Geoscience Reference
In-Depth Information
the uniform distribution above. Draw the
corresponding cdf to the probability density
function (pdf) above.
Question 2:
What is the value of
c
that makes
f(z)
a licit
probability distribution? Write your answer in
terms of
a
and
b
.
Question 3:
What is the expected value (or mean) of the
variable
Z
in terms of
a
,
b
, and
c
? Solve the
integral.
Question 4:
What is the variance of the variable
Z
in
terms
a
,
b
, and
c
? Solve for the expected
value of
Z
2
and solve for the variance using
σ
2
=
E{Z2} − [E{Z}]
2
.
Question 5:
What is the 90 % probability interval? Write
out the function corresponding to the cdf and
solve for the 5th and 95th quantiles.
The objective of this exercise is to become familiar with the
different ways to use declustering to infer a representative
probability distribution. Declustering software and the speci-
fied datasets are required.
Question 2:
Setup and run polygonal declustering to get a
map that looks like the one to the right. Plot a
declustered histogram of the gold grades.
Question 3:
Cell declustering is widely used because it
is robust in 3-D and is less sensitive to edge
effects. Run cell declustering for a range of
cell sizes—explain your choice of param-
eters. Plot the declustered mean versus cell
size, choose a cell size, and justify your
choice. Compare results to those obtained
above.
2.6.5
Part Five: Large Declustering
Consider the 3-D Au/Cu data in
largedata.dat
. This
data will be used in some subsequent exercises. We need de-
clustered distributions for the two variables in all rock types.
Question 1:
Consider cell declustering on a by-rock type
basis and considering all of the data together.
Compare the results and comment on the pre-
ferred approach. Prepare a reasonable set of
plots to support your conclusions including
the declustered mean versus cell size plot(s)
and tables of declustered mean and standard
deviation values.
Question 2:
Assemble the reference distributions for
subsequent modeling (based on your chosen
method).
2.6.4
Part Four: Small Declustering
References
Abramovitz M, Stegun I (1964) Handbook of mathematical functions.
Dover Publications, New York, p 1046
Anderson T (1958) An introduction to multivariate statistical analysis.
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Borradaile GJ (2003) Statistics of earth science data. Springer,
Heidelberg
David M (1977) Geostatistical ore reserve estimation. Elsevier,
Amsterdam
Davis JC (1986) Statistics and data analysis in geology, 2nd edn. Wiley,
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de Moivre A (1738) The doctrine of chances: or, a method for calculat-
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fall, London
Deutsch CV (1989) DECLUS: A FORTRAN 77 program for deter-
mining optimum spatial declustering weights. Comput Geosci
15(3):325-332
Deutsch CV (2002) Geostatistical reservoir modeling. Oxford Univer-
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Deustch CV, Journel AG (1997) GSLIB: geostatistical software library
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Dillon W, Goldstein M (1984) Multivariate analysis: methods and
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Gauss CF (1809) Theoria Motus Corporum Coelestium in sectioni-
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reprinted 1963, Dover, New York
Consider the 2-D data in
red.dat
(see right). The 67 drill
hole intersections have a hole ID, location, thickness, four grade
values, and a rock type. The area is from 20,100 to 20,400 in
the northing direction and -600 to 0 in elevation. The rock type
is simply a flag that specifies below or above -300 m. There
is a difference below that elevation that warrants our attention.
Question 1:
Plot a location map of the thickness and the
gold grade. Plot a histogram of all the gold
grades without any declustering weight.
