Geoscience Reference
In-Depth Information
the required software before beginning the exercise. The data
files are available for download from the author's website—
a search engine will reveal the location.
the irst 67 rows because the distance and the
squared difference should be zero.
HINT: There is no easting to calculate the distance
between points, just elevation and northing.
Question 2: Group the values into sets (these sets could
also be considered lags or bins) of, say, 200
pairs. Calculate the average distance, covari-
ance between the pairs of values, correlation
coeficient, and variogram for each bin. Plot
the results.
Question 3: Perform reasonable sensitivity studies with
different number of lags. Comment on the
spatial continuity of the normal scores of
thickness.
6.6.1
Part One: Hand Calculations
The following data set is taken from Practical Geostatistics
2000 (Clark and Harper). You are being asked to review this
data and calculate some variograms. The empty boxes have
no data. Consider the data to be spaced on a square grid of
side a . Consider the horizontal direction (across the page)
to be the X direction. Consider the vertical direction (up the
page) to be the Y direction.
6.6.3
Part Three: Large Set of Data
Consider the normal scores of Cu data in the largedata.
dat data file. In practice, the data would be separated by
rock type, but consider all data for this exercise.
Question 1: Choose an areal and vertical grid size for
variogram map calculation. Note that this
grid size has nothing to do with the ulti-
mate grid size in geostatistical modeling. It
should be about the same as the spacing of
the data. The number of grid cells to specify
for variogram map calculation should be
such that the total distance is about one half
of the domain size.
Calculate the variogram map (variogram
volume in 3-D). Plot the horizontal slice
through the center of the volume (the
example above came from a vein-type gold
deposit with 140 intersections). Try a smaller
cell size and a larger cell size to ensure that
the results are stable with respect to the grid
size. Comment on any areal anisotropy and
the azimuth directions for subsequent direc-
tional variogram calculations. Plot XZ and
YZ sections through the variogram map. The
only sections through a variogram map that
make sense are those through the origin.
Question 1:
Contour the data, show some basic statistics
and comment.
Question 2:
Calculate the semivariogram for distances of
a and 2 a in the X direction, distances of a and
2 a in the Y direction, distances of √2a and
2√2a in the 45° direction and distances of √2a
and 2√2a in the − 45° direction. Tabulate and
plot your results. Comment.
6.6.2
Part Two: Small Set of Data
Question 1: Consider the thickness in the data ile red.
dat . Normal score transform the thick-
ness and perform calculations with the nor-
mal score transform of thickness. Assem-
ble all of the data pairs in Excel (there
should be 67 × 67 = 4,489 pairs, but only
(4489 - 67)/2 = 2211 unique pairings). The
columns of interest are the distance between
the pairs, the values of thickness for both
points and the squared difference between the
values. Sort the data by the distance. Remove
Question 2:
Given the data spacing in the largedata.
dat dataset and your work with variogram
maps in Question 1, discuss the selection
of variogram parameters such as the angle
tolerances, lag spacing, and lag tolerance.
Establish three directional directional vario-
grams. Experiment with different parameters
and establish the stability of your calculated
experimental variograms.
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