Table Of ContentGEOSOUNDPIRNIGN CIP1L ES,
ResisStoiuvnidtMiyen ags urements
�.,
· 1
SERIES
Methods in Geochemistry and Geophysics
1. A.S. RITCH! E
CHROMATOGRAPHY IN GEOLOGY
2. R. BOWEN
PALEOTEMPERATURE ANALYSIS
3. D.S. PARASNIS
MINING GEOPHYSICS
,·
4. I. ADLER
X-RAY EMISSION SPECTROGRAPHY IN GEOLOGY
5. THE LORD ENERGL YN AND L. BRE ALY
ANALYTICAL GEOCHEMISTRY
6. A.J. EASTON
CHEMICAL ANALYSIS OF SILICATE ROCKS
7. E.E. ANGINO ANO G.K. �ILLINGS
ATOMIC ABSORPTION SPECTROMETRY IN GEOLOGY
8. A. VOLBORTH
ELEMENTAL ANALYSIS IN GEOCHEMISTRY
A: MAJOR ELEMENTS
9. P.K. BHATTACHARYA ANO H.P. PATRA
DIRECT CURRENT GEOELECTRIC SOUNDING
10. J.A.S. ADAMS AND P. GASPARI NI
GAMMA-RAY SPECTROMETRY OF ROCKS
11. W. ERNST
GEOCHEMICAL FACIES ANALYSIS
12. P.V. SHARMA
GEOPHYSICAL METHODS IN GEOLOGY
13. C.H. CHEN (Editor)
COMPUTER-AIDED SEISMIC ANALYSIS AND DISCRIMINATION
148. H.P. PATRA and K. MALLICK
GEOSOUNDING PRICIPLES, 2. TIME-VARYING GEOELECTRIC
SOUNDINGS
-
METHODS IN GEOCHEMISTRY AND GEOPHYSICS, 14A
GEOSOUNDING
PRINCIP1L ES,
ResisStoiuvnidtMiyen ags urements
OTTO KOEFOED
Geophysical Laboratory
Department of Mining,
Delft University of Technology,
Delft, The Netherlands
ELSEVIER SCIENTIFIC PUBLISHING COMPANY
Amsterdam - Oxford - New York 1979
ELSEVIER SCIENTIFIC PUBLISHING COMPANY
Molenwerf 1
P. 0. Box 211, 1000 AE Amsterdam, The Netherlands
Distributors for the United States and Canada:
ELSEVIER SCIENCE PUBLISHING COMPANY INC.
52, Vanderbilt Avenue
New York, N.Y. 10017
First edition 1979
Second impression 1982
l.ihrary of Congress Cataloging in Publication Dala
Koefoed, Otto,
1913-
Geosounding principles.
(Methods in geochemistry and geophysics ; 14A
Bibliography: p.
Includes index.
CONTENTS: 1. Resistivity sounding measurements.
l. ProGpecting --Geophysical methods. I. Title.
TN269.K53. 622. ' .159 79-14798
ISBN o-444-41704-4 (v. l)
ISBN 0-444-41704-4 (Vol. 14A)
ISBN 0-444-41690·0 (Series)
e
© Els vier Scientific Publishing Company, 1979
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system
or transmitted in any form or by any means, electronic, mechanical, photocopying, recording
or otherwise, without the prior written permission of the publisher,
e
Elsevi r Scientific Publishing Company, P.O. Box 330, 1000 AH Amsterdam, The Netherlands
Printed in The Netherlands
For Netty in love and gratitude
VII
PREFACE
The technique of the interpretation of resistivity sounding measurements
has passed through a phase of stormy development during the past decade.
In
particular the publication, in 1970, of the application of the linear filter
method to resistivity sounding interpretation has made the computations
that are essential to an exhaustive interpretation of the measurements amen
able to execution at a reasonably low cost. A second development of the last
decade which is equally important to the practice of the interpretation of
resistivity soundings, has taken place in computer technology -a develop
ment towards ever smaller, ever cheaper and ever more variegated computers
and calculators. Together, these two developments have completely changed
the face of resistivity sounding interpretation. Formerly, most of the inter
pretation was done by approximate methods, and only large organizations
could afford an exact interpretation. At present, an exact interpretation of
the data is within the scope of every user of the resistivity sounding method.
In view of these changes in the technique and the practice of resistivity
sounding interpretation, it seemed timely to produce a book describing the
newly developed techniques. The present book is aimed at both those who
are engaged in research in the field. of resistivity sounding interpretation, and
those who apply the resistivity sounding method in practice. In the descrip
tion and development of those computational procedures that are intended
to be used for exact interpretation on a routine basis, special attention has
been devoted to the needs of users who have only limited computational
facilities at their disposal. All the essential computations for routine interpre
tation can now be carried out on fairly cheap desk calculators which even
smaller organizations can afford. Programs for these computations, written
Basic,
in are included in this book. For the benefit of isolated field parties,
programs·for those computations which can be carried out on a programm
able pocket calculator are also included. Since there is a multitude of types
of these calculators, each of them using its own programming language, a
0f
choice language had to be made. The language in which these programs
are presented is that of the Texas Instruments SR-52 programmable pocket
calculator -one which I found to be very serviceable for resistivity sounding
computations.*
It is essential that a book on a developing science should contain as much
recent information as possible. In this respect I have greatly. benefited by the
excellent relations that exist among the practioners of the geophysical pro-
*The more recent Texas Instruments pocket calculator TI-59 is also very suitable for the
purpose.
VIII
fession in Europe. The credit for having fostered these relations goes to the
European Association of Exploration Geophysicists, which has succeeded in
creating a climate in which good relations naturally develop. Among those
with whom I have had illuminating discussions at various times, I am grateful'
to R. Drecun, H. Flathe, D.P. Ghosh, A.C.R. Ketelaar, J. Lapajne, D. Ravnic
and F. Sumi. In addition to useful discussions, several people have contrib
uted to the present book by making typescripts of their papers available to
me prior to publication and, in a number of cases, by providing me with
additional unpublished information; for this I am indebted to the following:
M. Bemaqini and E. Cardarelli of the University of Rome; to Mrs. M.M. Cec
chi, M. Marchisio and C. Montani of the University of Pisa; to H.K. Johan
sen of the University of Lulea; to K. Mallick of the National Geophysical
Research Institute at Hyderabad; to D. Marsden, then of the University of
Leeds; and to A.A.R. Zohdy of the United States Geological Survey. In some
instances I have also made use of manuscripts sent to me for reference by
editors of geophysical journals. I am indebted to W. van Dalfsen, P.G. van
Dongen, G. de Snoo and F. Walter, all of the Groundwater Survey T.N.0. at
Delft, for providing me with valuable information, and to D.S. Parasnis for
valuable suggestions after he had read a part of the typescript of the present
book. I am indebted to' the Waterleiding Maatschappij "Overijssel" for
putting the results of their Salland geoelectrical survey at my disposal. I am
grateful to D.T. Biewinga of the Technological University, Delft, for carrying
out the Noordwijk resistivity survey, discussed in one of the sections of this
book. I am indebted to J.J. Swanink for his zeal and craftsmanship in mak
ing the drawings for this book.
My deepest gratitude is to my wife Netty, whose never-failing endurance
and encouragement created the atmosphere in which it was possible for me
to write this book.
IX
CONTENTS
VII
PREFACE .. . . XII
NOTATION . ..
1
CHAPTER 1. THE FIELD PROCEDURE AND METHOD OF MEASURING 1
1.1 Introduction .................. .. 1
1. 2 Electrode configurations ........... . 5
1. 3 The choice of the site of the measurement 7
1. 4 The current circuit . .. . .. ...... .
10
1. 5 The potential measuring circuit ..
1.6 Example of a complete instrument . . 14
CHAPTER 2. THE POTENTIAL DISTRIBUTION AT THE SURFACE OF A
19
HORIZONTALLY STRATIFIED EARTH .. .. .. ..... . .. .
19
2.1 Introduction ...... ........ . . .. ......... ... .. .. ... . . .. ..
2.2 The differential equation for a potential field with cylindrical symmetry and
its general solution .... . .. ..... .......... . . .. . ... ........ . 20
2.3 Adaptation of the solution to the boundary conditions ..... .. . ...... 2 3
2. 4 Summary .... .... .... .. .. . ........ .... ............... . 27
CHAPTER 3. THE KERNEL FUNCTION AND ITS RELATION TO THE SUB·
29
SURF ACE PARAMETERS . ....... .. .. . . . . ... .
29
3. 1 Introduction .... ..... .. . . . .. .......... . . .. .... ... .
3.2 Derivation of the Flathe recurrence relation . .. , , , , , , , . , . , .. , 30
3. 3 Derivation of the Pekeris recurrence relation . ...... .......... 33
35
3. 4 Discussion of the recurrence relations ..... .. .. .. . . .... ... .
3. 5 Ambiguity in the relation between the resitivity transform and the subsur-
38
face layer distribution . ... .. .... . . . ......... . . . .. ... .. . ..
CHAPTER 4. THE APP ARENT RESISTIVITY FUNCTION .. . .. . .. .. . . 41
4. 1 Definition of the apparent resistivity . . . . . . .......... ......... . 41
4.2 Calculation of the apparent resistivity from the field observations .. .. .. . 41
4.3 The.r elation between the apparent resistivity and the resistivity transform
function for symmetrical linear electrode configurations . . . .. ... .. . .. . 4 2
4.4 The relation between the apparent resistivity and the resistivity transform
function for dipole electrode configurations ........ .. ... ... . . . .. . 45
49
4.5 Expressions for the apparent resistivity functions in logarithmic variables .. . 50
4.6 Principles of digital linear filtering ........ .. .... .. ........... .
53
4.7 Adjustment of the apparent resistivity curves in Schlumberger measurements
CHAPTER 5. METHODS FOR THE DETERMINATION OF RESISTIVITY
59
FILTERS .. . .. . .. .. . ..... . . . . ... .. ........
59
5.l Introduction ... . .... . .. . .. .. ....... .. .... .. ... ... .
59
5. 2 Determination of resistivity filters by direct integration . ...· . .....
62
5. 3D etermination of resistivity filters by Fourier transformation .... . .
68
5.4 Determination of the horizontal shift between input and output samples .. .
71
5.5 Determination of resistivity filters by the least-squares method ....... . .
x
78
5. 6 Determination of resisti�ity filters by division of Z-transforms ....... .. .
5.7 Auxiliary functions for the determination and for the testing of resistivity
83
filters . . . . . .... ..... ..... . .. .. .. . .......... .. .. ..... .
CHAPTER 6. THE COMPUTATION OF APPARENT RESISTIVITY MODEL
CURVES . . ... .. . . . . ." .... . . .. . .. .. . . . .... .. .. . 89
6.1 Published collections of model curves ........ . . . .. . . . . .... .. . 89
6.2C omputation of model curves by numerical integration ....... .. . .. 89
6.3 Computation of model curves by the image point method ..... . . .. .. 90
6. 4 Computation of model curves by decomposition into partial fractions .. . 91
6.5 Computation of model curves by the linear filter method . . . .. .. 9 2
CHAPTER 7.: APPROXIMATE INTERPRETATION METHODS .... 10 3
7. 1 The auxiliary point method . . . . .... ... .. . ... . ........ . . . . 10 3
7. 2In terpretation methods using three-layer model curves ........ .. . ... . 107
7. 3I nterpretation method using two-layer resistivity transform curves ...... . 11 2
115
7.4 Equivalence rules . ...... .. .. ...... ..... .. . ........... . ..
118
7 . 5T he Dar Zarrouk curve ... ........ . .............. .. .. .....
7 . 6E xamples of application of approximate interpretation methods . ...... 1 22
CHAPTER 8. THE DERIVATION OF SCHLUMBERGER APPARENT RESIS
TIVITY CURVES FROM APPARENT RESISTIVITY CURVES
IN OTHER ELECTRODE CONFIGURATIONS . . . . . . . . . . . . 1 33
8. 1 Linear filter methods for the conversion of apparent resistivity curves in
133
other configurations into Schlumberger apparent resistivity curves ...... .
8.2T he Patella method of converting dipole apparent resistivity curves into
Schlumberger apparent resistivity curves ......... ......... ...... 1 35
CHAPTER 9.
ITERATIVE INTERPRETATION METHODS . ..... ...... . 141
9.1 Some general considerations ....................... ........ . 114481
9.2 Non-automatic iterative interpretation methods . .. ........ ...... . .
9.3 Examples of application of non-automatic iterative interpretation ....... 1 5 4
9.4 Automatic iterative interpretation by the method of steepest descent ... . . 1 60
9.5 Automatic iterative interpretation by solution of matrix equations .. . ... . 170
9. 6 The Marsden method of automatic iterative interpretation . ..... .. .... 17 4
9.7 The Zohdy method of automatic iterative interpretation ... . .... .. ... . 175
9.8 A fast method of automatic iterative interpretation . . ............ ... 179
9.9 Ex�mples of application of automatic iterative interpretation . .. ....... 185
CHAPTER 10. DIRECT INTERPRETATION METHODS ........ .. .. .... 19 3
193
10.1 Non-automatic direct interpretation methods . .. .......... . . .... .
10. 2T he Kunetz-Rocroi automatic direct interpretation method .... . ..... 19 6
10.3T he Koefoed automatic direct interpretation method .......... ... . . 201
10.4 The Szaraniec automatic direct interpretation method ......... ... . . 204
10.5 The revised Koefoed method of automatic direct interpretation ...... . . 208
10.6 Examples of application of direct interpretation . .\ . .. .. ... .... .. . . 21 5
CHAPTER 11. THE EFFECTS OF DEVIATIONS FROM THE FUNDAMENTAL
ASSUMPTIONS .. . ... .... ...... . . .. .. .·. . .. .. . .. . 223
11.1 The influence of anisotropy ................ .... .. .. ..... ... 223
11.2T he influence of a continuous change of the resistivity .. ... .· . .... ... 227
231
11.3T he influence of a slope of the boundary plane ..... .......... ... .
11.4 The influence of vertical contact planes . .......... ............ . 237
1 1.5 Marine. resistivity sounding measurements ..... ..... ... . ...... ... 239
