Geostatistics for Natural Resources Characterization Part 1

NATO ASI Series Advanced Science Institutes Series

A series presenting the results of activities sponsored by the NATO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities.

The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division

A Life Sciences Plenum Publishing Corporation B Physics London and New York

C Mathematical D. Reidel Publishing Company and Physical Sciences Dordrecht, Boston and Lancaster

D Behavioural and Social Sciences Martinus Nijhoff Publishers E Engineering and The Hague, Boston and Lancaster

Materials Sciences

F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York and Tokyo

Series C: Mathematical and Physical Sciences Vol. 122 - Part 1

Geostatistics for Natural Resources Characterization Part 1

edited by

G. Verly Department of Applied Earth Sciences, Stanford University, Stanford, U.S.A.

M. David Departement de Chimie Mineral , Ecole Poly technique, Montreal, Canada

A. G. Journel Department of Applied Earth Sciences, Stanford University, Stanford, U.S.A.

and

A. Marechal S.N. Elf Aquitaine (Production), Pau, France

D. Reidel Publishing Company

Dordrecht / Boston / Lancaster

Published in cooperation with NATO Scientific Affairs Division

Proceedings of the NATO Advanced Study Institute on Geostatistics for Natural Resources Characterization Stanford Sierra Lodge, South Lake Tahoe, California, U.S.A. September 6 - 17,1983

Library of Congress Cataloging in Publication Data

NATO Advanced Study I nstitute on Geostatistics for Natural Resources Characterization (2nd: 1983: South Lake Tahoe, Calif.) Geostatistics for natural resources characterization. (NATO ASI series. Series C, Mathematical and physical sciences; vol. 122) "Proceedings of the NATO Advanced Study I nstitute on Geostatistics for Natural

Resources Characterization, Stanford Sierra Lodge, South Lake Tahoe, California, U.S.A., September 6-17,1983"-T.p. verso.

"Published in cooperation with NATO Scientific Affairs Division." I ncludes bibliographical references and index.

1. Mine valuation-Statistical methods-Congresses. 2. Geology-Statistical methods­Congresses. I. Verly, G. (Georges) II. North Atlantic Treaty Organization. Scientific Affairs Division. III. Title. I V. Series: NATO ASI Series. Series C, Mathematical and physical sciences; Vol. 122. TN272.N38 1983 ISBN -13:978-94-0 1 0-8157 -3 DOl: 10.1007/978-94-009-3699-7

553'.0724 84-2155 e-ISBN-I3:978-94-009-3699-7

Published by D. Reidel Publishing Company PO. Box 17,3300 AA Dordrecht, Holland

Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 190 Old Derby Street, Hingham, MA 02043, U.S.A

In all other countries, sold and distributed by Kluwer Academic Publishers Group, PO. Box 322, 3300 AH Dordrecht, Holland

D. Reidel Publishing Company is a member of the Kluwer Academic Publishers Group

AI! Rights Reserved © 1984 by D. Reidel Publishing Company, Dordrecht, Holland. Softcover reprint of the hardcover 1st edition 1984

No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

TABLE OF CONTENTS

FOREWORD

ACKNOWLEDGEMENTS

LIST OF PARTICIPANTS

PART I - VARIOGRAM

LECTURES

- IMPROVING THE ESTIMATION AND MODELLING OF THE VARIOGRAM M. Armstrong

2 - TOWARDS RESISTANT GEOSTATISTICS N. Cress;e

CONTRI BUTIONS

3 - STATISTICAL INFERENCE OF THE SEMIVARIOGRAM AND THE QUADRATIC MODEL

xiii

xiv

xv

1

21

M. Al faro 45

4 - USE OF THE JACKKNIFE METHOD TO ESTIMATE AUTOCORRELATION FUNCTIONS (OR YARIOGRAMS) C.F. Chung 55

5 - COMPUTING VARIOGRAMS IN FOLDED STRATA-CONTROLLED DEPOSITS M. Dagbert, M. David, D. Croze1, A. Desbarats 71

6 - THE YARIOGRAM AND KRIGING: ROBUST AND RESISTANT ESTIMATORS P.A. Dowd 91

vi TABLE OF CONTENTS

7 - THE VARIOGRAM AND ITS ESTIMATION H. Omre

8 - INFERENCE FOR SPATIAL AUTOCORRELATION FUNCTIONS P. SwHzer

PART II - PRECISION Of GLOBAL ESTIMATION

LECTURE

9 - PRECISION Of ESTIMATION OF RECOVERABLE RESERVES: THE NOTION OF CONDITIONAL ESTIMATION VARIANCE R. froidevaux

CONTRIBUTIONS

10 - ESTIMATION VARIANCE OF GLOBAL RECOVERABLE RESERVE ESTIMATES B.E.Buxton

11 - COMBINING LOCAL KRIGING VARIANCES FOR SHORT-TERM MINE PLANNING Y.C. Kim, E.Y. Baafi

12 - APPLICATION OF A GEOSTATISTICAL METHOD TO QUANTITATIVELY DEFINE VARIOUS CATEGORIES Of RESOURCES R. L. Sabourin

PART III - KRIGING

LECTURE

13 - CONDITIONAL BIAS IN KRIGING AND A SUGGESTED CORRECTION

107

127

141

165

185

201

M. David, D. Marcotte. M. Soulie 217

CONTRI BUTIONS

14 - POSITIVE KRIGING R.J. Barnes. T.B. Johnson

15 - CORRECTING CONDITIONAL BIAS K. Guertin

16 - mAD AND CONDITIONAL QUANTILE ESTIMATORS A.G. Journel

231

245

261

TABLE OF CONTENTS

17 - KRIGING SEISMIC DATA IN PRESENCE Of fAULTS A. Marechal

18 - CO-KRIGING - NEW DEVELOPMENTS D. E. Myers

PART IV - INDICATOR KRIGING

LECTURE

19 - THE PLACE or NON-PARAMETRIC GEOSTATISTICS A.G. Journel

CONTRIBUTIONS

20 - INDICATOR KRIGING AS APPLIED TO AN ALLUVIAL GOLD DEPOSIT

vii

271

295

307

B.M. Davis 337

21 - ESTIMATING LOCAL RECOVERABLE INDICATOR KRIGING

RESERVES VIA

I.C. Lemmer 349

22 - CONDITIONAL RECOVERY ESTIMATION THROUGH PROBABILITY KRIGING - THEORY AND PRACTICE J. Sullivan 365

PART V - RECOVERABLE RESERVES

LECTURES

23 - RECOVERY ESTIMATION: A REVIEW OF MODELS AND METHODS A. Marechal 385

24 - THE SELECTIVITY OF THE DISTRIBUTIONS AND THE "SECOND PRINCIPLE OF GEOSTATISTICS" G. Matheron 421

CONTR I BUTI ONS

25 - LOCAL ESTIMATION Of THE RECOVERABLE RESERVES: COMPARING VARIOUS METHODS WITH THE REALITY ON A PORPHYRY COPPER DEPOSIT D. Guibal. A. Remacre

26 - ISOfACTORIAL MODELS AND CHANGE Of SUPPORT G. Matheron

435

449

viii TABLE OF CONTENTS

27 - GEOSTATISTICAL APPLICATION IN TABULAR STYLE LEAD-ZINC ORE AT PINE POINT CANADA G.F. Raymond

28 - LOCAL ESTIMATION OF THE BLOCK RECOVERY FUNCTIONS A. Soares

29 - THE BLOCK DISTRIBUTION GIVEN A POINT MULTIVARIATE NORMAL DISTRIBUTION G. Verly

PART VI - SPECTRAL ANALYSIS AND DATA ANALYSIS

LECTURE

30 - THREE-DIMENSIONAL. FREQUENCY-DOMAIN SIMULATIONS OF GEOLOGICAL VARIABLES L. Borgman. M. Taheri. R. Hagan

CONTRI BUTlONS

31 - FACTORIAL KRIGING ANALYSIS: A SUBSTITUTE TO SPECTRAL ANALYSIS OF MAGNETIC DATA A. Galli. F. Gerdll-Neuillet. c. Dadou

32 - THE FACTORIAL KRIGING ANALYSIS Of REGIONALIZED DATA. ITS APPLICATION TO GEOCHEMICAL PROPECTING L. Sandjivy

33 - THE ANALYSIS OF SECOND-ORDER STATIONARY PROCESSES: TIME SERIES ANALYSIS. SPECTRAL ANALYSIS. HARMONIC ANALYSIS. AND GEOSTATISTICS

469

485

495

517

543

559

A.R. Solow 573

FOREWORD

Since October 1975 and the first NATO ASl "Geostat - Roma 1975", there has not been an advanced workshop on geostatistics where experts from throughout the world could meet, teach and debate without the pressure of an ordinary professional confer­ence. This second NATO ASI "Geostat - Tahoe 1983" was intended as a high-level teaching activity yet opened to all new ideas and contributions to the discipline of geostatistics. It was expected that the institute would bridge the gap since "Geostat -Roma 1975" and establish the state of the art of the discipline as of 1983.

"Geostat - Tahoe 1983" fulfilled all expectations. The institute, held in September 1983 at the Stanford Sierra Lodge near Lake Tahoe, California, was attended by all major players in the field, representing evenly the academy and the industry of 23 different countries. Twelve guest lecturers were backed by some 50 original contributions. Particularly important for the future was the active participation of graduate students, glvlng evi­dence of the dynamism of a still very young discipline.

Applications of geostatistics are no longer limited to the mining industry, and the original scope of the ASI had to be wid­ened to witness the progress made in such fields as hydrology, soil sciences, pollution control and geotechnical engineering. Also important was the cross-fertilization from oiher statistical branches such as spectral analysis and robust statistics.

The NATO ASI "Geostat - Tahoe 1983" will be remembered as a major milestone in the development of the discipline. I invite all of you who did not make it to the ASI to dive into these pro­ceedings and share a bit of the excitement that pervaded this summer's end at Lake Tahoe.

A.G. Journel Director of the ASI

ACKNO\{LEDGEMENTS

The Scientific Affairs Division of NATO is gratefully acknowledged for having sponsored this Advanced Study Institute. Additional support was, provided by Stanford University, Ecole Poly technique de Montreal, and Ecole des Mines de Paris.

We thank the group of following companies which helped finance the Institute:

BRGM, France CERCHAR, France COGEMA, France Elf Aquitaine (Production), France Schlumberger E.P.S., France TECMIN, France Shell, Netherlands

We are especially grateful to the team of Stanford students who made possible the organization of the ASI.

The overwhelming success of this Institute would not have been possible without the dedication of our lecturers and contributors.

Stanford, October 1983

xi

The Organizing Committee

George Verly Michel David Andre Journel Alain Marechal

LIST OF PARTICIPANTS

ALFARO, Marco: Professor, Departemento Minas, Universidad de Chile, Casilla 2777,Santiago, Chile.

AMEGEE, Kodjo: Student, Departement of Agricultural Engineering, Oregon State University, Corvallis, Oregon 97331, U.S.A.

ARMSTRONG, Margaret: Research Engineer,Centre de Geostatistique, ENSMP, 35 rue st. Honore, 77305 Fontainebleau, France.

BAECHER Gregory B.: Professor, Departement of Civil Engineering, Masachusset Institute of Technology, Cambridge, Massachusetts 02139, U.S.A.

BAElE steve M.: Mining Engineer, u.s. Borax Corp., 3075 Wishire Blvd., Los Angeles, California 90010, U.S.A.

BALlA, Lobo Mineral Technology Development Center, J1. Jendral Sudirman Ho.623, Bandung, Indonesia.

BARNES, Randal J.: Instructor, Colorado School of Mines, Golden, Colorado 80401, U.S.A.

BELISLE, Jean Marc: Project Manager, Geostat Systems Interna­tional, 5180 Queen Mary, Suite 370, Montreal, Quebec H3X 3E7, Canada

BERLANGA, Juan M. :-Professor, Division de Posgrado, Fac. Inge­nieria , Universidad de Mexico, Mexico D.F. 04510, Mexico

BILOHICK, Richard A.: entific Systems, 15241, U.S.A.

Statistician, Consolidation Coal Co., Sci-Consol Plaza Pittsburgh, Pennsylvania

xiii

xiv LIST OF PARTICIPANTS

BONHAM-CARTER, Graeme F.: Research Scientist, Geological Survey of Canada, 601 Booth street. Ottawa, Ontario K1A OE8, Canada

BORGMAN, Leon E.: Prof. of Geology and Statistics, Dept. of Sta­tistics, University of Wyoming, Laramie, Wyoming 82071, U.S.A.

BRYAN, Rex, C.: Director, Geostat Systems Inc., P.O. Box 1193, Golden, Colorado 80402. U.S.A.

BUXTON, Bruce: Student. Dept. of Applied Earth Sciences. Stanford University, Stanford, California 94305, U.S.A.

CAMISAHI-CALZOLARI, f.A.M.G.: Project Head, Nuclear Development Corp .• Uranium Evaluation Group, Private Bag X256 Pretoria 0001. South Africa

CARR. James R.: Professor, Dept. of Geological Engineering, Uni­versity of Missouri. Rolla, Missouri 65401. U.S.A.

CHICA-OLMO, Marion: Student, Centre de Geostatistique, EHSMP, 35 rue st. Honore. 77305 Fontainebleau. France

CHILES. Jean-Paul: Mining Engineer. B.R.G.M.. B.P.6009, 45018 Orleans. France

CHU, Darong: Student, 1126 C San Pablo Av., "3, Albany, Cali­fornia 94706. U.S.A.

CHUNG, Chang-Jo r.: Research Scientist. Geological Survey of Canada. 601 Booth Street. Ottawa, Ontario K1A OE8, Canada

CLARK, Isobel: Managing Director, Geostokos Ltd., 8a. Lower Grosvenor Place. London SW1W DEN. United Kingdom

CRESSIE, Noel A.C.: Senior Lecturer, Dept.of Math. Sciences, The Flinders University, Bedford Park, S.A. 5042, Australia.

CULHANE, Patrick, G.: Manager, Appl ications Service, Sohio Petroleum Company, 100 Pine Street, San Francisco, California 9411" U.S.A.

DAGBERT, Michel: Manager, Geostat Systems International, 5180 Queen Mary, Suite 370, Montreal, Quebec H3X 3E7, Canada

DAMAY, Jacques: Director Minas-Exploracion, S.M.M.P., Alfonso XII-3D, Madrid (14), Spain

DAVID, Michel: Professor. Dept. de Genie Mineral. Ecole Poly­technique, C.P. 6079 Suec. A, Montreal, Quebec H3C 3A7, Can­ada.

LIST OF PARTICIPANTS xv

DAVIS, Bruce M.: Chief Geostatistician,. st. Joe American Corp., 2002 N. Forbes Blvd, Tucson, Arizona 85705, U.S.A.

DAVIS, Michael W.: Principal Geostatistician, Fluor Mining and Metal Inc., 10 Twin Dolphin Drive; Redwood City, Cal ifornia 94065, U.S.A.

DERAISME, Jacques: Research Engineer, Centre de Geostatistique, ENSMP, 35 rue st. Honore, 77305 Fontainebleau, France

DESBARATS, Alexandre: Student, Dept. of Applied Earth Sciences, Stanford University, Stanford, California 94305, U.S.A.

DEVARY, Joseph L.: Research Scientist, Pacific Northwest Labora­tory , P.O. Box 999, Richland, Washington 99352, U.S.A.

DIEHL, Peter: Student, Franckerstr. 2, 2300 Kiel " West Germany

DOWD, Peter A.: Lecturer, University of Leeds, Leeds LS2 9JT, England, United Kingdom

DUBRULE, Olivier: Senior Technical Analyst, Sohio Petroleum Com­pany, 100 Pine Street, San Francisco, California 9411" U.S.A.

DUNN, Mark R.: Research Mathematician, Shell Development Com­pany, P.O. Box 1380, Houston, Texas 77001, U.S.A.

ENGLUND, Evan J.: Sr. Minerals Geologist, Exxon Minerals Com­pany, P.O. Box 4508, Houston, Texas 77210, U.S.A.

ERWIN, Les: Geologist, Texaco USA, Bellaire Research Lab., P.O. Box 425, Bellaire, Texas 77401, U~S.A.

FLATMAN, George T.: Statistician, U.S. EPA EMSL-LV, Station EAD, P.O. Box 15027, Las Vegas, Las Vegas, Nevada 89114, U.S.A.

FRANCOIS-BONGARCON, Dominique: Vice-president, Geomath Inc., 4891 Independence st., Suite 250, Wheat Ridge, Colorado 80033, U.S.A.

FROIDEVAUX, Roland: Senior Geostatistician, David Robertson and Associates, 145 King st. West, 24th floor, Toronto, Ontario M5H lU, Canada,

GALLEGO, Alejandrino: Ingenierio de Minas, S.M.M. penarroya, Alfonso XII-3D, Madrid (14), Spain

GALLI, Alain: Research Engineer, Centre de Geostatistique, EHSMP, 35 rue st. Honore, 77305 fontainebleau, france

xvi LIST OF PARTICIPANTS

GASCOINE, Chris E.: Technical Specialist Geostatistics, Esso Resources Canada ltd., 339 - 50 Avenue S.E., Calgary, Alberta T2G 2B3, Canada

GERDIl-NEUIllET, Francoise: Engineer,TOTAl-CFP, 39-43 Quai Andre Citroen, 75015 Paris, France

GERKEN, Dennis J.: Independence st., U.S.A.

Senior Software Manager, Geomath Inc., 4891 Suite 250, Wheatridge, Colorado 80033,

GIRARDI, Jorge P.: Researcher, Inst. de Investigaciones Mineras, Universidad Nacional de San Juan, Avda. libertador Gral. San Martin 1109 (oeste), 5400 San Juan, Argentina

GIROUX, Gary H.: Partner, Montgomery Consultants ltd., 203-2786 W. 16th Ave., Vancouver, British Colombia V6K 3C3, Canada

GLASS, Charles Engineering, U.S.A.

E.: Professor, Dept. of Minning & Geological University of Arizona, Tucson, Arizona 85721,

GUARASCIO, Massimo: Professor, Inst. di Geologia Applicata, Uni­versita di Roma, via Endessiana 18, Roma 00184, Italy

GUERTIN, Kateri: Student, Dept. of Applied Earth Sciences, Stan~ ford University, Stanford, California 94305, U.S.A.

GUIBAl, Daniel: Senior Geostatistician, Siromines, 71 York Street, Sydney, NSW 2000, Australia

HAGAN, Randy: Geomathematician, Anaconda Minerals Co., 555 17th street, Denver, Colorado 80202, U.S.A.

HElWICK. Sterling. J. Jr.: Researcher. Exxon Production Research Co., P.O. Box 2189, Houston, Texas 77001, U.S.A.

HERNANDEZ-GARCIA, Gustavo: Engineer, Secretaria de Energia, Minas e Industria Paraestatal, San luis Potosi 21'-1er. Piso, Mexico D.F. 06700. Mexico

HODOS. Ellen F.: Mining Consultant, Placer Service Corp .• 12050 Charles Drive Suite A, Nevada City, California 95959

ISAAKS, Edward H.: Student. Dept of Applied Earth Sciences, Stanford University. Stanford. California 9~305. U.S.A.

JARVIS, Merigon M.: Processing Geophysicist. Compagnie Generale de Geophys;que, 47/55 The Vale, Acton, london W3 7RR, England

LIST OF PARTICIPANTS xvii

JONES. Thomas A.: Sr. Research Associate. Exxon Production Research Co .• P.O. Box 2189, Houston, Texas 77001, U.S.A.

JOURNEL. Andre G.: Professor. Dept. of Applied Earth Sciences, Stanford University, Stanford, California 94305, U.S.A.

KIM. Young C.: Professor, Dept. of Mining and Geolological Engi­neering., University of Arizona, Tucson. Arizona 85721. U.S.A.

KLEINGELD, W.J.: Ore Evaluation Manager, De Beers Consolidated Mines Ltd., P.O. Box 616, Kimberley 8300, South Africa

KNUDSEN, Pete H.: Professor, Mining Engineering Dept., Montana College of Mineral Sciences and Technology. Butte, Montana 59701, U.S.A.

KULKARNI, Ram B.: Head Systems Engineering Group, Woodward-Clyde Cons .• One Walnut Creek Center, 100 Pringle Ave., Walnut Creek. California 94596, U.S.A.

KWA, Leong B.: Student, Mackay School of Mines, University of Nevada, Reno. Nevada 89557, U.S.A.

LAILLE, Jean-Paul: Research Engineer, Centre de Geostatistique, ENSMP, 35 rue st. Honore, 77305 Fontainebleau, France

LAJAUNIE. Christian: Research Engineer, Centre de Geostatisti­que, ENSMP, 35 rue st. Honore, 77305 Fontainebleau. France

LEMMER, Carina: Senior Analyst, Technical Systems, Gold Field SA, P.O. Box 1167, Johannesburg 2000, South Africa

LONERGAN E.T.: Project Supervisor, Placer Development Ltd., P.O. Box 49330, Bentall Postal Station, Vancouver, British Colombia V7X lPl, Canada

LUDVIGSEN, Erik: Head of Divison, Division of Mining Engineering, The Norwegian Institute of Technology, 7034 Trondheim-NTH, Norway

LUSTER, Gordon R.: Student, Dept. of Applied Earth Sciences, Stanford University, Stanford, California 94305, U.S.A.

LYEW-AYEE, Parris A.: Director Bauxite Division, Jamaica Bauxite Institute, P.O. Box 355, Kingston 6. Jamaica. W.I.

MAINVILLE, Alain: Student, Dept. de Genie Mineral, Ecole Poly­technique. C.P. 6079 Succ. A. Montreal, Quebec H3C 3A, Canada

xviii LIST OF PARTICIPANTS

MALLET, Jean Laurent: Professor, Ecole Nationale Superieure de Geologie, B.P. 452, 54001 Nancy, france

MAO, Nai-hsien: Geophysicist, U.C. Lawrence Livermore National Lab., P.O. Box 808, MaO stop L224, Livermore, Cal ifornia 94550, U.S.A.

MARBEAU, Jean-Paul: President, Geomath Inc., 4891 Independence st., Suite 250, Wheatridge, Colorado 80033, U.S.A.

MARCOTTE Denis: Research Associate, Ecole Poly technique, C.P. 6079 Succ. 3A, Canada

Dept. de Genie Mineral, A, Montreal, Quebec H3C

MARECHAL, Alain: Engineer, Societe Elf Aquitaine Prod., DOTI-De­veloppement, 64018 Pau, france

de MARSILY, Ghislain: Centre d'informatique Geologique, ENSMP, 35 rue st. Honore, 77305 fontainebleau, france

MATHERON, Georges: Director, Centre de Geostatistique, ENSMP, 35 rue st. Honore, 77305 fontainebleau, france

MILIORIS, George: Student, Dept. of Mining and Metallurgical Engineering, Me GO I University, 3480 University St., Mont­real, Quebec H3A 2A7, Canada

MOREAU, Alain: Student, Dept. de Genie Mineral, Ecole Poly tech­nique, C.P. 6079 Succ. A, Montreal, Quebec H3C 3A, Canada

MDUSSET-JONES, Pierre: Professor, Mackay School of Mines, Uni­versity of Nevada, Reno, Nevada 89557, U.S.A.

MUGE, fernando: Professor. CVRM - Instituto Superior Technico, Av. Rovisco Pais, 1096 Lisboa, Portugal

MYERS. Jeffrey C.: Student, Colorado School of Mines, Golden. Colorado 80401, U.S.A.

MYERS. Donald E.: Professor, Dept. of Mathematics, University of Arizona, Tucson, Arizona 85721. U.S.A.

NEUMAN, Schlomo P.: Professor, Dept. of Hydrology and Water Resources, University of Arizona, Tucson, Arizona 85721, U.S.A.

OMRE, Henning: Student, Dept. of Applied Earth Sciences, Stanford University, Stanford, California 94305, U.S.A.

LIST OF PARTICIPANTS xix

OOSTERVELD. M.M.: Ore Evaluation Consultant. Anglo American Corp .• 14 Kekewitch Drive. Kimberley 8301. South Africa

PARKER. Harry M.: Manager. Geology and Geostatistics. Fluor Min­ing and Metal Inc .• 10 Twin Dolphin Drive. Redwood City. Cali­fornia 94065. U.S.A.

PAULSON, Gary D.: Sr. Minerals Geologist, Exxon Minerals Com­pany. P.O. Box 4508. Houston. Texas 77210. U.S.A.

PEREIRA. Henrique G.: Professor. CVRM - Instituto Superior Tech­nico. Av. Rovisco Pais, 1096 Lisboa, Portugal

RAO. A.R.: Professor, School of Civil Engineering, Purdue Uni­versity. West Lafayette. Indiana 47907. U.S.A.

RAYMOND. Gary F.: Sr. Mine Project Engineer. Cominco. Ltd .• P.O. Box 2000. Kimberley. British Colombia V1A 2G3. Canada

REMACRE, Armando: Student. Centre de Geostatistique. ENSMP, 35 rue st. Honore, 77305 Fontainebleau. France

RENARD. Didier: Research Engineer. Centre de Geostatistique. ENSMP. 35 rue st. Honore. 77305 Fontainebleau. France

RIVOIRARD, Jacques: Research Engineer. Centre de Geostatistique. ENSMP, 35 rue st. Honore. 77305 Fontainebleau. France

ROGADO. Jose Q.: Professor. CVRM - Instituto Superior Technico. Av. Rovisco Pais. 1096 Lisboa. Portugal

ROYER. Jean-Jacques: Research Engineer. CRPG-CNRS. 15 rue N.-D. des Pauvres. 54501 Vandoeuvre les Nancy. France

RUTLEDGE. Robert w.: 172 Burns Road. Turramurra, N.S.W. 2074. Australia

SABOURIN. Raymond L.: Mining Geologist and Geostatistician. Fed­eral Government. 555 Booth st .• Ottawa. Ontario K1A OE8. Can­ada

SANDJIVY. Luc: Research Engineer, Centre de Geostatistique. ENSMP. 35 rue st. Honore. 77305 Fontainebleau, France

SANS, Henri: Geostatistician. COGEMA. B.P. 4. 78141 Velizy-Vil­lacoublay. france

de Sarquis, Maria A.M.: Researcher. Inst. de Investigaciones Mineras, Universidad Nacional de San Juan, Avda. Libertador Gral. San Martin 1109 (oeste). 5400 San Juan, Argentina

xx LIST OF PARTICIPANTS

SCHAEBEH, Helmut: Visiting Scholar. Dept. of Geology and Geophy­sics, University of California at Berkeley, Berkeley, Califor­nia 94707, U.S.A.

SCHECK, Donald E.: Professor, Dept. of Industrial and Systems Engineering, 313 Engineering Bldg., Ohio University, Athens, Ohio 45701, U.S.A.

SINCLAIR, Alistair J.: Professor, Dept. Geological Sciences, University of British Columbia, Vancouver, British Colombia V6T 2B4, Canada

SINDING-LARSEN, Richard: Professor, Dept. of Geology, Trondheim University, 7001 Trondheim, Norway

SOARES, Amilcar 0.: Research Fellow, CVRM - Instituto Superior Technico, Av. Rovisco Pais, 1096 Lisboa, Portugal

SOLOW, Andrew R.: Student, Dept. of Applied Earth Sciences, Stan­ford University, Stanford, California 94305, U.S.A.

SOULIE, Michel: Professor, Dept. de Genie Civil, Ecole Poly tech­nique, C.P. 6079 Succ. A, Montreal, Quebec H3C 3A7, Canada.

STEFFENS, Francois E.: Professor, Dept. of Statistics, UNISA, P.O. Box 392, Pretoria, South Africa

SULLIVAN Jeffrey: Student, Dept. of Applied Earth Sciences. Stan­ford University, Stanford, California 94305, U.S.A.

SWITZER, Paul: Professor, Dept. of Statistics, Stanford Univer­sity, Stanford, California 94305, U.S.A.

TAHERI, Mojtaba S.: Principal Investigator - Geostatistician, Dept. de Ciencias de la Tierra, INTEVEP, Apartado 76343, Cara­cas - 1070A, Venezuela

TROCHU, Francois: Student, Dept. de Genie Civil, Ecole Poly tech­nigue, C.P. 6079 Succ. A, Montreal, Quebec H3C 3A7, Canada.

UNAL, Ahmet: University, U.S.A.

Student, Virginia Polytechnic Institute and State 213 Holden Hall, Blacksburst, Virginia 24061,

UYTTENDAELE, Michel: Student, Dept. de Geologie, Universite de liege, 45 Avenue des Tilleuls, B-4000 Liege, Belgium

VALENTE, Jorge: Head of Mining Division, Paulo Abib Eng. S.A., R. Martim Francisco 331/402, CEP 30.000 - Bello Horizonte, Brazil

LIST OF PARTICIPANTS xxi

VERLY. Georges: Student. Dept. of Applied Earth Sciences. Stanford University. Stanford. California 94305. U.S.A.

VIERA-BRAGA. Lu;z P.: Student. Dept. d'Informatique Recherche Operationnelle. Universite de Montreal. C.P. Succursale A.Montreal. Quebec H3C 3J. Canada

et de 6128.

WEBSTER. Richard: Sr. Experimental Station.

Principal Scientific Officer. Rothamsted Harpenden. Herts AL5 2JQ. England

YANCEY. James D.: Sr. Research Associate. Arco Oil & Gas Co .• P.O. Box 2819. Dallas. Texas 75221. U.S.A.

YOUNG. Dae S.: Professor. Mining Engineering Dept.. Michigan Technological University. Houghton. Michigan 49931. U.S.A.