## [ai-geostats] Simulating an autocorrelated field

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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
Message 1 of 3 , Jun 13, 2005
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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@...
• 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, 2005
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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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>
>* To unsubscribe to ai-geostats, send the following in the subject or in the body (plain text format) of an email message to sympa@...
>
>Signoff ai-geostats
>
• ... 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, 2005
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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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