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Advanced Geostatistics in the Mining Industry
NATO ADVANCED STUDY INSTITUTES SERIES
Proceedings of the Advanced Study Institute Programme, which aims Of the dissemination of advanced knowledge and
the formation 0/ contacts among scientists from different countries
The series is published by an international board of publishers in conjunction with NATO Scientific Affairs Division
A Life Sciences B Physics
C Mathematical and
Physical Sciences
D Behavioral and Social Sciences
E Applied Sciences
clAu ~
Plenum Publishing Corporation London and New York
D. Reidel Publishing Company Dordrecht and Boston
Sijthoff International Publishing Company Leiden
Noordhoff International Publishing Leiden
Series C - Mathematical and Physical Sciences
Volume 24 - Advanced Geostalist;cs in the Mining Industry
Advanced Geostatistics in the Mining Industry Proceedings oj the NATO Advanced Study Institute
held at the !stitulo di Geologia Applicata
oj the University oj Rome. Italy . 13-25 October 1975
edited by
M . GUARAS C IO 1.\"lil li lo di GeO/OKill A p.pliclI lII. Uni\"l'rsillllli ROllla, ROil/I', I lu/y
M . DAV ID Dept. ,II' Gellie M illeral, Eco/,> P"lI'lecirniqlll', M Olllreal, Canada
C. H U IJB REGTS Celllr" r/I' MorplwfoJ:ie M(lIhhl!Oliqlll'. ENSMP. FOlllai,reblellll, Frnnce
D. Reidel Publishing Company
Dordrecht- Holland BOSlon-U.S.A.
Published in cooperation w ith NATO Scientifi c Affairs Division
Library of Congre\\ Cataloging in Publication Data
Nato Advanced Study Institute, Rome. 1975, Advaneed gco,talistics in Ihe mining industry.
(NATO advanced study institutes series: Series C. Mathcmatical and physical seienees: v. 24)
Bibliography' p. L M ines a nd m incral resources-Statistieal methods-Congresses.
Economie-StatistiGII methods-Congresses. I. Guaraseio. M., 1944-Michel IIL Huijbrcgts. C IV. Title. V. Series. TN153.N33 1975 622',On 76_13915 ISBN-13: 978-94-010-1472-4 e-ISBN-13: 978-94-010-1470-0 001: 10.1007/978-94-010-1470-0
Published by D. Reidel Publishing Company P.D. Box 17. Dordrecht. Holland
Sold and distributed in the U.S.A .. Caoada, and Mexico by 0, Reidel Publi~hing Company. Inc. Lineoln Building. 160 Old Derby Street. Hingharn. Mass. 02043. U.S.A.
All Rights Reservcd
Softcover reprint of the hardcover I st edition 1976
2. Geology, 11. David.
No part of the material protected by this copyright notiee may be reproduced or ulilized in any form or by any means, electronic or meehanical, incJuding photocopying, recording or by any informational storage and retrieval system, without written pcrmission from thc copyright owner
TABLE OF CONTENTS
FOREWORD
ACKNOWLEDGEMENTS
LIST OF PARTICIPANTS
PART I - BASIC CONCEPTS
LES CONCEPTS DE BASE ET L'EVOLUTION DE LA GEOSTATISTIQUE MINI ERE G. Matheron
LE CHOIX DES MODELES EN GEOSTATISTIQUE G. Matheron
PART II - KRIGING
THE PRACTICE OF KRIGING M. David
LINEAR ESTIMATION OF NON STATIONARY SPATIAL PHENOMENA P. Delfiner
HOW TO ADAPT KRIGING TO NON-CLASSICAL PROBLEMS: THREE CASE STUDIES J . P. Chiles
OPTIMAL INTERPOLATION USING TRANSITIVE METHODS
IX
X
XI
3
11
31
49
69
M. Alfaro and F. Miguez 91
APPLICATION OF TWO METHODS FOR THE INTERPRETATION OF THE UNDERLY ING VARIOGRAM R. Sabourin 101
PART III - ORE- WASTE DISCRIMINATION
SELECTION AND GRADE-TONNAGE RELATIONSHIPS C. Huijbregts 113
VI TABLE OF CONTENTI
SELECTING MINEABLE BLOCKS: EXPERIMENTAL RESULTS OBSERVED ON A SIMULATED OREBODY A. Marechal 137
PLANNING FROM ESTIMATES: SENSITIVITY OF MINE PRODUCTION SCHEDULES TO ESTIMATION METHODS P. A. Do~d and M. David 163
CONVEX ANALYSIS FOR MINE SCHEDULING A. G. Journel ISS
ORE GRADE DISTRIBUTIONS AND CONDITIONAL SIMULATIONS - TWO GEOSTATISTICAL APPROACHES A. G. Journel
THE PROBLEM OF ORE VERSUS WASTE DISCRIMINATION FOR INDIVIDUAL BLOCKS: THE LOGNORMAL MODEL P. Switzer and H. M. Parker
PART IV - THEORETICAL NEW DEVELOPMENTS
A SIMPLE SUBSTITUTE FOR CONDITIONAL EXPECTATION: THE DISJUNCTIVE KRIGING G. Matheron
FORECASTING BLOCK GRADE DISTRIBUTIONS: THE TRANSFER FUNCTIONS G. Matheron
THE PRACTICE OF TRANSFER FUNCTIONS: NUMERICAL METHODS AND THEIR APPLICATION A. Marechal
PART V - INDUSTRIAL APPLICATIONS
A REVIEW OF THE DEVELOPMENT OF GEOSTATISTICS IN SOUTH AFRICA
195
203
221
237
253
D. G. Krige 279
THE POTENTIAL OF GEOSTATISTICS IN THE DEVELOPMENT OF MINING R. w. Rutledge
APPLICATION DE LA GEOSTATISTIQUE AU NIVEAU D'UN GROUPE MINIER J . Damay
LA GEOSTATISTIQUE AU B.R.G.M. B. Lallement
GEOSTATISTICS IN PETROLEUM INDUSTRY A. Haas and C. Jousselin
295
31 ;
32J
TABLE OF CONTENTS VII
PART VI - CASE STUDIES
IMPROVING THE URANIUM DEPOSITS ESTIMATIONS (THE NOVAZZA CASE) M. Guarascio 351
A 2-DIMENSIONAL GEOSTATISTICAL STUDY OF A SKARN DEPOSIT, YUKON TERRITORY, CANADA A. J. Sinclair and J. R. Deraisme 369
A CASE STUDY : MULTIVARIATE PROPERTIES OF BENTONITE IN NORTHEASTERN WYOMING L. E. Borgman and R. B. Frahme 381
SOME PRACTICAL COMPUTATIONAL ASPECTS OF MINE PLANNING I. Clark
PART VII - INTERFACE WITH OTHER DISCIPLINES
NEW PROBLEMS AT THE INTERFACE BETWEEN GEOSTATISTICS AND GEOLOGY F. P. Agterberg
GEOSTATIStIQUE ET ANALYSE DES DONNEES J. P. Orfeuil
BAYESIAN DECISION THEORY APPLIED TO MINERAL EXPLORATION AND MINE VALUATION J. M. Rendu
PART VIII - GLOSSARY OF FRENCH-ENGLISH GEOSTATISTICAL TERMS
391
403
423
435
TENTATIVE GLOSSARY OF GEOSTATISTICAL TERMS AND NOTATIONS 449
FOREWORD
When Prof. Hatheron was asked to delineate the history of geostatistics, he objected that such discipline is still too "young" to be treated from a historical point of view. The more and more increasing practical applications requiring newer and newer methodologies would rather suggest the necessity of emphasizing the steps taken and the results obtained up to now. The reason of certain epistemological choices as well as the difficulties and success in establishing a dialogue with the people most likely to benefit from the results of geostatistics are necessary premises to understand the present status of this discipline. The human bearing of characters of the persons that have introduced and studied this science blending theory with economic practics is a factor playing a not inconsiderable role in the development of geostatistics.
These concepts were the guidelines in organizing the ASI-Geostat 75. Canada, France and Italy are three different situations in an industrial and academic context, especially in the interaction between these fields . Yet it was our impression that the time had come to assemble experts, scholars, and other people interested in geostatistics in orde r to evaluate its present position on various levels in the different count ries and to discuss its future prospects . Prof. Hatheron and Hr. Krige as well as other prominent people were of the same opinion.
The Programme of the Institute was organized in such a way as to introduce in a logical orde r the various arguments in order to balance theoretical and methodological lessons. Experts in the various fields of geostatist i cs were invited to deal with the items of the programme. Twenty-nine nations were represented testifying to the fact that geostatistics has already an international audience on both the academic and industrial world.
The result of the Institute is this book which is hoped to give a comprehensive view of the present state-of-the art of geostatistics.
Acknowledgements
We are very grateful to the Scientific Affair Division of NATO for being the main sponsor of the ASI - Geostat 75. The Institute would not have been possible. however. without additional generous help from the Ecole Poly technique. Montreal: the National Research Council of Canada: the Ecole des Mines. Paris; and from the CNR-CS per la Geologia Tecnica at the University of Rome.
We are especially grateful to the Istituto di Geologia Applicata of the University of Rome for providing unlimited secretarial facilities.
Particularly, we would like to thank Dr. Francesca Esu Cugusi (CNR-CS per la Geologia Tecnica) for her precious contribution.
We also wish to express our gratitude to all contributors and participants who with their overwhelming performance have contributed to the success of the ASI-Geostat 75.
Rome, December 1975
Massimo Guarascio Michel David Charles Huijbregts
LIST OF PARTICIPANTS
AGTERBERG, Fritz: Chief Geomathematics Section , Geological Survey of Canada, Energy-Mines and Resources Canada, 601 Booth Street , Ottawa, Ontario KIA DEB , Canada
ALFARO , Marco : Head Geomathematics Dept ., Centro de Calculo , Escuela Tecnica Superior de Minas, Rios Rosas 21, Madrid 3 , Spain
AMARANTE , Manuela: Geologist, Servi~o Fomento Mineiro, Rua Amieira, S. Mamede Infesta, Portugal
ANDOLFATO, Ugo: Geologist, Agip S.p.A.-Attivita Minerarie, 20097 S. Donato Milanese (MI ) , Italy
ARVIDSSQN, Sven : Mining Engineer, National Swedish I ndustrial Board, Bureau of Minerals , Box 16315, S-103 26 Stockholm 16, Sweden
BELISLE, Jean Marc: Research Assistant, Dept. de Genie Mineral , Ecole Poly technique, C.P . 6079 Succ. A, Montreal, Quebec H3C 3A7 , Canada
BILLETTE, Noel: Student, Dept . de Genie Mine ral , Ecole Poly techmque, C.P. 6079 Succ. A, Montreal, Quebec H3c 3A7, Canada
BILODEAU , Mi chel : Lecturer, Dept . of Mining & Metal Eng. , McGill University, P.O. Box 6070 Station A, Montreal, Quebec H3C 3GI, Canada
BONDURANT, Ellen J.: Student, Colorado School of Mines, Golden, Colorado 80401, U.S.A.
BORGMAN, Leon : Prof. of Geology and Statistics , Geology Dept . and Statistics Dept., University of Wyoming, Laramie , Wyoming 82070 , U.S .A.
BOTMAN, A.G.: Mining Engineer, Mining Dept., Intern'l Institute for Aerial Survey and Earth Sciences, 3 Kanaalweg, Delft, The Netherlands
XII LIST OF PARTICIPANTS
BROOKER , Peter: of Ade laide,
Lecturer , Dept. of Economic Geology. Adelaide, South Australia 5000
University
BUTZ. Todd: Student, University of Missouri, Rolla , Missouri, U.S
CAMELLINI. Paolo : Statistician, Italminiere. Via Santa Te r esa 5, Rome, Italy
CETINCELIK, Muammer: Head of Nuclear Section , Mineral Research and Exploration , Institute of Turkey, MTA-Ankara, Turkey
CHILES, Jean Paul: matique, 35 rue
Mining Engineer, Centre de Morphologie MatheSaiot Honore . 77305 Fontainebleau , France
CLARK. Isobe 1: Lecturer , Dept. of Mining and Mineral Technology. Imperial College of Science and Technology , London SW7, U.K .
CLARK , Malcom: Research Associate, Dept. of Geography, London School of Economics. Houghton St., London WC2A 2AE. U.K.
CLARK, Tom: Student, Mi ning Dept., Colorado School of Mines, Golden, Colorado 80401, U.S .A.
COLADON , Marc: Ing . de Mines, eEA-GAM, Avenue de Montredon 92 , Marseille 13008 , France
CORTEZ , Leopoldo: Assistant Professor , Nucleo de Tratamento de Minerios, Instituto Superior Tecnico, Av. Rovisco Pais, Lisboa I , Portugal
COSTER , William : Geologist, Occidental Minerals Corporation , Wheat Ridge, Colorado, U.S .A.
DAGBERT, Michel: Research Associate, Dept. de Genie Mineral , Ecole Poly technique, C.P. 6079 Succ . A, Montreal, Quebec H3C 3A7 , Canada
DAMAY, Jacques: Ing . de Mines, Chef de Projects, Societe Penarroya, 1 Blv de Vaugirard, 75751 Paris XV-Cedex I, France
DAVID , Michel: Associate Professor, Dept. de Genie Mineral , Ecole Poly technique, C.P. 6079 Succ . A, Montreal, Quebec H3C 3A7 , Canada
DELFINER , Pierre: Ing. de Recherches, Princeton University, Princeton , New Jersey, U.S .A. / Centre de Horphologie Hathematique , Fontainebleau, France
DESSENIBUS , Armando: Research Assistant , Facoltii d'Ingegneria , Universita di Trieste, Via Valerio 21, Tr ieste, Italy
LIST OF PARTICIPANTS
DIETZEL , Gerard: leum. Co. Ltd.,
DOWD , Peter A.: ty, Leeds LS2
Xiii
Dr. Geology and Mathematics , Brunei Shell PetroSeria, State of Brunei, Borneo
Research Associate, Mining Dept ., Leeds Universi-9JT , Yorkshire, England
EL KHAIER, Abdelhak : Mining Engineer, Office Cherifien des Phosphate s , 3D5 Bd. Mohammed V, Rahat, Marocco
FLINT, David : Geologist, Dept . of Geology, Universi ty of Alberta, Edmonton , Alberta , T6G 2EI Canada
FRICIERI, Toni Fabrizio: Mining Engineer , AGIP S.p.A.-Attivita Mine rarie, 20097 S. Donato Mi jane!;e (MI ) , Italy
GASPARDVI C, Nevenka : Mathemati c ian , INA , Proleterskish Brigada 78, Zagabria, 41000 Yugoslavia
GUERARDI, Sergio : Geologist, Soc i e ta RiMin, Via Po 51, Rome, Ital y
GONZALEZ, Jorge Alberto: Director , System Dept ., CENTROMIN-PERU, Casilla 24 12 , Lima , Peru
GUARASCID, Ma ssimo : Assistant Professo r , Istituto di Geologia Applicata. Universita di Roma . Via Eudossiana 18, Rome, Italy
HAAS, Andre: Ing. de Mines. SNPA-Dept . Recherche en Geophysique, Ave. du Prt. Angot, 64000 Pau , France
HILL, Ge offrey : Statistician, CSIRO Australia , (H.D. Canberra), Math . and Statistics. Pr i vate Bag I, Glen Osmond, South Austalia
HOFMANNER, F.: Mining Engineer , Holderbank, Management und Beratung AG. Technische Stelle, CH-511 3, Holderbank (AG), CH .
HOWARTIl , Richard: College. London
Research SW7 2BP ,
Associate . England
Dept. of Geology, Imperial
HUIJBREGTS, Cha r les : Research Associate , Centre de Morphologie Mathematique, ENSMP, 35 rue St . Honore. 77305 Fontainebleau, France
IANNELLO , Pasquale: Geolog i st , ITALSIDER, S.p.A., Via Co r s ica 4, Genova, Italy
IPPATI , Filiberto: Mini ng Eng ineer, SICAl, Viale Liegi 33 , Rome, Italy
XIV LIST OF PARTICIPANTS
JOURNEL, Andre: Maitre de Recherches , Cent r e de Morphologie Mathematique , 35 rue St. Honore, 77305 Fontainebleau, France
JOUSSELIN, Claude: lngenieur. SNPA-Recherches en Geophysique, Ave du Prt. Angot, 64000 Pau, France
KHATTAB , Khattab M. : Mathematical Geologist , International Nickel Co. of Canada Ltd., Exploration Dept ., Copper Cliff, Ontario POR I NO Canada
KRIGr., Danie 1 G.: glovaal House,
Financial Engineer, Anglo Transvaal Cons. , An-56 Main Street , Marshalltown, TVL, South Africa
LALLEMENT, Be rnard: Ing . de Mines, BRGM-Orleans la Source, B.P. 6009, 45100 Orleans, France
LEACH, Brian: Consultant, AMDEt, Flemington Street . Frewville. Adelaide, South Australia
I.E DO, Raymonde: Student, Dept. de Genie Mineral, Ecole Poly technique, C. P. 6079 Succ. A, Montreal, Quebec H3C 3A7, Canada
LEYMARIE , Pierre : Geologist, Centre de Reche r ches Petrographique et Geochimiques - C. O. I, Vandoeuvre 54500, Nancy, France
LLANA, Agustin Horacio: troleum, MIJ. B.V. -
Mining Engineer, Shell International PeP. O. Box 162, The Hague, The Netherlands
MAIGNAN, Michel: Ing . de Mines, Swiss Aluminium Ltd., Feldeggst r . 4 - CH-8034, Zurich, Switze r land (CH)
HARBEAU , Jean Paul: Ing . de Recherches, Centre de Morphologie Mathematique, 35 rue St . Honore , 77305 Fontainebleau, France
MARECHAL, Alain : Maitre de Recherches , Centr e de Morphologie Mathematique, ENSMP , 35 rue St . Honore, 77305 Fontainebleau, France
MATHERON, Georges: Professor , Director , Centre de Morpho l ogie Mathematique, ENSMP, 35 rue St. Honore, 77305 Fontainebleau, Fr ance
MATULICH, Angelo: Chief Geologist , Texasgulf Canada, Box 2002 , Timmins , Ontario P4N 6M5. Canada
MIGUEZ MARIN, Felix: Geologist , Centro de Ca l culo de la Escuela Tecnica Superior de Ingenieros de Minas, Rios Rosas 21 , Madrid 3, Spain
LIST OF PARTICIPANTS xv
MOUSSET-JONES, Pierre: Associate Professor, Mackay School of Mines, Reno, Nevada 89507, U.S.A .
HUGE, Fernando: Mining Engineer , Nucleo de Tratamento de Minerios, Instituto Superior Tecnico, Ave . Rovisco Pais , Lisboa I , Portugal
NISKANEN, Pentti : Mining Engineer, Outokumpu Oy., P .O. Box 10280-00101 , Helsinki 10, Finland
ORFEUIL, J ean Pierre: Ing. de Recherches, C.M.M.-ENSMP, 35 rue St. Honore, 77305 Fontainebleau, France
PARKER, Harry McDougal: Geologist, The Hanna Mining Co . , 100 Erieview Plaza, Cleveland, Ohio 44114, U.S.A .
PEREIRA , Henrique: Mining Engineer, Nucleo de Tratamento de Mineiros, Instituto Sup. Tecn., Av. Rovisco Pais , Lisboa I, Portugal
PRELLER, Alej andro: se 25, Madrid 20,
Project Engineer, Fraser Espanola , S.A. , OrenSpain
QUINLAN, Terry: Geologist and Mathematician, Geopeko Limited, Chatswood, Australia
RASPA, Giuseppe: Research Associate, Istituto di Geologia Appli cata, Universita di Roma , Via Eudossiana 18, Rome, Italy
RENDU , Jean Michel: Mining Engineer, Anglovaal Ltd . Anglovaal House , 56 Main Street, Marshalltown, TVL , South Africa
REYES , Italo: Mining Engineer, Aceries Paz del Rio, S.A., Bogota, Colombia
RIVERON, Etienne: Geologist , CEA-Direction des Productions, Ave. du Gl. de Gaulle, 92260 Fontenay, France
ROADIFER , Roy: Mining Engineer , Mobil Oil Corporation, 221 Nassau Street, Princeton , New Jersey 08540, U.S.A .
ROGADO, Jose Quintino: Prof. of Mining, Instituto Superior Tecnico, Av. Rovisco Pais , Lisboa I, Portugal
ROYLE , Allen Graham: Lecturer, Mining Dept., Universi t y of Leeds , Leeds LS2 9JT , Yorkshire , England
RUTLEDGE, Robert W.: Box 483 , G.P . O. ,
Manager , Systems and Computers , CSR Ltd . , Sydney 2001, Australia
XVI LIST OF' PARTICIPANTS
SABOURIN, Raymond: Mining Engineer , Energy Mines and Resources Canada, 601 Booth Street, Ottawa, Ont. KIA OE8, Canada
SANDEFUR, Robe r t L. : Mining Engineer, Utah International Inc. , 550 California St., S. Francisco , California 94104 , U. S.A.
SANS, Henri: rng. Consultant, Servicios Industriales PENOLES, Piso 14, Apartado postal 686, Mexico I D.F., Mexico
SINCLAIR, Alastair J .: Prof. of Geo l ogy , Dept . of Geological Sciences, Un i versity of B.C., Vancouver, B.C. V6T IW5, Canada
SINDING LARSEN, Richard : Mining Geologist , Geological Survey of Norway , P.B. 3006 , 7001 Trondheim, Norway
STEPHENS , Michael: Prof. of Statistics, Dept . of Mathematics and Applied Mathematics, McMaster Unive r sity, Hamilton, Ont., Canada
SWITZER, Paul: Prof . of Statistics, Dept. of Statistics, Standford University, Standford, California 94305, U.S.A .
TACIER, Jean Daniel: Geologist, Eidg . Technische Hochschule , Lehrstuhl fur math . Statistik, Claussiusstr. 55, 8006 Zurich , Switzerland (CH)
UCCELLA , Lucio : Project Engineer, Soc. Min. Pertusola, Piazzale Flaminio 9, Rome, Italy
VALERA , Roberto: Prof. of Mining Geology, Dept. of Geology and Mineral Deposits , Universitadi Cagliari , Cagliari, Sardegna, Italy
VAN DER GEEST, P.A.G.: Mining Engineer, KoninkUjke - Shell Exploratic en Productie Labo ratorium, Postbus 60, Rijswijk, The Netherlands
WELLS , Howard: Prof. of Mining, University of the Witwatersrand, Dept. of Mining Engineering , I Jan Smuts Ave., Johannesburg 2001, South Africa
WHITTEN , Timothy E.H.: University , Dept. of 60201, U.S.A .
Prof . of Geological Sciences, Northwesten Geological Sciences , Evanston, Illinois