Excerpts from Introductory Chapters in PG2000 and Case
Studies
Practical Geostatistics 2000: Data sets
The sort of applications presented within the book are
mainly geological with some hydrology and environmental case studies. The
potential applications include any form of measurable spatial data and some
which cannot be given a quantitative measure, such as rock type, land use etc.
We have included applications of geostatistical techniques in the following
fields (so far):
- Coal:
a simulated set of data based on a real coal seam in Southern
Africa. Boreholes drilled into the coal seam are measured
for: thickness of coal (metres), energy content or `calorific value' of
coal (Megajoules per tonne); ash content (%) and sulphur content (%).
Three co-ordinates in metres are available for the top of the coal seam
where intersected by the drillhole.
- GASA:
this data set is named for the Geostatistical Association of South Africa
and was used in an illustration of geostatistical techniques at a meeting
in April 1987 in Johannesburg.
The sample data are taken from deep boreholes drilled into a typical Witwatersrand type gold reef. The measurements of
interest are the grade of the gold in grams per tonne of rock (parts per
million) and the thickness of the reef intersection in the borehole
(centimetres). The 27 boreholes lie approximately 1 kilometre apart and
constitute a typical data set for the planning and design of a new Wits
gold mine. The values have been disguised by a factor but are otherwise
unaltered. Co-ordinates are in metres.
- Samples:
this data set is based on a Wits type gold mine some decades into
production. The samples are chipped from the face of the reef in a
working section of the mine (stope). As the face advances, new chip
samples are taken. Values within a stope are traditionally estimated
using the sample values from the face. This data is totally fictitious
except for the locations of the samples, which are taken from a real Wits
type gold mine.
- Copper:
a simulation based on a stockpile of mined material in the former Soviet Union. Boreholes have been drilled into the
dump. The drill core is cut every 5 metres and assayed for copper and
cobalt content in percentage by weight. This is the only three
dimensional set of tutorial data. Co-ordinates are in metres.
- Geevor:
this is sample data from a hydrothermal tin deposit in Cornwall, England.
The mineralisation appears as a continuous vein which is sub-vertical.
Samples of around 1kg are chipped across the vein, which averages about
24 inches wide. Measurements are grade of tin in pounds of black tin
(SnO2) per ton of rock. The thickness of the vein or 'lode' is measured
to the nearest inch. Co-ordinates are in feet along section and elevation
above an arbitrary base level. Clark, I., 1979, "Does
geostatistics work?", Proc. 16th APCOM, Thomas J O'Neil, Ed.,
Society of Mining Engineers of AIME Inc, New York, 213-225.
- Wolfcamp:
measurements of water pressure (potentiometric level) in 85 water wells
in the Texas
panhandle. This data set was part of a study carried out by the Office
for Nuclear Waste Isolation in the mid 1980's on a potential site for a
high level nuclear waste repository. The Wolfcamp aquifer underlies the
planned repository. One aspect of repository planning is to quantify the
risks inherent in a breach of the storage facility. Should radionuclides
leak into the local aquifers, the scope and speed of potential
contamination has to be assessed. The pressure of fluid within the
aquifer was one of several variables used to determine the travel path
and speed of travel for escaped radionuclides.
Reference: Harper, W.V., and
Furr, J.M., 1986. "Geostatistical analysis of potentiometric data in the
Wolfcamp Aquifer of the Palo Duro Basin, Texas", BMI/ONWI-587, April,
Office of Nuclear Waste Isolation, Battelle Memorial institute, Columbus, Ohio.
- Scallops:
Scallop data were collected during a 1990 survey cruise off the east
coast of North America. Scallop counts
were obtained using a dredge. Any scallop smaller than 70 mm was termed a
prerecruit. Total catch is the sum of prerecruits and recruits.
Measurements included in the data file are:
- National Marine Fisheries Service (NMFS) 4 digit strata
designator in which the sample was taken;
- sample number per year ranging from 1 to approximately 450;
- location in terms of latitude and longitude of each sample in the
Atlantic Ocean;
- total number of scallops caught at the sample location;
- number of scallops whose shell length is smaller than 70
millimeters;
- number of scallops whose shell length is 70 millimeters or
larger.
Reference: Ecker, M.D.,
and Heltshe, J.F. 1994. "Geostatistical estimates of Scallop
Abundance", In, Case Studies in Biometry, Lange et al., editors. Wiley, New York
- Dioxin:
A truck transporting dioxin contaminated residues dumped an unknown
quantity of these wastes onto a farm Road in Missouri. In November, 1983, the U.S.
EPA collected samples of the site. In order to reduce the number of
samples required, samples were composited along transects. The transects
run parallel to the highway, and this direction is designated as the
X-direction. The direction perpendicular to the highway is designated as
the Y-direction. Data are TCDD concentration
(tetrachlorodibenzo-p-dioxin) in micro grams per kilogram (mug/kg).
Co-ordinates and transect length are given in feet. Reference:
Zirschy, J.H., and Harris, D.J. 1986. "Geostatistical analysis of
hazardous waste site data". Journal of Environmental Engineering,
112:770-784.
- Organics:
Data are Soil Organic Matter values (in grams per kilogram) derived from
soil samples taken in a research field at the University of Nebraska
West Central Research and Extension Center
near North Platte, Nebraska, USA.
Data were taken as part of experiments on variable-rate fertilizer
technology. Co-ordinates are in metres. Reference. Gotway, C.A.
and Hergert, G.W. (1997). ``Incorporating Spatial Trends and Anisotropy
in Geostatistical Mapping of Soil Properties''. Soil Science of America
Journal, 61:298-309
- Velvetlf:
Subsample of the number of velvetleaf weeds counted in 7 meter² area in a
field in Nebraska.
Data were collected by Gregg Johnson (see 2nd reference), as part of a
research program in weed management at the University of Nebraska.
References: Data set taken
from: Gotway, C.A., and Stroup, W.W. 1997.
"A generalized linear model approach to spatial data analysis and
prediction". Journal of Agricultural, Biological, and Environmental
Statistics, 2:157-178.
Data collected by: Johnsen,
G.A., Mortensen, D.A.,, and Gotway,
C.A. 1996.
"Spatial and temporal analysis of weed seedling populations using
geostatistics". Weed Science, 44:704-710.
Practical
Geostatistics 2000: Case Studies – new data sets
o Sunshine Mine: This data set
was provided by Pierre Mousset-Jones of Mackay School of Mines in Reno, Nevada.
The data is a historical sampling set from development drives in an almost
vertical vein. Silver and gold assay are available, as well as the width of the
vein.
o
o Brooms Barn: This is another
soil science application, data supplied by Dick Webster -- co-author of Webster
& Oliver's excellent "Geostatistics for Environmental
Scientists". Brooms Barn is an agricultural experimental station in East
Anglia (UK) which hosts several fields within its area. The data set includes
Potassium (K mg/l), Phosphorus (P mg/l) and pH levels in the soil. Over 400
samples were collected on a regular grid at 40 metres spacing. The data file
consists of 434 samples and the following fields for each sample: East and North
position on the sampling grid -- this is not in metres but in grid spacing,
i.e. 1 unit of distance equals 40 metres; K -- potassium value in the soil,
mg/l; log10 K -- logarithms to the base 10 of K values; pH -- universal
measurements for acidity (or lack of) in the soil; P -- phosphorus levels in
the soil, mg/l; log10 P -- logarithm to the base 10 for P values.
o
o Brenda Mine: this example
was provided by our esteemed colleague Pierre Mousset-Jones. The major feature
of this data set is that it is a full three dimensional example. Brenda Mine is
a porphyry copper/molybdenum deposit in the southern interior of British
Columbia, approximately 22 kilometers west of Peachland in the Central
Okanagan, and was closed for economic reasons around 1990. In its time Brenda
Mines processed 182 million tonnes of rock. The data file Old_Brenda.dat
contains 1,856 samples. Core sections are between 2 and 56 in length (we assume
this to be feet). The longer cores are generally very low grade The data file supplied comprises the
following information: X_co-ordinate; Y_co-ordinate; Z_co-ordinate; Cu%; Mo%; length_of_core;
From (top of core section sample
relative to collar); To (bottom of sample relative to borehole collar).
Practical Geostatistics 2000
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