HISTORY OF GEOSTATISTICS - PAST, PRESENT AND FUTURE

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HISTORY OF GEOSTATISTICS - PAST, PRESENT AND
FUTURE

• Donald E. Myers
• University of Arizona
• http//www.u.arizona.edu/donaldm

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OUTLINE

• IAMG
• PROBLEMS/OBJECTIVES
• WHAT WAS USED BEFORE
• MATHERON, GANDIN and MATERN
• COMPUTING
• OTHER PEOPLE
• WHERE IS IT GOING?
• CONFERENCES
• SOME BOOKS

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IAMG

• 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

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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

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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

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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

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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

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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

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WHAT WAS USED BEFORE -I?

• Voronoi diagrams, Thiessen polygons, (used by
  Descartes in 1600s 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

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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
• 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

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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

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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

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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

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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)

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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)439-68.
• Random Sets and Integral Geometry. J. Wiley.
  (1975)

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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

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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

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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

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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 1940s, early 1950s
  (Illiac, prototype for computer at Aberdeen
  Proving Grounds, 1 K random access memory)
• http//www.cs.uiuc.edu/about/history.php

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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.old-computers.com/museum/computer.asp?c274

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COMPUTING -III

• Geostatistics Software
• 1970s 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)
• 1990s ISATIS (workstation software,
  Fontainebleau, GeoVariances)

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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?id107
• More complete list including various commercial
  software packages

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OTHER PEOPLE -I

• Michel David
• Obituary -Mathematical Geology 37 (2005) 449-450
• Michel David obituary.pdf
• Started program at the Ecole Polytechnique-Montrea
  l, brought over from France
• Geostatistical Ore Reserve Estimation (1977)
• Short courses and consulting

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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

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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

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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, 1979-1980
• Geostatistics for Environmental Scientists (2001)
  with M. Oliver
• Noel Cressie
• Statistics for Spatial Data (1993)
• Brian Ripley
• Spatial Statistics
• Contributor to R

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WHERE IS IT GOING?

• Multivariate methods
• Simulation
• Space-time modeling
• Multi-point modeling
• New(er) applications
• Ecology
• Image Analysis
• Connections with other methods

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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

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CONFERENCES -II

• 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 1996
• GEOENV II Valencia 1998

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CONFERENCES -III

• GEOENV III Avignon 1999
• GEOENV IV Barcelona 2002
• GEOENV V 2005
• GEOENV VI 2006 Rhodes, Greece
• GEOENV VII 2008 Southhampton, UK

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SOME OTHER BOOKS -I

• An Intro. To Applied Geostatistics, E.
  Issaks and M. Srivastav
• Geostatistics Modeling Spatial Uncertainty,
  Jean-Paul 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

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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

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IAMG
http//www.iamg.org