i.-i. Royer and A. Shtuka : Stochastic Imaging of Environmental Data
111
define a random grid path;
visit sequentially each grid point a
if A(a) is empty simulate a new Z using the interval [0;1]; else
- generate a list of values Zy(a) = F-l(a; V) where V is a regular grid
defined in [0;1];
- compute the local variogram y* (h) for each Zy( a) using the
neighbourhood A(a);
- extract a sublist of values Zw w E V for which Iy*(h) - y(h)1 < 0 ;
- simulate a new Zy by choosing at random in sublist Zw;
•
go to the next point in the random grid path;
5.4 Discussion
The accounting for the variogram constraint using this algorithm is relatively fast
in terms of computing time compared to annealing methods, allowing interactive
simulation as large as 2500 points (less than 10 seconds on a HP90001710,
including visualization).
The variogram computed on Zs(x) is quite the same as the imposed variogram (see
Fig. 6). Because the variogram constraint restricts the interval on which the Monte
Carlo method is performed, the final cdf computed on Zs may differ slightly from
the imposed cdf F(z).
Practically, the order of magnitude of the differences IF(z) - F* (z)1 is small
compared to the experimental errors (see Fig. 5). However, the above algorithm is
sensitive to the extrema zmin and zmax used to build the indicator functions.
6
CASE STUDY
6.1 Data Set
The DSI simulation was tested on a data set from ESA published in the "GSLIB:
Geostatistical Software Library and Users' Guide" by Deutsch and 10urnel (1992)
using the files true.dat and cluster.dat.
The data are intended to represent a hazardous waste site. They were created using
simulated annealing on a 50 x 50 regular grid. The variogram is isotropic and
comprises two nested structures with an exponential and nugget components.
A set of 140 data values was selected at random as sample point values (Fig. 1).
The a priori cdf, experimental variogram was then computed on the sample point
values.
111
define a random grid path;
visit sequentially each grid point a
if A(a) is empty simulate a new Z using the interval [0;1]; else
- generate a list of values Zy(a) = F-l(a; V) where V is a regular grid
defined in [0;1];
- compute the local variogram y* (h) for each Zy( a) using the
neighbourhood A(a);
- extract a sublist of values Zw w E V for which Iy*(h) - y(h)1 < 0 ;
- simulate a new Zy by choosing at random in sublist Zw;
•
go to the next point in the random grid path;
5.4 Discussion
The accounting for the variogram constraint using this algorithm is relatively fast
in terms of computing time compared to annealing methods, allowing interactive
simulation as large as 2500 points (less than 10 seconds on a HP90001710,
including visualization).
The variogram computed on Zs(x) is quite the same as the imposed variogram (see
Fig. 6). Because the variogram constraint restricts the interval on which the Monte
Carlo method is performed, the final cdf computed on Zs may differ slightly from
the imposed cdf F(z).
Practically, the order of magnitude of the differences IF(z) - F* (z)1 is small
compared to the experimental errors (see Fig. 5). However, the above algorithm is
sensitive to the extrema zmin and zmax used to build the indicator functions.
6
CASE STUDY
6.1 Data Set
The DSI simulation was tested on a data set from ESA published in the "GSLIB:
Geostatistical Software Library and Users' Guide" by Deutsch and 10urnel (1992)
using the files true.dat and cluster.dat.
The data are intended to represent a hazardous waste site. They were created using
simulated annealing on a 50 x 50 regular grid. The variogram is isotropic and
comprises two nested structures with an exponential and nugget components.
A set of 140 data values was selected at random as sample point values (Fig. 1).
The a priori cdf, experimental variogram was then computed on the sample point
values.