Geoscience Reference
In-Depth Information
Fig. 10.3
Schematic of a point
being drawn using Monte Carlo
Simulation
C
G
H
C
G
C
0.78
Random Number
1.55
Simulated Value
variogram obtained from the simulated values is similar
to the variogram of the original values.
14. Verify that the model presents a reasonable spatial dis-
tribution and that no other errors or omissions have
been made in simulating each stationary domain.
The price to pay for using SGS is that the values will show
less connectivity than the original data. This is due to the
maximum entropy property of the Gaussian distribution. The
significance of this issue is generally small, depending on
the overall spatial distribution and the definition of station-
ary domains used. Conditional simulations are much more
sensitive to departures from strict stationarity compared to
estimation methods, and so domain definition is key to ob-
taining representative simulation models.
A Monte Carlo simulation (MCS) technique is used to
draw a simulated value from the estimated conditional dis-
tribution at each node, see Step 7 above. A random number
between 0 and 1 is generated, and the simulated value is ob-
tained by reading the associated quantile from the estimated
cumulative distribution. Figure
10.3
illustrates this with an
example for a Cu grade distribution.
70 or 80 %. In these types of distributions, a few high values
contain most of the metal in the drill hole database. Random
despiking is fast and usually does not create artifacts in the
later back-transformed distribution. A general rule-of-thumb
is that, for distributions with more than 50 % percent of tied
values, the local-average despiking method (Verly
1984
)
may be safer and worth the extra effort it requires. In areas
where there may be too few data, a global transformation
table can be used.
The search path needs to be random to avoid artifacts in
the simulated model. It is also important to ensure that each
cell is visited once and only once. Nodes that already have a
value are skipped, and the original preserved in the simula-
tion.
The data can be assigned to grid nodes, which signifi-
cantly speeds up the simulation. This is because searching
for previously simulated nodes and original data is accom-
plished in one step and based on a regular grid. However,
there is a price to pay, since assigning the closest of several
possible data to a node will lose some information. This loss
of information is dependent on the data density and the node
spacing. The node spacing in the vertical direction should be
the same as the original composite length, which ensures that
most of the drill hole data would be used, the possible excep-
tion being inclined or sub-horizontal drill holes, as well as
twinned, or closely drilled holes.
The number of data to be used in the simulation (original
composites and previously simulated nodes) can be a conse-
quential decision. More data gives a more accurate estimate
of the conditional mean and variance and results in better
reproduction of the variogram model, but will take longer to
run. Also, fewer data can provide a more robust model with
respect to departures from strict stationarity, better reproduc-
ing the local variability.
Simple kriging should be used to estimate the Gaussian
mean and variance. In certain circumstances, practitioners
use ordinary kriging instead, generally with the intention of
avoiding the consequences of departures from stationarity.
10.2.1.1 Practical Considerations in the
Implementation of SGS
The transformation of the data to a standard normal distribu-
tion using the normal scores (NS) transform is a graphical
one-to-one (rank preserving) transform and was discussed
in Chap. 2.
Declustering weights are recommended for performing
the transformation. Another potentially significant issue is
despiking. Despiking is the term used to describe the process
of removing the ties that the original variable may present,
and may be significant since the NS transform does not
allow for ties. The method chosen for resolving the ties can
be consequential, particularly for distributions that have a
very significant percentage of ties. This is common, for ex-
ample, in data from epithermal Au deposits, where usually
most sampled values are below detection limit, perhaps up to
