Geoscience Reference
In-Depth Information
Question 3:
Create 100 realizations and plot a map of the
probability of each category. This map should
look like a kriged model.
simulation with a search radius of 10 grid
units and 16 previously simulated grid nodes.
Use the reference variogram given above.
Note the CPU time for 100 realizations. Cre-
ate four realizations for checking. Plot maps
of four realizations. Plot the histogram of the
simulated values and compare to the refer-
ence distribution. Calculate and plot the var-
iogram with the input reference variogram
model.
Question 2:
The distinguishing characteristic of sequential
simulation is the Markov screening assump-
tion; however, it can cause poor variogram
reproduction. Create four realizations with
4, 8, 16, and 32 previously simulated grid
nodes and the multiple grid search turned off.
Add coordinates and calculate the omnidi-
rectional variogram. Comment on variogram
reproduction. Run the “4” and “8” cases with
a multiple grid and comment on variogram
reproduction.
Simulation is at the scale of the data, that is, composite data
of some specified length. The grid specification in simulation
programs is not a
block size
, it is the spacing of point scale
simulated values. For this reason, we simulate at least 10 point
values within the smallest selective mining unit (SMU) size
ultimately desired. Geostatistical simulation involves many
locations simultaneously. This involved excessive CPU time
and storage requirements in the early days of simulation. Fast
unconditional simulation techniques were devised and krig-
ing was used as a post processor for conditioning.
Question 3:
Give the equation for conditioning uncon-
ditional realizations to local data. Clearly
explain how this could be implemented in
practice.
Question 4:
Use turning bands to simulate 4 unconditional
realizations of a 50 by 50 by
5
(because the
turning bands algorithm is dimension depen-
dent—the tb3d program is for 3-D only)
domain (spacing set to 1 in all directions)
using the reference variogram given above.
Plot the central 2-D slice of the realizations.
Check histogram and variogram reproduction
of the realizations.
Question 5:
Use LU simulation to simulate 4 uncondi-
tional realizations of a 50 by 50 by
1
domain
(spacing set to 1 in all directions) using the
reference variogram given above. Plot the
realizations. Check histogram and variogram
reproduction.
Question 6:
Condition these realizations to the four
Gaussian data values given above.
10.9.2
Part Two: Sequential Gaussian
Simulation
Sequential simulation is common because simulation and
conditioning to local data is accomplished in one step. His-
torically, conditional simulation was divided into two steps:
unconditional simulation and kriging for conditioning. Ma-
trix methods and moving average methods were used for un-
conditional simulation, but they were really only applicable
for small grids. Turning bands was (and still is) used for un-
conditional simulation on larger 3-D grids.
A small 2-D example will be considered for testing some
alternative Gaussian simulation methods.
Consider a grid of 50 by 50 grid cells each 1 unit square.
There are four regularly spaced data (see the picture below).
Two data are at the mean, one is a high value and one is low.
The variogram is omnidirectional spherical with a range of
10 grid units.
Consider unconditional and conditional simulation of a 50
by 50 domain. Such a small grid permits fast calculations
and testing of methods such as LU simulation that requires
a small grid size.
Sequential Gaussian simulation (SGS) is popular because
of its simplicity and flexibility. SGS draws realizations from
the multivariate Gaussian distribution by recursive applica-
tion of Bayes Law. This part focuses on the application and
limitations of SGS.
Question 1:
Setup a 2-D Gaussian simulation with the
conditioning data described above. Run the
