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  • Pierre Goovaerts
    Nov 30, 2000
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      One of the primary objectives of stochastic simulation
      is to reproduce patterns of spatial variability and
      in sequential simulation it is ensured by using
      previously simulated values to derive probability
      distributions to be sampled randomly. As a consequence, you
      should make sure that the number of selected points
      (data and simulated values) and the size of the search window
      is large enough to allow one to incorporate information
      up to the range of spatial correlation.
      Of course, this may become impractical as the number of simulated
      values increases, hence the concept of multiple-grid simulation
      implemented in the new version of Gslib and that I strongly
      recommend to use.

      Here is the description that I give in my book, page 379.

      "The use of a search neighborhood limits reproduction of the input
      covariance model to the radius of that neighborhood. Another obstacle
      to reproduction of long-range structures is the screening of distant
      data by too many data closer to the location being simulated. The
      multiple-grid concept (G\'omez-Hern\'andez, 1991; Tran, 1994) allows
      one to reproduce long-range correlation structures without having to
      consider large search neighborhoods with too many conditioning data.
      For example, a two-step simulation of a square grid 500X500
      could proceed as follows:

      1. The attribute values are first simulated on a coarse grid (e.g.,
      25x25) using a large search neighborhood so as to reproduce
      long-range correlation structures. Because the grid is coarse, each
      neighborhood contains few data, which reduces the screening effect.

      2. Once the coarse grid has been completed, the simulation continues
      on the finer grid 500X500 using a smaller search neighborhood
      so as to reproduce short-range correlation structures. The
      previously simulated values on the coarse grid are
      used as data for the simulation on the fine grid.

      A random path is followed within each grid.

      The procedure can be generalized to any number of intermediate grids;
      this number depends on the number of structures with different ranges
      final grid spacing.


      ________ ________
      | \ / | Pierre Goovaerts
      |_ \ / _| Assistant professor
      __|________\/________|__ Dept of Civil & Environmental Engineering
      | | The University of Michigan
      | M I C H I G A N | EWRE Building, Room 117
      |________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
      _| |_\ /_| |_
      | |\ /| | E-mail: goovaert@...
      |________| \/ |________| Phone: (734) 936-0141
      Fax: (734) 763-2275


      On Tue, 21 Nov 2000, WARR Benjamin wrote:

      > Hi All,
      > When performing SIS we have a choice of the max. no. of data nodes and
      > simulated nodes to use . Is there a general rule defining the number of
      > simulated nodes ? A ratio between the two, beyond which we are really
      > risking artefact creation ? Or any work which highlights the effect of
      > using either a dense set of simulated nodes as opposed to a sparse set. I
      > have thought about the issue and other than an effect on the time taken to
      > simulate the full domain I can't see why a choice of the number of simulated
      > nodes will alter the realisations to a great extent. Any conficting
      > thoughts.
      > Benjamin Warr
      > Research Associate to Prof. Ayres,
      > PhD Student of Geostatistics for Natural Resource Evaluation at Reading
      > University, Soil Science.
      > Postal Address:
      > Centre for the Management of Environmental Resources (CMER)
      > INSEAD
      > Boulevard de Constance,
      > 77305 Fontainebleau Cedex,
      > France
      > Tel: 33 (0)1 60 72 40 00 ext. 4926
      > Fax: 33 (0)1 60 74 55 64
      > e-mail: benjamin.warr@...

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