Geostatistics for Natural Resources Characterization: Part 1

586 Pages·1984·20.59 MB·English

by  Margaret Armstrong (auth.), Georges Verly, Michel David, Andre G. Journel, Alain Marechal (eds.)

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 In stitute 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 In stitute 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 methods
Congresses. I. Verly, G. (Georges) II. North Atlantic Treaty Organization. Scientific Affairs
Division. III. Title. IV . Series: NATO ASI Series. Series C, Mathematical and physical
sciences; Vol. 122.
TN272.N38 1983 553'.0724 84-2155
ISBN -13:978-94-0 10 -8157 -3 e-ISBN-I3:978-94-009-3699-7
DOl: 10.1007/978-94-009-3699-7
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 xiii
ACKNOWLEDGEMENTS xiv
LIST OF PARTICIPANTS xv
PART I - VARIOGRAM
LECTURES
- IMPROVING THE ESTIMATION AND MODELLING OF THE
VARIOGRAM
M. Armstrong 1
2 - TOWARDS RESISTANT GEOSTATISTICS
N. Cress;e 21
CONTRI BUTIONS
3 - STATISTICAL INFERENCE OF THE SEMIVARIOGRAM AND THE
QUADRATIC MODEL
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
107
H. Omre
8 - INFERENCE FOR SPATIAL AUTOCORRELATION FUNCTIONS
P. SwHzer 127
PART II - PRECISION Of GLOBAL ESTIMATION
LECTURE
9 - PRECISION Of ESTIMATION OF RECOVERABLE RESERVES:
THE NOTION OF CONDITIONAL ESTIMATION VARIANCE
R. froidevaux 141
CONTRIBUTIONS
10 - ESTIMATION VARIANCE OF GLOBAL RECOVERABLE RESERVE
ESTIMATES
B.E.Buxton 165
11 - COMBINING LOCAL KRIGING VARIANCES FOR SHORT-TERM
MINE PLANNING
Y.C. Kim, E.Y. Baafi 185
12 - APPLICATION OF A GEOSTATISTICAL METHOD TO
QUANTITATIVELY DEFINE VARIOUS CATEGORIES Of
RESOURCES
R. L. Sabourin 201
PART III - KRIGING
LECTURE
13 - CONDITIONAL BIAS IN KRIGING AND A SUGGESTED
CORRECTION
M. David, D. Marcotte. M. Soulie 217
CONTRI BUTIONS
14 - POSITIVE KRIGING
R.J. Barnes. T.B. Johnson 231
15 - CORRECTING CONDITIONAL BIAS
K. Guertin 245
16 - mAD AND CONDITIONAL QUANTILE ESTIMATORS
A.G. Journel 261
TABLE OF CONTENTS vii
17 - KRIGING SEISMIC DATA IN PRESENCE Of fAULTS
A. Marechal 271
18 - CO-KRIGING - NEW DEVELOPMENTS
D. E. Myers 295
PART IV - INDICATOR KRIGING
LECTURE
19 - THE PLACE or NON-PARAMETRIC GEOSTATISTICS
A.G. Journel 307
CONTRIBUTIONS
20 - INDICATOR KRIGING AS APPLIED TO AN ALLUVIAL GOLD
DEPOSIT
B.M. Davis 337
21 - ESTIMATING LOCAL RECOVERABLE RESERVES VIA
INDICATOR KRIGING
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 435
26 - ISOfACTORIAL MODELS AND CHANGE Of SUPPORT
G. Matheron 449
viii TABLE OF CONTENTS
27 - GEOSTATISTICAL APPLICATION IN TABULAR STYLE
LEAD-ZINC ORE AT PINE POINT CANADA
G.F. Raymond 469
28 - LOCAL ESTIMATION OF THE BLOCK RECOVERY FUNCTIONS
A. Soares 485
29 - THE BLOCK DISTRIBUTION GIVEN A POINT MULTIVARIATE
NORMAL DISTRIBUTION
G. Verly 495
PART VI - SPECTRAL ANALYSIS AND DATA ANALYSIS
LECTURE
30 - THREE-DIMENSIONAL. FREQUENCY-DOMAIN SIMULATIONS OF
GEOLOGICAL VARIABLES
L. Borgman. M. Taheri. R. Hagan 517
CONTRI BUTlONS
31 - FACTORIAL KRIGING ANALYSIS: A SUBSTITUTE TO
SPECTRAL ANALYSIS OF MAGNETIC DATA
A. Galli. F. Gerdll-Neuillet. c. Dadou 543
32 - THE FACTORIAL KRIGING ANALYSIS Of REGIONALIZED
DATA. ITS APPLICATION TO GEOCHEMICAL PROPECTING
L. Sandjivy 559
33 - THE ANALYSIS OF SECOND-ORDER STATIONARY PROCESSES:
TIME SERIES ANALYSIS. SPECTRAL ANALYSIS. HARMONIC
ANALYSIS. AND GEOSTATISTICS
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 confer
ence. 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 evi
dence 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 wid
ened 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 pro
ceedings 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.
The Organizing Committee
George Verly
Michel David
Andre Journel
Alain Marechal
Stanford, October 1983
xi