4Re: AI-GEOSTATS: AI-GEOSTATS
- Nov 30, 2000Hi,
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
> 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)
> Boulevard de Constance,
> 77305 Fontainebleau Cedex,
> 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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