Geoscience Reference
In-Depth Information
4.7
Exercises
The objective of this exercise is to construct trend models
for a 2-D example and a larger 3-D example. Some specific
(geo)statistical software may be required. The functionality
may be available in different public domain or commercial
software. Please acquire the required software before begin-
ning the exercise. The data files are available for download
from the author's website—a search engine will reveal the
location.
4.7.1
Part One: Basic Statistics
Consider the 2-D data in
red.dat
. A small exploratory
data analysis is required for the five different variables in
this dataset: thickness, gold grade, silver grade, copper grade
and zinc grade.
Question 1:
Tabulate the key statistics for each variable:
number of data, minimum, maximum, mean
and variance. Plot histograms of the different
variables and comment on the results.
Question 2:
Plot probability plots of the variables on arith-
metic or logarithmic scaling as appropriate.
Comment on outliers, inlection points or any
other interesting features.
Question 3:
Plot scatterplots between all pairs of variables
and create a matrix of correlation coeficients
to summarize how the variables relate to one
another.
Question 4:
Repeat the previous question with normal
scores of all the variables.
Question 2:
There are a number of programs to get the
contour lines in a “point-data” format for
gridding algorithms. Create a gridded model
of your contour map. Ensure that the map is
smooth with no artifacts from your chosen
gridding algorithm.
Question 3:
Calculate residuals as
res = thickness-thick-
nesstrend
. Plot a histogram of the residuals.
Plot a cross plot of the residuals versus the
thicknesstrend
values. Comment on any fea-
tures that would make it awkward to simulate
the thickness residuals independently of the
thickness trend.
4.7.2
Part Two: 2-D Trend Modeling
Consider the 2-D data in
red.dat
. There is a significant
trend with lower thickness at depth (below about − 250 m) to
the North and South.
Question 1:
Create a contour map that represents the
trend. Take care that the contours do not too
closely match short scale variations. The gen-
eral rule is to match large scale variations at
a scale of greater than 2-3 times the drillhole
spacing.
Kriging or inverse distance (or some other
gridding algorithm) can be used as well; how-
ever, hand contouring is robust and gives an
improved understanding of the data. Post the
thickness data with the thicknesses posted
on the map. Hand contour the map. Choose
your own contour intervals; however, you
could take 0.5, 1.0, 2.0, 5.0, or 10.0 if you are
unsure.
4.7.3
Part Three: 3-D Trend Modeling
Consider the 3-D data in
largedata.dat
for 3-D trend
modeling. Build a trend model for the copper grade.
Question 1:
Build a smooth vertical average of the grades
by averaging the grades in vertical slices.
The 1-D averaging program can be used for
