Transcript Slide 1

HISTORY OF GEOSTATISTICS PAST, PRESENT AND FUTURE
Donald E. Myers
University of Arizona
http://www.u.arizona.edu/~donaldm
International Association of Mathematical Geology
2008 Distinguished Lecturer
OUTLINE
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IAMG
PROBLEMS/OBJECTIVES
WHAT WAS USED BEFORE
MATHERON, GANDIN and MATERN
COMPUTING
OTHER PEOPLE
WHERE IS IT GOING?
CONFERENCES
SOME BOOKS
IAMG
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www.iamg.org
Formed in Prague in 1968
Earth science in broad sense
Celebrated 25th anniversary in Prague
Publishes three journals
Annual conferences
Five previous Distinguished Lecturers
PROBLEMS/OBJECTIVES -I
• Given data for some characteristic at
multiple locations in space,
predict/estimate value at non-data location
– Local or global?
• Single value or probability distribution?
• Predict/estimate average over an area or
volume
• Provide some measure of uncertainty or
reliability
PROBLEMS/OBJECTIVES -II
• Applications in
– Mining
– Hydrology
– Petroleum
• Yarus-Chambers Armchair overview.pdf
• Petroleum geostatistics.pdf
• Petroleum geostatistics Part 2.pdf
– Soil Science
– Ecology
– Epidemiology
PROBLEMS/OBECTIVES -III
– Environmental monitoring and assessment
– Agronomy
– Atmospheric Sciences
– Any discipline with spatial data
• Complications with spatial data
– Often expensive to collect and/or difficult
– Point data vs non-point data
– Hard data vs soft data
GEOSTATISTICS -I
• Data, non-random sample from one
realization of a random function
– Model based, not design based
• Values at two close locations are more
similar than for two locations far apart?
• Spatial correlation
– Variogram, covariance function
– Must be estimated/fitted
– Functions of distance & direction
– Variogram interpretation and modeling.pdf
GEODSTATISTICS -II
• Incorporates information about proximity of
each data location to every other data
location
• Incorporates information about proximity of
each data location to estimation point
• Estimator is a weighted linear combination
of data values
• Weights do not directly depend on the
data values
WHAT WAS USED BEFORE -I?
• Voronoi diagrams, Thiessen polygons,
(used by Descartes in 1600’s but not
named until much later)
– Nearest neighbor, Polygonal method
• Strictly geometric
• Inverse Distance Weighting
• Weighted linear combination, weights
inversely proportional to distance from
data location to estimation point
WHAT WAS USED BEFORE-II?
• Advantages/disadvantages Nearest Neighbor
– Does not incorporate characteristics of data
– Very dependent on the pattern of data locations
• Advantages/disadvantages Inverse Distance
Weighting
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Does not incorporate characteristics of data
Does not incorporate pattern of data locations
Very dependent on pattern of data locations
Petroleum geostatistics vs deterministic methods.pdf
WHAT WAS USED BEFORE-III?
• Spline (1-D drafting tool)
• None of the above directly address
– Estimating spatial averages
– Provide measures of uncertainty
• None of the above generate alternative
scenarios, i.e., simulation
– Useful in planning
– Possible alternative to estimation/prediction
Bertil Matern
• 1917– Student of Harald Cramer
– Professor of Mathematical Statistics in
Forestry
• Spatial Variation- 1960 (Swedish)
– Applications to forestry
– Importance of spatial dependence and
variation noted as early as 1947
– Published in English in 1986
Lev Gandin
• 1921-1927
– Born in Lenningrad
– Musician, Chess player or Mathematician?
– USSR Main Geophysical Lab and Lenningrad
Hydrometeorological Institute 1943-1981
– Objective Analysis of Meteorological Fields
(1963)- (Russian)
• Translated into English 1965
– Lost position in 1981
– Nat. Centers for Envir. Prediction1987
• Lev Gandin, 1921-1997.pdf
Georges Matheron - I
• 1930-2000
– Matheron obituary.pdf
• Traité de Géostatistique appliquée, tome 1
(1962), tome 2 (1963). Paris: Editions
Technip.
• Centre de Geostatistiques et Morphologie
Mathematiques, Ecole des Mines de Paris
(Fontainebleau)
Georges Matheron -II
• The theory of regionalized variables and
its applications. Paris School of Mines
publication, (1971)
• The intrinsic random functions and their
applications. Adv Appl Prob 5: (1973)43968.
• Random Sets and Integral Geometry. J.
Wiley. (1975)
Georges Matheron - III
• Also did fundamental work on flows in
porous media
• Assembled group of students and
researchers
• Strong ties with mining industry, petroleum
industry
• Hydrology research group at
Fontainebleau
Georges Matheron -IV
• Was acquainted with Matern and Gandin
and their work
• Influenced by work of D. Krige (South
Africa)
• Mathematical Morphology group became
separate
The Big Names
• Gandin was and is very well known in
climatology, perhaps less so outside of
that field
• Matern was and is well known in forestry
and later perhaps in statistics
• Matheron was not as well known in
statistics originally but ideas were spread
by his students and contacts in industry
COMPUTING -I
• The works of Matheron, Gandin and
Matern all had their origins in earlier work
by Kolmogorov, Wiener, etc but!
– To actually use the ideas and results required
extensive computing, the timing was right
– Mainframe computers- late 1940’s, early
1950’s (Illiac, prototype for computer at
Aberdeen Proving Grounds, 1 K random
access memory)
– http://www.cs.uiuc.edu/about/history.php
COMPUTING -II
• VAX 11/780 1978(CERN)
– www.webmythology.com/VAXhistory.htm
• IBM PC
1981
• inventors.about.com/library/weekly/aa031599.htm
– 4.77 mhz, 16 k memory, no hard disk
• www-03.ibm.com/ibm/history/exhibits/pc/pc_1.html
• www.oldcomputers.com/museum/computer.asp?c=274
COMPUTING -III
• Geostatistics Software
– 1970’s BLUEPACK (Fontainebleau)
– 1988 GEOEAS (EPA) for DOS on PC
• Geostatistics tutorial using GeoEAS.pdf
– 1992 GSLIB Fortran codes
– 1996 VARIOWIN (Windows version of Vario
and PreVar)
– 1990’s ISATIS (workstation software,
Fontainebleau, GeoVariances)
COMPUTING -IV
– geostatistics add-on for ArcGIS
– Spatial Analyst in S-Plus
– gstat, geoR packages in R
• Overview gstat and geoR.pdf
• gstat tutorial.pdf
– Proc in SAS
– SGems
• www.ai-geostats.org/index.php?id=107
– More complete list including various
commercial software packages
OTHER PEOPLE -I
• Michel David
– Obituary -Mathematical Geology 37 (2005)
449-450
• Michel David obituary.pdf
– Started program at the Ecole PolytechniqueMontreal, brought over from France
– Geostatistical Ore Reserve Estimation (1977)
– Short courses and consulting
OTHER PEOPLE -II
• Andre Journel
– Brought over from Fontainebleau to start
program at Stanford (supported by Fluor)
– Mining Geostatistics (1978) with Ch.
Huibregts
– GSLIB (1992) with C.. Deutsch
– Short courses, consulting
– Links to industry
OTHER PEOPLE -III
• John Davis
– Formerly head of the Mathematical Geology
group at the Kansas Geological Survey
– Statistics and Data Analysis in Geology
(1973)
– One of founders of IAMG
– First IAMG Distinguished Lecturer
Daniel Merriam
– One of the founders of IAMG
– Hosted Matheron on several occasions
OTHER PEOPLE -IV
• Krige, Danie G. 1919– "A statistical approach to some basic mine valuation problems
on the Witwatersrand". J. of the Chem., Metal. and Mining Soc.
of South Africa 52 (1951): 119-139.
– Tribute to Krige.pdf
• Richard Webster
– Rothamstead Research Center (UK)
– Four seminal articles about applications in soil science, 19791980
– Geostatistics for Environmental Scientists (2001) with M. Oliver
• Noel Cressie
– Statistics for Spatial Data (1993)
• Brian Ripley
– Spatial Statistics
• Contributor to R
WHERE IS IT GOING?
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Multivariate methods
Simulation
Space-time modeling
Multi-point modeling
New(er) applications
– Ecology
– Image Analysis
• Connections with other methods
CONFERENCES -1
• Initially geostatistics had many of its own
conferences (with proceedings)
– NATO ASI, Rome 1975
– NATO ASI, Lake Tahoe 1983
– NATO ASI, Il Ciocco (Italy) 1987
– Avignon, Fr. 1988
– Troia , Portugal 1992
– Wollongong, Australia 1996
CONFERENCES -II
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South Africa 2000
Banff, Canada 2004
Santiago, Chile 2008
Geostatistics for the Next Century Montreal 1993
• Geostatistics and the Environment conferences
(with proceedings)
– GEOENV I
– GEOENV II
1996
Valencia 1998
CONFERENCES -III
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GEOENV III Avignon 1999
GEOENV IV Barcelona 2002
GEOENV V 2005
GEOENV VI 2006 Rhodes, Greece
GEOENV VII 2008 Southhampton, UK
SOME OTHER BOOKS -I
– An Intro. To Applied Geostatistics,
E. Issaks
and M. Srivastav
– Geostatistics: Modeling Spatial Uncertainty, JeanPaul Chilès and Pierre Delfiner
– Geostatistics for Natural Resources Evaluation, P.
Goovaerts
– Multivariate Geostatistics, H. Wackernagel
– Geostatistics and Petroleum Geology, M Hohn
– Model Based Geostatistics, Peter J. Diggle and Paulo
Justiniano Ribeiro
SOME OTHERBOOKS -II
– Stochastic Modeling and Geostatistics I:
Principles, Methods and Case Studies, J.
Yarus and R. Chambers, AAPG
– Stochastic Modeling and Geostatistics II:
Principles, Methods and Case Studies, T.C.
Coburn, AAPG
– Interpolation of Spatial Data: Some theory for
kriging, M. Stein
IAMG
http://www.iamg.org