-log power spectrum and inverse transform. Is there an
      analoguos technique for the 2- (or n-) dim. case ?

      A possibly related question: How to produce a field with given (geometric
      or stochastic) multifractal structure ?


      Thanks for any hint
      Peter


      =================================================================
      Dr. Peter Bossew
      Department of Physics and Biophysics, University of Salzburg, Austria

      peter.bossew@...
      peter.bossew@...
    • Syed Shibli
      Have a look at Alexis Brandeker s pages (specifically his MSc thesis), among many on the Internet with sources for generating multidimensional fBm (power law)
      Message 2 of 3 , Jun 13 4:45 AM
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        Have a look at Alexis Brandeker's pages (specifically his MSc thesis), among many on the Internet with sources for generating multidimensional fBm (power law) distributions, including multifractals.

        The link is http://www.astro.su.se/~alexis/. You may want to write him for the C code.

        The 1D fBm (and fGn) time series are just generalisations of n-dimensional fractal distributions.

        Annealing is fine as well.

        Cheers

        Syed

        On Monday, June 13, 2005, at 12:17PM, Peter Bossew <Peter.Bossew@...> wrote:

        >Hi list,
        >
        >I need to generate a field f(x,y) with given variogram. More precisely, I
        >have N points (x,y) and I want to assign f(x,y) such that the variable f
        >has a spatial autocorrelation structure according to a given variogram
        >model.
        >
        >My impression is that the way to do it is simulated annealing, as
        >described in chapter 11 of the GSLIB manual. Is that correct ? Any other
        >methods ? Is there any easy-to-use & free software for this purpose ? Any
        >recommended literature ?
        >
        >For time series (1-dim case with regular grid) there is the possibilty of
        >random walk, or more generally Levy flights to produce autocorrelated
        >series, or alternatively, define a Fourier spectrum with given slope of
        >the continous log-log power spectrum and inverse transform. Is there an
        >analoguos technique for the 2- (or n-) dim. case ?
        >
        >A possibly related question: How to produce a field with given (geometric
        >or stochastic) multifractal structure ?
        >
        >
        >Thanks for any hint
        >Peter
        >
        >
        >=================================================================
        >Dr. Peter Bossew
        >Department of Physics and Biophysics, University of Salzburg, Austria
        >
        >peter.bossew@...
        >peter.bossew@...
        >
        >
        >
        >* By using the ai-geostats mailing list you agree to follow its rules
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      • Ruben Roa Ureta
        ... It is easy to simulate a Gaussian random field of given geometry with given spatial correlation function using the package RandomFields, in the free GNU
        Message 3 of 3 , Jun 13 6:07 AM
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          > Hi list,
          >
          > I need to generate a field f(x,y) with given variogram. More precisely, I
          > have N points (x,y) and I want to assign f(x,y) such that the variable f
          > has a spatial autocorrelation structure according to a given variogram
          > model.
          >
          > My impression is that the way to do it is simulated annealing, as
          > described in chapter 11 of the GSLIB manual. Is that correct ? Any other
          > methods ? Is there any easy-to-use & free software for this purpose ? Any
          > recommended literature ?

          It is easy to simulate a Gaussian random field of given geometry with
          given spatial correlation function using the package RandomFields, in the
          free GNU statistical system R. For example, i could make N.sim such random
          fields with a Gaussian variogram and save them all as text files with
          these lines of code:
          --------------
          mcolasim9<-function(N.sim){
          #Grid definition
          x<-seq(1,180,1)
          y<-seq(1,540,1)
          #Variogram model
          param<-c(6.63,2.24,1.82,4.36)
          #Major loop
          for(i in 1:N.sim){
          mcola<-GaussRF(x=x,y=y,param=param,grid=TRUE,model="gauss")
          file1.out<-paste("mcolasim9",i,"txt",sep=".")
          write(t(mcola),file1.out,ncol=ncol(t(mcola)))
          }
          }
          ---------------
          RandomFields will use simulated annealing if convenient but will use
          another method if this other method is best for the case at hand, and will
          select the method automatically. You can also force RandomFields to use a
          given method if you want.
          In R 2.1.0, from
          citation("RandomFields")
          i get
          Martin Schlather, (). RandomFields: Simulation and Analysis of
          Random Fields. R package version 1.2.16.
          http://www.unibw-hamburg.de/WWEB/math/schlath/schlather.html
          Cheers,
          Ruben
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