Geoscience Reference
In-Depth Information
10.9.3
Part Three: Simulation with 3D Data
Question 1:
Recall the Markov model and the implicit
cross variogram that is used if this model is
adopted for cosimulation.
Question 2:
Consider the Markov assumption with (a)
bitumen as the primary variable, and (b) ines
as the primary variable. Plot the implicit cross
variogram from the Markov model with the
experimental cross variograms. Comment on
any mismatch.
Question 3:
Perform sequential Gaussian simulation for
bitumen and cosimulation of ines collocated
to bitumen. Simulate one realization and
check the crossplot of simulated values. If
you have time, run ten realizations and record
the correlation coeficient from each set of
realizations, and plot a histogram of correla-
tion coeficients. Comment on how this com-
pares to the expected correlation coeficient.
The stepwise conditional transformation is becoming more
commonly used to avoid the requirement for cross vario-
grams.
Question 4:
Explain the stepwise conditional transforma-
tion and perform the transformation twice
with the
oilsands-3D.dat
: (a) ines
conditional to bitumen, and (b) bitumen
conditional to ines. Cross plot the trans-
formed values and conirm that there is no
cross correlation.
Question 5:
For both cases, calculate the cross variogram
between the transformed values in all three
directions. Comment on any non-zero corre-
lations that appear.
Question 6:
Perform sequential Gaussian simulation for
bitumen and ines. Simulate one realization
and check the crossplot of simulated values
(after back transformation). Comment on how
this compares to the original data crossplot.
As above, if you have time run ten realiza-
tions, record the correlation coeficient from
each set of realizations, and plot a histogram
of correlation coeficients. Comment on how
this compares to (1) the expected correlation
coeficient, and (2) the correlation coeficient
distribution from Part One.
Theoretically, simulation requires an incremental effort to
estimation kriging. In practice, however, the generation of
multiple realizations through simulation can amount to a
significant increase to computation and time requirements.
Consider the 3D data from
largedata.dat
. You may
wish to recall your work/results of previous exercises where
you created a model of kriged estimates using parameters
that were refined after cross validation.
Question 1:
Using the same grid deinition and similar
parameters from kriging (as you determined
in Exercise 5), generate 10 realizations of
Au. For four realizations (it should not mat-
ter which you select), plot the middle slice of
the model and compare this to the same slice
from the kriged model. Comment on any dif-
ferences/similarities between (a) the kriged
model and a simulated realization, and (b)
one realization to another realization.
Question 2:
Create a map of local averages (also referred to
as the E-Type estimate). For this E-type model,
plot the middle slice and compare it to the
same slice from the kriged model. Comment
on any similarities/differences that you note.
Question 3:
Calculate probability maps at 10 % and 90 %
probability. What can you say about the
information conveyed in the 10 % probability
map?
Question 4:
Check the proportional effect of the inal
results.
Question 5:
Consider one realization, and scale this real-
ization to an arbitrary volume that consists of
3 × 3 grid points (that is average a total of 9
simulated values together to obtain a block
value).
Question 6:
Recalculate measures of uncertainty (etype,
local variance, and probability maps) as
above.
10.9.4
Part Four: Special Topics in Simulation
The objective of this exercise is experiment with multivariate
simulation approaches. Most geostatisticians do not go to the
trouble to calculate and fit a full model of coregionalization.
It is common to adopt the collocated cokriging shortcut or
to adopt a multivariate transformation such as the stepwise
transformation. Fitting an LMC is a challenge. Moreover,
many software do not permit the full model of coregionaliza-
tion to be used in cosimulation. Cokriging is more straightfor-
ward. The Markov model is used extensively in simulation.
References
Aarts E, Korst J (1989) Simulated annealing and boltzmann machines.
Wiley & Sons, New York
Abzalov M (2006) Localised uniform conditioning: a new approach for
direct modeling of small blocks. Math Geol 38(4):393-411
