Table Of ContentSEISMIC TOMOGRAPHY
SEISMOLOGY AND EXPLORATION GEOPHYSICS
Managing Editor:
G. NOLET, Department of Theoretieal Geophysics,
University of Utrecht, The Netherlands
Editorial Advisory Board:
B. L. N. KENNETI, Research School of Earth Sciences,
The Australian National University, Canberra, Australia
R. MADARIAGA, Institut Physique du Globe,
Universite Paris VI, France
R. MARSCHALL, Prakla-Seismos AG, Hannover, F.R.G.
R. WORTEL, Department of Theoretieal Geophysics,
University of Utrecht, The Netherlands
SEISMIC
TOMOGRAPHY
With Applications
in Global Seismology and
Exploration Geophysics
Edited by
GUUSTNOLET
Department of Theoretieal Geophysics,
Utrecht University, The Netherlands
D. REIDEL PUBLISHING COMPANY
A MEMBER OF THE KLUWER ACADEMIC PUBLlSHERS GROUP
DORDRECHTjBOSTONjLANCASTERjTOKYO
Library of Congress Cataloging in Publication Data
Seismie tomography.
(Seismology and exploration geophysies)
Bibliography: p.
Ineludes index.
1. Seismic waves-Data processing. 2. Tomography. I. Nolet,
Guust, 1945- . II. Series.
QE538.5.S429 1987 551.2/2 87-9826
ISBN-13: 978-90-277-2583-7 e-ISBN-13: 978-94-009-3899-1
001: 10.1007/978-94-009-3899-1
Published by D. Reidel Publishing Company,
P.O. Box 17, 3300 AA Dordrecht, Holland.
Sold and distributed in the U.S.A. and Canada
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In all other countries, sold and distributed
by Kluwer Academie Publishers Group,
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All Rights Reserved
© 1987 by D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of the hardcover 1s t edition 1987
No part of the material protected by this copyright ootiee may be reproduced or
utilized in any form or by any means, electrooie or mechanical
ineluding photocopying, recording or by any information storage and
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LIST OF CONTENTS
List of Authors vii
Preface ix
INTRODUCTION
1 G. Nolet -Seismic wave propagation and seismic tomography
PART I: BASIC THEORY
2 CB. Chapman -The Radon transform and seismic tomography 25
3 A. van der Sluis and H.A. van der Vorst - Numerical solution of large,
sparse linear algebraic systems arising from tomographic problems 49
4 E. Wielandt - On the validity of the ray approximation for interpreting
delay times 85
5 V. Cerveny - Ray tracing algorithms in three-dimensional laterally
varying layered structures 99
PART II: APPLICATIONS IN SEISMIC EXPLORATION
6 A. Tarantola -Inversion of travel times and seismic waveforms 135
7 S. Ivansson -Crosshole transmission tomography 159
8 P. Firbas -Tomography from seismic profHes 189
vi LIST OF CONTENTS
9 A. Nur - Seismic rock properties for reservoir descriptions and
monitoring 203
PART III: APPLIeATIONS IN GLOBAL SEISMOLOGY
10 G. Poupinet -Seismic data collection platforms for satellite transmission 239
11 A. Moretli and A.M. Dziewonski -The harmonic expansion approach to
the retrieval of deep Earth structure 251
12 N. Jobert and G. Jobert -Ray tracing for surface waves 275
13 G. Nolet -Waveform tomography 301
14 R. Snieder -Surface wave holography 323
15 L.J. Ruff -Tomographic imaging of seismic sources 339
References 367
Index 383
LIST OF AUTUORS
V. ~erveny Inst. of Geophysics, Ke Karlovu 3, Praha 2, Czechoslovakia.
C.R. Chapman Bullard Laboratories, Dept. of Earth Sciences, University of Cambridge, Madingley
Rise, Madingley Road, Cambridge, CB3 OEZ, UK.
A.M. Dziewonski Hoffman Laboratory, Harvard University, 20 Oxford Street, Cambridge MA 02138,
USA.
P.Firbas Geofyzika n.p. Bmo, Jecna 29a, 61246 Bmo, Czechoslovakia.
S.Ivansson Forsvarets Forskningsanstalt, PO Box 27322, S 10254 Stockholm, Sweden.
G. Jobert Institut de Physique du Globe, Universite de Paris 6, 4 Place Jussieu, F75252 Paris,
France.
N. Jobert Institut de Physique du Globe, Universite de Paris 6, 4 Place Jussieu, F75252 Paris,
France.
A. Morelli Hoffman Laboratory, Harvard University, 20 Oxford Street, Cambridge MA 02138,
USA.
G. Nolet Department of Theoretical Geophysics, Budapestlaan 4, 3584 CD Utrecht, The
Netherlands.
A. Nur Rock Physics and Borehole Geophysics Laboratory, Dept. of Geophysics, Stanford
Universily, Stanford, CA 94305, USA.
G. Poupinet IRIGM, Observatoire de Grenoble, BP 68, F38402 St Martin d'Heres, France.
L.J. Ruff Department of Geological Sciences, University of Michigan, MI 48109 Ann ArbOf,
USA.
A. van der Sluis Mathematical Institute, Budapestlaan 6, 3584CD Utrecht, The Netherlands.
R. Snieder Department of Theoretieal Geophysics, Univefsity of Utrecht, Budapestlaan 4, P.O.
Box 80.021, 3508 TA Utrecht, The Netherlands.
A. Tarantola Institut de Physique du Globe, Universite de Paris 6, 4 Place Jussieu, F75252 Paris,
France.
R.A. van der Vorst Faculty of Mathematics and Informaties, Delft University of Technology, PO Box 356,
2600 AJ Delft, The Netherlands.
E. Wielandt Institute of Geophysics, Swiss Federal Institute of Technology (ETH), CH -8093 Zurich,
Switzerland.
vii
PREFACE
Methods to eonstruet images of an objeet from "projeetions" of x-rays, ultrasound or
eleetromagnetie waves have found wide applieations in eleetron mieroseopy, diagnostie
medicine and radio astronomy. Projeetions are measurable quantities that are a funetional -
usually involving a line integral - of physieal properties of an objeet. Convolutional
methods, or iterative algorithms to solve large systems of linear equations are used to
reeonstruet the objeet. In prineiple, there is no reasan why similar image reeonstruetions
ean not be made with seismie waves. In praetiee, seismic tomography meets with a number
of diffieulties, and it is not until the last deeade that imaging of transmitted seismie waves
has found applicatian in the Earth sciences.
The most important differenee between global seismie tomography and mare
eonventional applieations in the laboratory is the faet that the seismologist is eonfronted
with the lack of anything resembling a well-eontrolled experimental set-up. Apart from a
few nuelear tests, it is not in our power to locate or time seismie events. Apart from a few
seabattom seismographs, our sensors are located on land -and even there the availability of
data depends on eultural and politieal factors. Even in exploratian seismics, praetieal
faetors such as the east of an experiment put strong limitations on the eompleteness of the
data set.
The most eommonly used datum is the relative delay of a seismie wave. These delays
ean -in general -be obtained only with very low precision. Furthermore, unIike x-rays in a
human body, seismie waves in the Earth follow strongly eurved rays, and the geometry of
the ray is an extra unknown in the formulation of the problem.
These diffieulties notwithstanding, seismie tomography has already yielded useful
results, both in exploration seismies and in global seismology. In faet, some of the images
obtained are so speetaeular that many Earth scientists may be tempted to forget about the
limited resolution or the large errors in the final result.
This book deseribes the state of the art in seismie tomography, with an emphasis on the
methods, rather than on the results. An introduetory ehapter has been ineluded to make the
book aeeessible to non-speeialists or students with only a limited knowledge of seismie
wave propagation. The remainder of the book has been divided in three parts. The first part
eontains a few ehapters with theoretieal results that are basie to any application of seismie
tomography. Even though some of these ehapters eontain newand important theoretieal
results, I have asked the authors to give these ehapters a slight tutorial flavour, so as to
ix
x PREFACE
bridge the gap between the introduction and the more specialist contributions. This is
followed by a section on applieations in exploration seismies. The book is concluded by a
number of chapters describing applications in global seismology. The division between
"exploration" seismies and "global" seismology is not striet, and it is certainly not my
intention to encourage readers to skip part of the book: most of the chapters contain
material of very general interest to all Earth scientists working with tomographie methods.
No effort has been made to make the notation uniform, or to eliminate redundancies.
Thus, every chapter can be read independently and it should be fairly easy to make a
selection for a one- or two-semester course for graduate students.
I wish to thank Michiel ten Raa and Roger Cooper of Reidel Publishing Company for
stimulating me to edit this book. Several interested students: Tijmen-Jan Moser, Berend
Scheffers, Hong-Kie Thio and Alet Zielhuis assisted in the textprocessing and
proofreading.
Utrecht, January 1987
Guust Nolet
Chapter 1
Seismie wave propagation and seismie tomography
G. Nolet
This ehapter develops the basie prineiples of seismie tomography and serves as a general
introduction to this book.
1. Introduction
Ever sinee the first seismometers were plaeed on the surfaee of the Earth near the end of
the 19th eentury, seismie waves have been used to loeate remote "objects". The first
applieations involved the loeation of earthquake epicenters in far-away regions. Efforts
during the first World War to locate heavy artillery by seismie and aeoustie means evolved
later to the first exploration methods for oil and gas (Bates et al., 1982). The imaging
technique in exploration seismies -eommonly referred to as migration -has been improved
ever sinee: at first it merely involved the interpretation of arrival times of observed seismie
pulses in terms of the depth and slope of refteeting surfaees; later, eomplete seismie reeords
were used and imaging methoos were developed that are firmly based on the aeoustie wave
equation (see Claerbout, 1985, for referenees).
Imaging in global seismology stayed far behind the developments in exploration
seismies for several reasons: in eontrast to artifieial sources, earthquakes are uneontrolled,
badly plaeed sourees of wave energy; the Earth is only sparsely covered with
seismometers; instrument responses were for a long time widely different and reeording
was -and often is -not in digital form, although reeent developments may soon ehange this
for the better (Nolet et al., 1986). Thus, seismologists are faeed with the paradox that the
available data contain erueial gaps, despite their enormous volume. The most powerful
data souree in global seismology is not in faet the eolleetion of individual seismograms
G. Nolet (ed.), Seismic Tomography, 1-23.
© 1987 by D. Reidel Publishing Company.
