SEISMOLOGY AND EXPLORATION GEOPHYSICS. Managing Editor: Editorial Advisory Board:

Transcription

1 SEISMIC TOMOGRAPHY

2 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

3 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

4 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, II. Series. QE538.5.S / ISBN-13: e-isbn-13: : / Published by D. Reidel Publishing Company, P.O. Box 17, 3300 AA Dordrecht, Holland. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norweil, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academie Publishers Group, P.O. Box 322, 3300 AH Dordrecht, Holland. All Rights Reserved 1987 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover 1 st 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 retrieval system, without written oermission from the coovri!!ht owner

5 LIST OF CONTENTS List of Authors Preface vii ix INTRODUCTION 1 G. Nolet - Seismic wave propagation and seismic tomography PART I: BASIC THEORY CB. Chapman - The Radon transform and seismic tomography A. van der Sluis and H.A. van der Vorst - Numerical solution of large, sparse linear algebraic systems arising from tomographic problems E. Wielandt - On the validity of the ray approximation for interpreting delay times V. Cerveny - Ray tracing algorithms in three-dimensional laterally varying layered structures PART II: APPLICATIONS IN SEISMIC EXPLORATION A. Tarantola - Inversion of travel times and seismic waveforms S. Ivansson - Crosshole transmission tomography P. Firbas - Tomography from seismic profhes

6 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 11 A. Moretli and A.M. Dziewonski - The harmonic expansion approach to the retrieval of deep Earth structure 12 N. Jobert and G. Jobert - Ray tracing for surface waves 13 G. Nolet - Waveform tomography 14 R. Snieder - Surface wave holography 15 L.J. Ruff - Tomographic imaging of seismic sources References Index

7 LIST OF AUTUORS V. ~erveny C.R. Chapman A.M. Dziewonski P.Firbas S.Ivansson G. Jobert N. Jobert A. Morelli G. Nolet A. Nur G. Poupinet L.J. Ruff A. van der Sluis R. Snieder A. Tarantola R.A. van der Vorst E. Wielandt Inst. of Geophysics, Ke Karlovu 3, Praha 2, Czechoslovakia. Bullard Laboratories, Dept. of Earth Sciences, University of Cambridge, Madingley Rise, Madingley Road, Cambridge, CB3 OEZ, UK. Hoffman Laboratory, Harvard University, 20 Oxford Street, Cambridge MA 02138, USA. Geofyzika n.p. Bmo, Jecna 29a, Bmo, Czechoslovakia. Forsvarets Forskningsanstalt, PO Box 27322, S Stockholm, Sweden. Institut de Physique du Globe, Universite de Paris 6, 4 Place Jussieu, F75252 Paris, France. Institut de Physique du Globe, Universite de Paris 6, 4 Place Jussieu, F75252 Paris, France. Hoffman Laboratory, Harvard University, 20 Oxford Street, Cambridge MA 02138, USA. Department of Theoretical Geophysics, Budapestlaan 4, 3584 CD Utrecht, The Netherlands. Rock Physics and Borehole Geophysics Laboratory, Dept. of Geophysics, Stanford Universily, Stanford, CA 94305, USA. IRIGM, Observatoire de Grenoble, BP 68, F38402 St Martin d'heres, France. Department of Geological Sciences, University of Michigan, MI Ann ArbOf, USA. Mathematical Institute, Budapestlaan 6, 3584CD Utrecht, The Netherlands. Department of Theoretieal Geophysics, Univefsity of Utrecht, Budapestlaan 4, P.O. Box , 3508 TA Utrecht, The Netherlands. Institut de Physique du Globe, Universite de Paris 6, 4 Place Jussieu, F75252 Paris, France. Faculty of Mathematics and Informaties, Delft University of Technology, PO Box 356, 2600 AJ Delft, The Netherlands. Institute of Geophysics, Swiss Federal Institute of Technology (ETH), CH Zurich, Switzerland. vii

8 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

9 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