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

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Softcover reprint of the hardcover I st edition 1976

2. Geology, 11. David.

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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