SEISMIC SURFACE WAVES IN A LATERALLY INHOMOGENEOUS EARTH

Transcription

1 SEISMIC SURFACE WAVES IN A LATERALLY INHOMOGENEOUS EARTH

2 MODERN APPROACHES IN GEOPHYSICS formerly Seismology and Exploration Geophysics VOLUME 9 Managing Editor: G. NOLET, Department of Theoretical Geophysics, University of Utrecht, The Netherlands Editorial Advisory Board B. L. N. KENNETT, 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 Theoretical Geophysics, University of Utrecht, The Netherlands The titles published in this series are listed at the end of this volume.

3 SEISMIC SURFACE WAVES IN A LA TERALL Y INHOMOGENEOUS EARTH Edited by V. I. KElLIS-BOROK Institute of Physics of the Earth, Academy of Sciences of the u.s.s.r., Moscow, u.s.s.r. With contributions by A. L. Levshin*, T. B. Yanovskaya**, A. V. Lander*, B. G. Bukchin*, M. P. Barmin*, L. I. Ratnikova* and E. N. Its** * Institute oj Physics oj/he Earth, Academy o[sciences o(the U.S.S.R., Moscow, u..)'.s.r. ** Faculty oj Physics, Leningrad State University, Leningrad, u.s.s. R. KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON

4 Library of Congress Cataloging-in-Publication Data Poverkhnostnye selsmicheskie volny v gorizontal'no-neodnorodnoi Zemle. English. Seismic surface waves in a laterally inhomogeneous earth / edited by V. I. Keilis Borck; with contributions by AL Levshin... ret al.]. p. cm. - (Modern approaches in geophysics; 9) Translation of: Poverkhnostnye seismicheskie volny v gorizontal 'noneodnorodnoi Zemle. Includes index. ISBN-13: e-isbn-13: DOl: / Seismic waves. I. Kellis-Borck, VladimirIsaakovich. II. Levshin, A. L. (Anatolil L'vovich), Ill. Title. IV. Series. QE538.5.P '2-dc Puhlished hy Kluwer Academic Puhlishers, P.O. Box 17,3300 AA Dordrecht. The Netherlands. Kluwer Academic Publishers incorporates tht: publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distrihuted in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed hy Kluwer Academic Puhlishers Group, P.O. Box 322, 33()O AH Dordrt:cht, The Netherlands. Originally puhlished as Poverkhnostnye seismieheskie volny v gorizontai'no-neodnorodnoi Zemle Translated from the Russian hy A. L. Petrosyan Ill'ill/n/1l1I (liid /1'(''' /1(111('1' All Rights Reserved This English edition IYWI hy Kluwer Academic Publishers Original IYX6 by Nauka, Moscow Softcover reprint of the hardcover 1 st edition 1989 No part of the material protected hy 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.

5 CONTENTS Introduction VII PART 1. THEORY C H APT E R 1. Surface waves in vertically inhomogeneous media 1.1. Equations of motion for an elastic medium 1.2. Sources of seismic disturbance 1.3. Surface waves due to a point source in a vertically varying halfspace 1.4. Physical interpretation; some simple examples 1.5. Sphericity corrections; variational formulas 1.6. Effects of anelasticity 1.7. Synthetic seismograms CH APTER 2. Surface waves in media with weak lateral inhomogeneity Formulation of problems of surface wave propagation in a halfspace with weak lateral inhomogeneity Propagation of harmonic surface waves Propagation of transient surface waves Calculation of geometrical spreading for space-time rays Reflection and refraction of space-time rays at a discontinuity Space-time rays and geometrical spreading in the spherical case On the configuration of space-time rays 6g CH APTER 3. Surface waves in media involving vertical contacts Statement of the problem A review of available theoretical results Approximate calculation of surface wave reflection and transmission coefficients at a contact A numerical method for determining the displacement field Oblique contact and other possible refinements 93 C H A PT E R 4. Computation techniques for surface waves On the matrix method for one-dimensional boundary value problems A numerical method for solving one-dimensional boundary value problems 100 v g

6 VI CONTENTS 4.3. Dynamic ray tracing 4.4. Calculation of reflection and transmission coefficients PART 2. INTERPRETATION OF SURFACE WAVE OBSERV ATIONS 129 CHAPTER 5. Recording, identification, and measurement of surface wave parameters 13 I 5.1. Recording techniques and equipment in surface wave observations 13 I 5.2. Basics of surface wave processing Frequency-time analysis Linear polarization analysis Spatial analysis of surface waves 17~ CHAPTER 6. Methods for quantitative interpretation of observations I ~ A review of recent approaches to the inversion of surface wave data 1 ~ Least squares and singular value decomposition I ~ Quadratic programming methods I ~ Modelling experimental data in a block structure 1<J I 6.5. Backus-Gilbert method 2() I 6.6. Surface wave tomography based on a combined use of phase and group velocities for different periods 2 I The influence of lateral inhomogeneity on the measurement of surface wave attenuation ~. Anisotropy or inhomogeneity? Estimation of earthquake source parameters 229 CHAPTER 7. Some results from studies of regional lithospheric structure hy surface waves The method of path elimination in a study of the Eurasian crust Results obtained by the Backus-Gilbert method Anomalous Rayleigh surface waves in northeast Eurasia 273 References Index 291 2~ I

7 INTRODUCTION Surface waves form the longest and strongest portion of a seismic record excited by explosions and shallow earthquakes. Traversing areas with diverse geologic structures, they 'absorb' information on the properties of these areas which is best retlected in dispersion, the dependence of velocity on frequency. The other properties of these waves - polarization, frequency content, attenuation, azimuthal variation of the amplitude and phase - arc also controlled by the medium between the source and the recording station; some of these are affected by the properties of the source itself and by the conditions around it. In recent years surface wave seismology has become an indispensable part of seismological practice. The maximum amplitude in the surface wave train of virtually every earthquake or major explosion is being measured and used by all national and international seismological surveys in the determination of the most important energy parameter of a seismic source, namely, the magnitude M,. The relationship between M, and the body wave magnitude fi1t, is routinely employed in identification of underground nuclear explosions. Surface waves of hundreds of earthquakes recorded every year are being analysed to estimate the seismic moment tensor of earthquake sources, to determine the periods of free oscillations of the Earth, to construct regional dispersion curves from which in turn the crustal and upper mantle structure in various areas is derived, and to evaluate the dissipative parameters of the mantle material. Work has begun on surface wave 'tomography' of the Earth's mantle - identification of lateral inhomogeneities and elastic anisotropy from worldwide seismic observations. Surface waves from explosions and earthquakes are being used to study relatively inaccessible areas, for instance in a search for major sedimentary basins in the Arctic shelf. These spectacular successes of surface wave seismology have been made possible by recent developments in long-period seismic instrumentation, seismic arrays, and the array-like use of national and international networks of long-period stations. On the other hand, computerization has helped in the development of methods for the analysis of surface wave observations that could more accurately estimate surface wave dispersion and polarization. Techniques of quantitative data interpretation have been developed that can effectively determine velocity and density models consistent with the observations and evaluate the non-uniqueness and resolution of the data. All these results were essentially based on an advanced theory and efficient techniques for calculating the spectral characteristics and wave fields of surface waves in vertically and radially varying structures. VII

8 Vlll INTRODUCTION The progress in surface wave seismology highlighted the inadequacies in the theoretical model of the medium underlying data interpretation as contrasted with the presently available accuracy and detail in the observations, as well as with the problems that needed to be solved. The structures studied today have considerable near-surface and deep lateral inhomogeneities that manifest themselves both as smooth variations in velocity and density with distance (within major blocks of the continental and oceanic lithosphere) and as sharp contrasts in velocity and density at boundaries between blocks with differing deep structure, in subduction zones, geosynclinal depressions, intra-continental basins, rifts, island arcs etc. In recent years investigators in the USSR and elsewhere have been conducting a number of theoretical and experimental studies (on models and in the field) of surface wave effects caused by such lateral inhomogeneities. This work has yielded results that are valuable for applications: approaches have been found that have enabled the treatment of observations, under certain assumptions, within the framework of laterally varying models and the derivation of meaningful information on the inhomogeneities using theoretically sound methods (from the standpoint of physics). It has become possible to pose new problems for surface wave seismology that arc based on advanced concepts of the properties of seismic field" in inhomogeneous media. This monograph is an attempt to present a unified exposition of these novel theoretical and interpretation approaches, as well as of their application in specific problems. The book consists of two parts. The first part is devoted to forward problems in the surface wave seismology of inhomogeneous media. Chapter I presents the fundamentals of surface wave theory for vertically and radially varying media. A description of seismic sources is provided based on the theory of stress glut; the main properties of waves excited by some kinds of point sources are considered together with various factors that affect them; examples are discussed for the simplest (classical) sources. Included is an account of efficient methods for incorporating sphericity, anelasticity, and the main properties of seismograms. Chapter 2 is concerned with smooth lateral inhomogeneities as they affect the surface wave field. Asymptotic approaches are described providing ray representations for the leading term in the displacement transported by harmonic and transient surface waves. Transient wave fields are being studied by spatial ray tracing; the fundamentals of the theory of space-time surface wave rays are presented for media involving smooth lateral inhomogeneities. Chapter 3 propounds an approximate technique for treating a vertical contact in surface wave propagation. The technique uses Green functions to calculate reflection and transmission coefficients for plane waves incident at an arbitrary angle on a plane vertical contact between two quarter-spaces of differing structure. The accuracy of the method is evaluated by comparison with the results of more exact calculations that include the contribution of diffracted waves. Complications are considered such as inclined contact discontinuities or fault zones with very low rigidity. Chapter 4 contains algorithms for solving forward problems in surface wave theory. It describes the algorithms the authors used to compute spectral parameters for vertically varying media, reflection and transmission coefficients for vertical contacts. We present ray-geometric algorithms for media involving smooth lateral inhomogeneities. Each technique is illustrated by practical examples.

9 INTRODUCTION IX The second part of the book treats questions arising In data analysis and interpretation. Chapter 5 describes the modern methods in use for recording and analyzing long-period information. A mathematical model of the dispersed seismic signal is presented and examined. The potential and limitations of spectral and frequencytime methods of signal separation and dispersion measurement are demonstrated. Polarization and spatial analysis are used to provide ways of separating interfering waves and measuring their parameters. Chapter 6 considers quantitative interpretation of surface wave dispersion. It begins with a review of recent progress. Two different approaches are considered in great detail which allow extraction of local information from observations involving areas with different deep structures. One of these approaches does not require prior information about the area of study and seeks lateral perturbations to phase and group velocities using a two-dimensional analogue of the widely known Backus-Gilbert technique. The other implies a regionalization of the study area and determines regional dispersion curves for individual laterally homogeneous regions using nonlinear programming methods. Errors are examined that arise in the interpretation of surface wave data hecause of neglected lateral inhomogeneities, along with some inhomogeneityrelated phenomena that might he attributed to anisotropy. Inverse problems for earthquake sources hased on surface wave ohservations are formulated. Chapter 7 gives an account of some results in the interpretation of surface waves recorded hy seismological stations. Crustal velocity structures are presented for a number of areas in Eurasia obtained by successive elimination of paths and maps of group velocity distribution for some continental and oceanic areas. Dispersion and polarization effects due to an extended anomalous zone in northeastern Siberia are studied, the zone being located around a hypothetical continental riftogenesis area. This monograph is a joint work by several authors. The Introduction, Chapter I (except for Section 1.2), Sections 5.1, 5.5, and 6.7 are written by A. L. Levshin; Chapters 2 and 3 (excluding Section 3.4), Sections 4.1, 4.3, 6.1, 6.5, 6.6 and 7.2 are by T. B. Yanovskaya; A. V. Lander is responsible for Sections 5.2 through 5.4, and 7.3, B. G. Bukchin for Sections 1.2, 3.4, and 6.9, M. P. Barmin for Sections 4.2,6.2 through 6.4, L. I. Ratnikova for Sections 6.8 and 7.1, E. N. Its for Section 4.4. The materials used were collected in collaboration with K. A. Berteussen, P. Malischewski, T. M. Sabitova, S. E. Kapitanova, O. E. Starovoit, A. N. Nesterov and published in joint papers. We are sincerely grateful to all these colleagues.