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Re: GEOSTATS: Random vectors

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  • Colin Daly
    My original message to the site was as follows ... It s been so long since I sent this that I guess some of you will have retired and your children will be
    Message 1 of 2 , Feb 15, 1999
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      My original message to the site was as follows

      > Hi,
      >
      > I hope this doesn't constitute what Gregoire calls a very stupid
      > problem!
      >
      > 1) Does anyone know a free/cheap plotting tool for vector fields. (At
      > each point x of a 3d (or 2d) array, I have a vector v(x). Thus my plot
      > will be lots of little arrow)
      >
      > 2) Has anyone done any work or heard of any work on Random Tensor
      > fields. I've made a start and got somewhere (for what it's worth) but I
      > don't want to reinvent the wheel.
      >
      > Colin
      >

      It's been so long since I sent this that I guess some of you will have
      retired and your children will be reading my final response. So for those
      who replied - sorry it took me so long to get back!

      Anyhow - I had a good number of replies and some people wanted to get
      replies forwarded so here they are

      1) Pat Lapcevic has a homemade (fortran) program which I'm going to try
      and get hold of. He also suggests GRIDBUILDER - a finite element grid
      builder from Rob McLaren (email mclaren@...). He doesn't
      know the cost and I've not yet got a reply from Rob.

      2) Med Bennett suggests some IDL commercial software (@:$1500). Check it at
      http://www.rsinc.com

      Another commercial suggestion was from C TECH Development
      http://www.ctech.com

      3) Denis Marcotte informs us that Matlab has Quiver and Quiver3 for 2 and 3d
      respectively.

      ... while GillesG@... suggests a SCI-LAB solution. Sci-Lab being a
      Matlab type solution. Information at
      http://www-rocq.inria.fr/scilab/scilab.html
      Download from ftp://ftp.inria.fr/INRIA/Projects/Meta2/Scilab

      4) Denis Allard and Katherine Campbell tell us that (at least) in 2d there
      is an Splus solution to plotting vectors and Katherine provides us with some
      code

      plot(lrange$x,lrange$y,type="n",axes=F,xlab="",ylab="")
      draw.vectors(slope[1:2,,])


      draw.vectors <- function(z) {
      # Assume z is 2 x n x m
      n <- dim(z)[2]
      m <- dim(z)[3]
      zmax <- max(sqrt(z[1,,]^2+z[2,,]^2))
      tz <- 0.5*z/zmax
      for (i in 1:n) {
      for (j in 1:m) {
      arrows(i-tz[1,i,j],j-tz[1,i,j],
      i+tz[1,i,j],j+tz[2,i,j],
      size=.02,open=T,rel=F)
      }
      }
      }

      Thanks for that Katherine

      5) alistair@... has seen some stuff in SAS which he believes to be
      usefull.

      6) Dan Cornford suggests the NEUROSAT page for some work on wind field
      models for random vector fields and asks when or where we might meet random
      tensor fields.

      Well a quick reply is to note that Permeability, Stress, Strain etc. etc.
      are 2nd order tensors - their covariances need to expressed fully with a 4th
      order tensor. They tend to occur quite often when modelling Petroleum
      reservoirs - although in practice there is usually no need to consider the
      general case and the tensor is treated as diagonal.

      As we know, the class of isotropic covariance functions in 3d is a subclass
      of the 1d covariance functions (eg the 1d spherical (or triangular model) is
      not +ve definite in 3d). From here, you can ask yourself what are the
      conditions for isotropy of a random vector field (eg. Yaglom 1986) - that
      is when the covariance is independent of the choice of orthogonal co-ord
      system. It turns out that this imposes some restrictions on the form of
      covariance function (Yaglom). I was just looking at how this generalises to
      tensors. (The real purpose for me was to check the functional form of a
      covariance tensor that was provided by a third party - as it's behavior
      seemed a bit odd)

      Anyhow - many thanks to all who replied. I'll check things out in a bit
      more detail and if anything blows me away I'll be sure to pass it on.

      Colin




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