advances in geophysicszisin.geophys.tohoku.ac.jp/~sato/satohp2012/books_and...advances in geophysics...

Advances in

GEOPHYSICS

VOLUME 50

Advances in Geophysics

Volume 50

Earth Heterogeneity and Scattering Effectson Seismic Waves

Series Editor

RENATA DMOWSKA

School of Engineering and Applied Sciences

Harvard University

Cambridge, Massachusetts, USA

Guest Editors

HARUO SATO MICHAEL C. FEHLERDepartment of Earth,

Atmospheric, and Planetary Sciences,

Massachusetts Institute of Technology

Cambridge, USA

Department of Geophysics,

Graduate School of Science,

Tohoku University

Sendai, Japan

AMSTERDAM • BOSTON • HEIDELBERG • LONDONNEW YORK • OXFORD • PARIS • SAN DIEGO

SAN FRANCISCO • SINGAPORE • SYDNEY • TOKYOAcademic Press is an imprint of Elsevier

Academic Press is an imprint of Elsevier

Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands

32 Jamestown Road, London NW1 7BY, UK

360 Park Avenue South, New York, NY 10010–1710

30 Corporate Drive, Suite 400, Burlington, MA 01803, USA

525 B Street, Suite 1900, San Diego, CA 92101-4495, USA

First edition 2008

Copyright # 2008 Elsevier Inc. 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

Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in

Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: permissions@elsevier.

com. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.

com/locate/permissions, and selecting Obtaining permission to use Elsevier material

Notice

No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a

matter of products liability, negligence or otherwise, or from any use or operation of any methods,

products, instructions or ideas contained in the material herein. Because of rapid advances in the medical

sciences, in particular, independent verification of diagnoses and drug dosages should be made

ISBN: 978-0-12-374509-5

ISSN: 0065-2687

For information on all Academic Press publications

visit our website at books.elsevier.com

Printed and bound in Hungary

08 09 10 11 12 10 9 8 7 6 5 4 3 2 1

Dedicated to Keiiti Aki (1930–2005)Pioneer of short-period seismology

CONTENTS

CONTRIBUTORS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

Chapter 1

Coherent Back-Scattering and Weak Localization ofSeismic Waves

LUDOVIC MARGERIN

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. Weak Localization Effect: A Heuristic View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3. The Role of Source Mechanism and Wavefield Polarization . . . . . . . . . . . . . . . . . . . . . . . 6

3.1. Effect of Source Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2. Review of Multiple Scattering Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.3. Theoretical Results for Acoustic and Elastic Waves . . . . . . . . . . . . . . . . . . . . . . . . 10

4. Geophysical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.1. Measurement of the Dispersion Relation of Surface Waves . . . . . . . . . . . . . . . . . . 13

4.2. Measurement of the Diffusion Constant in Strongly

Scattering Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Chapter 2

Theory of Transmission Fluctuations in Random Media with aDepth-Dependent Background Velocity Structure

YINGCAI ZHENG AND RU-SHAN WU

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2. Acoustic Waves in Stratified Media and WKBJ Green Function . . . . . . . . . . . . . . . . . . 23

3. Rytov Solution to the Wave Equation in a Heterogeneous Medium . . . . . . . . . . . . . . . . 25

4. Complex Phase c Due to a Plane Wave Incidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5. Coherence Function Between Two Plane Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6. Coherence Functions Using Delta-Correlated Assumption . . . . . . . . . . . . . . . . . . . . . . . 33

7. Coherence Functions in a Constant Background Medium . . . . . . . . . . . . . . . . . . . . . . . 34

8. Numerical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

9. Validity of the Delta-Correlated Assumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

10. Discussions and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

vii

Chapter 3

Synthesis of Vector-Wave Envelopes in Random Elastic Mediaon the Basis of the Markov Approximation

HARUO SATO AND MICHAEL KORN

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

1.1. Markov Approximation for the Wave Envelope Synthesis . . . . . . . . . . . . . . . . . . . 44

1.2. Analyses of Seismogram Envelopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

1.3. Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2. Vector-Wave Envelopes for the Plane Wavelet Incidence . . . . . . . . . . . . . . . . . . . . . . . . 51

2.1. Three-Dimensional Random Elastic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.2. Two-Dimensional Random Elastic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3. Vector-Wave Envelopes for the Radiation from a Point Source . . . . . . . . . . . . . . . . . . . . 69

3.1. Three-Dimensional Random Elastic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.2. Two-Dimensional Random Elastic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4. Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.1. RTT with the Born Approximation Scattering Coefficients . . . . . . . . . . . . . . . . . . 83

4.2. Realistic ACFs for Random Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Chapter 4

Geometrical Optics of Acoustic Media with AnisometricRandom Heterogeneities: Travel-Time Statistics of

Reflected and Refracted Waves

AYSE KASLILAR, YURY A. KRAVTSOV AND SERGE A. SHAPIRO

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

2. Basic Elements of the GO Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

2.1. Basic Equations of the GO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

2.2. Model of Quasi-Homogeneous Fluctuations

of Medium Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

2.3. Travel-Time Covariance Function in a Medium

with Anisometric Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

2.4. Boundary of GO Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

3. Travel-Time Fluctuations in Reflection Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.1. Reflection Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3.2. Travel-Time Covariance Function for Small Offsets . . . . . . . . . . . . . . . . . . . . . . 104

3.3. Double Passage Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

4. Travel-Time Fluctuations in Refraction Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.1. Refracting Medium with a Constant Velocity Gradient . . . . . . . . . . . . . . . . . . . . 107

4.2. Travel-Time Variance along a Curvilinear Ray . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.3. Dependence of Travel-Time Variance on Offset . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.4. Inverse Problem Solution for Refraction Geometry . . . . . . . . . . . . . . . . . . . . . . . 112

5. Results of Numerical Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6. Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

viii CONTENTS

Chapter 5

Attenuation of Seismic Waves Due to Wave-InducedFlow and Scattering in Randomly Heterogeneous

Poroelastic Continua

TOBIAS M. MULLER, BORIS GUREVICH AND SERGE A. SHAPIRO

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

2. Meso- and Macroscopic Heterogeneity in the Earth and Its

Description as a Random Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

3. Attenuation and Dispersion of Seismic Waves due to

Wave-Induced Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

3.1. Biot’s Equations of Dynamic Poroelasticity and

Associated Green’s Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

3.2. The Basic Poroelastic Scattering Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

3.3. First-Order Statistical Smoothing Approximation . . . . . . . . . . . . . . . . . . . . . . . . . 134

3.4. Effective Fast Wave Number Accounting for

Conversion Scattering into Slow P Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

3.5. Attenuation and Dispersion due to Wave-Induced Flow . . . . . . . . . . . . . . . . . . . . 138

3.6. Asymptotic Behavior at Low and High Frequencies . . . . . . . . . . . . . . . . . . . . . . . 145

4. Attenuation of Seismic Waves in Random Porous

Media due to Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

4.1. The Generalized ODA Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

4.2. Effective Wave Number in 3-D Random Media . . . . . . . . . . . . . . . . . . . . . . . . . . 149

4.3. Scattering Attenuation and Asymptotic Behavior . . . . . . . . . . . . . . . . . . . . . . . . . 154

5. The Interplay Between Attenuation Due Interlayer Flow

and Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.1. 1-D Poroelastic Random Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

5.2. Asymptotic Scaling of Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

Chapter 6

Observing and Modeling Elastic Scatteringin the Deep Earth

PETER M. SHEARER AND PAUL S. EARLE

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

2. Data Stacking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

2.1. Shallow-Versus Deep-Earthquake Teleseismic P Coda . . . . . . . . . . . . . . . . . . . . . 170

2.2. Regional Variations in Teleseismic P Coda Amplitude . . . . . . . . . . . . . . . . . . . . . 170

3. Monte Carlo Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

3.1. Seismology Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

3.2. Monte Carlo Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

3.3. The Monte Carlo Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

3.4. Particle Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

3.5. Scattering Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

3.6. Intrinsic Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

4. Fit to Teleseismic P Coda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

ixCONTENTS

5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Chapter 7

A Scattering Waveguide in the HeterogeneousSubducting Plate

TAKASHI FURUMURA AND BRIAN L.N. KENNETT

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

2. Anomalous Intensity Patterns from Two Deep Events in the

Subducted Philippine Sea Plate and in the Subducted Pacific Plate . . . . . . . . . . . . . . . . 198

2.1. Separation of Low-Frequency Precursors and

High-Frequency Coda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

2.2. Frequency Selective Propagation Properties in the

Subducting Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

3. 2D FDM Modeling of Scattering Wavefield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

4. 2D FDM Modeling of Slab Guided Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

4.1. Base Model: High-Q and High-V Subduction Zone . . . . . . . . . . . . . . . . . . . . . . . 208

4.2. Heterogeneous Plate Model: Isotropic Heterogeneities

in the Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

4.3. Anisotropic Heterogeneities in the Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

4.4. Effect of Plate Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

4.5. Effect of Heterogeneity Scale in the Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

5. Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

Chapter 8

Laboratory Experiments of Seismic Wave Propagationin Random Heterogeneous Media

OSAMU NISHIZAWA AND YO FUKUSHIMA

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

2. Laboratory Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

2.1. Statistical Description of Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

2.2. Wave Fields in Random Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

3. Scale-Invariant Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

4. Waveform Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

4.1. Travel-Time Fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

4.2. Cross Spectra Between Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

4.3. Shear-Wave Particle Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

4.4. Waveform Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238

5. Key Features of Wave Fluctuation in Random Media . . . . . . . . . . . . . . . . . . . . . . . . . . 240

5.1. Masking Signal Waves by Small-Scale Heterogeneities . . . . . . . . . . . . . . . . . . . . 240

5.2. Boundary Between EHM and SRM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

5.3. Diffraction of Scattered Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

x CONTENTS

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

6.1. Validity of Equivalent Homogeneous Medium Assumption . . . . . . . . . . . . . . . . . 243

6.2. Random Media Effect on Seismic Data Processing . . . . . . . . . . . . . . . . . . . . . . . 244

6.3. Role of Laboratory Experiments for Studying Seismic

Wave Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Chapter 9

Measurements of the Earth at the Scale of Logs,Crosswells, and VSPs

ARTHUR C.H. CHENG

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

2. Acoustic Logging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

2.1. Dipole Logging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

2.2. Modern Array Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

2.3. Depth of Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

3. Crosswell Seismic Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

3.1. Resolution of a Crosswell Seismic Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

4. Vertical Seismic Profiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

5. Discussions and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

Chapter 10

Coda Energy Distribution and Attenuation

KAZUO YOSHIMOTO AND ANSHU JIN

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265

2. Coda Energy Distribution and Measurement on QP,S�1

using Local Seismograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

2.1. Uniformity of Coda Energy Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268

2.2. Nonuniform Coda Energy Distribution in

Tectonically Active Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

3. Temporal Decay Rate of Coda Energy: QC�1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

3.1. Lapse-Time Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

3.2. Frequency Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

3.3. Geographic Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

3.4. Temporal Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

3.5. Models to Explain the Spatio-Temporal Correlation

Between QC�1 and Seismicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

4. Closing Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

xiCONTENTS

Chapter 11

Imaging Inhomogeneous Structures in the Earth byCoda Envelope Inversion and Seismic Array Observation

KIN’YA NISHIGAMI AND SATOSHI MATSUMOTO

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301

2. Analysis of Seismic Network Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

2.1. Inversion of Coda Envelope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

2.2. Kirchhoff Coda Migration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

3. Analysis of Seismic Array Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307

3.1. Detection of Seismic Signals by Array Observations . . . . . . . . . . . . . . . . . . . . . . 307

3.2. Single-Scattering Model for Seismic Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

3.3. Characteristics of Coda Waves Based on Array Observations . . . . . . . . . . . . . . . . 311

3.4. Scatterer/Inhomogeneity Distribution Inferred from

Seismic Array Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

4. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

Chapter 12

Source Effects From Broad Area Network Calibrationof Regional Distance Coda Waves

WILLIAM SCOTT PHILLIPS, RICHARD JEROME STEAD, GEORGE EDWARD

RANDALL, HANS EDWARD HARTSE AND KEVIN MITSUO MAYEDA

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

2. Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

3. Coda Calibration Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

3.1. Coda Start Time Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

3.2. Coda Shape Calibration and Amplitude Measurement . . . . . . . . . . . . . . . . . . . . . 331

3.3. Intrastation Site Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

3.4. 2-D Path and Interstation Site Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

3.5. Source to Coda Transfer Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

4. Coda Spectral Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349

Chapter 13

Seismic Wave Scattering in Volcanoes

EDOARDO DEL PEZZO

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

1.1. Volcanic Earthquakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

1.2. A Brief Review of Coda-Q�1 Observation on Volcanoes . . . . . . . . . . . . . . . . . . . 354

xii CONTENTS

2. Separated Estimates of Intrinsic and Scattering Attenuation . . . . . . . . . . . . . . . . . . . . . 357

2.1. The Method of Wennerberg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

2.2. The Energy-Flux Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

2.3. 2-D Transport Theory Applied to Volcanic Tremor . . . . . . . . . . . . . . . . . . . . . . . 360

3. Diffusion Model Applied to Shot Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

3.1. Uniform Half Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

3.2. Two-Layer Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363

4. Energy-Transport Theory Applied to Earthquake Data . . . . . . . . . . . . . . . . . . . . . . . . . 365

4.1. Uniform Half Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365

4.2. Possible Bias Introduced by Assuming a Uniform Diffusive Layer . . . . . . . . . . . . 366

4.3. Coda-Localization Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

5. Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369

Chapter 14

Monitoring Temporal Variations of Physical Propertiesin the Crust by Cross-Correlating the Waveforms of

Seismic Doublets

GEORGES POUPINET, JEAN-LUC GOT AND FLORENT BRENGUIER

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

2. Selection of Doublets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374

3. Basic Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

3.1. Time Delays Measured from Cross-Correlation

or Cross-Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375

3.2. Cross-Spectral Moving Window or Cross-Correlation

Moving Window Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

4. Relocating Doublets from P and S Travel-Time Delays . . . . . . . . . . . . . . . . . . . . . . . . 378

4.1. Double-Difference Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

4.2. Two Synthetic Examples with IASP91 Travel Times . . . . . . . . . . . . . . . . . . . . . 379

4.3. Possible Technical and Intrinsic Difficulties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

5. An Example of Observed Delays: An Excellent Doublet in Japan . . . . . . . . . . . . . . . . 382

6. Slope of the Delay in the Coda and the Measurement of

S-Velocity Temporal Variation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

7. Possible Artifacts in DVS/VS Measurement: Arguments from

the Coda of Spatial Doublets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385

8. Search for Temporal Variation of S-Wave Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . 389

9. Search for Temporal Variation of Coda Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . 390

10. “Virtual Doublets” Computed by Cross-Correlating Seismic Noise . . . . . . . . . . . . . . . 391

11. PKP from Teleseismic Doublets and the Rotation

of the Inner Core . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

12. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

xiiiCONTENTS

Chapter 15

Seismogram Envelope Inversion forHigh-Frequency Seismic Energy Radiation from

Moderate-to-Large Earthquakes

HISASHI NAKAHARA

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402

2. Envelope Inversion Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

2.1. General Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403

2.2. A Classification of Current Envelope Inversion Methods . . . . . . . . . . . . . . . . . . . 404

2.3. The Method of Nakahara et al. (1998) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

3. Data Analysis and the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

3.1. An Example of Practical Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411

4. Compilation of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

4.1. Frequency Dependence of High-Frequency Seismic Energy . . . . . . . . . . . . . . . . . 414

4.2. Scaling of High-Frequency Seismic Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418

4.3. Spatial Relationship Between Asperities and

High-Frequency Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

Chapter 16

On the Random Nature of Earthquake Sources and GroundMotions: A Unified Theory

DANIEL LAVALLEE

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427

2. Random Model of Earthquakes Slip Spatial Distribution and

Consequences for the Ground Motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

2.1. From the Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429

2.2. . . . to the Ground Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

3. The 2004 Parkfield Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

3.1. Random Model of the Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435

3.2. Random Model of the Ground Motion PGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440

3.3. Random Model of the Ground Motion PGV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

4. The 1999 Chi-Chi Earthquake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

4.1. Random Model of the Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444

4.2. Random Model of the Ground Motion PGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

5. Limitations of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

6. Conclusion: From Randomness to Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454


References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458

GLOSSARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

xiv CONTENTS

CONTRIBUTORS

Numbers in parentheses indicate the pages on which the authors’ contributionsbegin.

BRENGUIER, F. (373) LGIT, Universite Joseph Fourier & CNRS, BP53, 38041,

Grenoble, France

CHENG, A.C.H. (247) Cambridge GeoSciences, 14090 Southwest Freeway, Suite

300, Sugar Land, TX 77478, USA

DEL PEZZO, E. (353) INGV - Osservatorio Vesuviano. Via Diocleziano, 328. 80124

Napoli January 21, 2008

EARLE, P.S. (167) United States Geological Survey, MS 966 DFC, Denver, CO

80225

FURUMURA, T. (219) Disaster Prevention Research Institute Kyoto University,

Gokasho, Uji, Kyoto, 611-0011

GOT, J.-L. (373) LGIT, Universite de Savoie & CNRS, 73000, Le Bourget du Lac,

France

GUREVICH, B. (123) Curtin University of Technology and CSIRO Division of

Petroleum resources, Perth, Australia

HARTSE, H.E. (319) Los Alamos National Laboratory

JIN, A. (265) 139W. Phillips Blvd. #315, Pomona, CA 91766, USA

KASLILAR, A. (95) Istanbul Technical University, Mining Faculty, Department of

Geophysics, 34390 Maslak, Istanbul, Turkey

KENNETT, B.L.N. (195) Research School of Earth Sciences, The Australian National

University, Canberra, ACT 0200, Australia

KORN, M. (43) Institute of Geophysics and Geology, University of Leipzig,

Talstrasse 35, D-04103 Leipzig, Germany

KRAVTSOV, Y.A. (95) Institute of Physics, Maritime University of Szczecin,

Szczecin, 70-500, Poland and Space Research Institute, Russian Academic

Science, Moscow, 117 997, Russia

LAVALLEE, D. (427) Institute for Crustal Studies, University of California, Santa

Barbara, California, USA

MARGERIN, L. (1) Centre Europeen de Recherche et d’Enseignement de Geosciences

de l’Environnement, Universite Aix-Marseille, CNRS, BP 80, 13545 Aix en

Provence, France

MATSUMOTO, S. (301) Institute of Seismology and Volcanology, Faculty of Sciences,

Kyushu University, Japan

MAYEDA, K.M. (319) Weston Geophysical Corporation

MULLER, T.M. (123) Geophysikalisches Institut, Universitat Karlsruhe, Germany

NAKAHARA, H. (401) Department of Geophysics, Graduate School of Science,

Tohoku University, Aoba-ku, Sendai 980-8578, Japan

xv

NISHIGAMI, K. (301) Disaster Prevention Research Institute, Kyoto University, Japan

NISHIZAWA, O. (219) National Institute of Advanced Industrial Science and Technol-

ogy, 1-1-1 Higashi, Tsukuba, Ibaraki, 305-8567, Japan

PHILLIPS, W.S. (319) Los Alamos National Laboratory

POUPINET, G. (373) LGIT, Universite Joseph Fourier & CNRS, BP53, 38041,

Grenoble, France

RANDALL, G.E. (319) Los Alamos National Laboratory

SATO, H. (43) Department of Geophysics, Graduate School of Science, Tohoku Uni-

versity, Aramaki-Aza-Aoba 6-3, Aoba-ku, Sendai-shi, Miyagi-ken, 980-8578,

Japan

SHAPIRO, S.A. (95, 123) Fachrichtung Geophysik, Freie Universitat Berlin, 74-100,

Haus D, 12249 Berlin, Germany

SHEARER, P.M. (167) Institute of Geophysics and Planetary Physics, U.C. San Diego,

La Jolla, CA 92093-0225

STEAD, R.J. (319) Los Alamos National Laboratory

WU R.-S. (21) Institute of Geophysics and Planetary Physics, University of

California, Santa Cruz, USA, 95064

YOSHIMOTO, K. (265) Natural/Basic and Applied Sciences, International Graduate

School of Arts and Sciences, Yokohama City University, 22-2 Seto, Kanazawa-ku,

Yokohama 236-0027, Japan

ZHENG, Y. (21) Institute of Geophysics and Planetary Physics, University of

California, Santa Cruz, USA, 95064

xvi CONTRIBUTORS

PREFACE

Seismic waves generated by earthquakes have been interpreted to provide us informa-tion about the Earth’s structure across a variety of scales. As a scientific activity of theCommission on Seismological Observation and Interpretation of the IASPEI, focusingon the seismic wave scattering in the Earth from heterogeneities having various types andscales, we organized a task group on “Scattering and Heterogeneity of the Earth.” As thefirst product of this task group, Wu and Maupin (2007) edited a book entitled “Advancesin Wave Propagation in Heterogeneous Earth” as the 48th volume of “Advances inGeophysics” (Series Editor, R. Dmowska). That volume mainly contains introductions toand basic review of modeling methods for elastic waves in laterally heterogeneousstructures that are most commonly used in contemporary seismology.

For short-period seismic waves (e.g., those having periods less than 1 s), scattering dueto randomly distributed small-scale heterogeneities in the Earth significantly changes theenvelope of seismograms with increasing travel distance and excites coda waves. Modelsof propagation through deterministic structures such as those with horizontally uniformvelocity layers used in traditional seismology cannot explain these phenomena.In addition to the invention of the velocity tomography, the study of coda waves in theheterogeneous lithosphere started by Aki (1969) marked a new era in short-periodseismology. The former reveals the existence of three-dimensional deterministic hetero-geneity from onset readings; the latter reveals the existence of small-scale randomheterogeneity. The two approaches are complementary for the construction of a unifiedimage of the real Earth; however, here we mainly focus on the latter subject, seismicwave scattering by random small-scale heterogeneity in the Earth.

This book is edited as the second product of the task group. Topics covered are recentdevelopments in wave theory and observation including: weak localization of seismicwaves, synthesis of short-period seismic wave envelopes, laboratory investigations ofultrasonic wave propagation in rock samples, coda wave analysis for mapping mediumheterogeneity and for monitoring temporal variation of physical properties in the crust,radiation of short-period seismic waves from an earthquake fault, and borehole measure-ments of Earth properties on a range of scales. Various types of forward modeling andinversion schemes are introduced.

As a compelling description of the value of the study of the field of seismic wavescattering in the heterogeneous Earth, we refer to words of late professor Keiiti Aki in aletter he wrote to Dr. V.I. Kelis-Borok in 2003 from his lecture note (Aki, 2003), “. . . Toa geodynamicist, the earth’s property is smoothly varying within bodies bounded bylarge-scale interfaces. Most seismologists also belong to this ‘smooth earth club,’because once you start with an initial model of smooth earth your data usually do notrequire the addition of small-scale heterogeneity to your initial model. As summarizedwell in a recent book by Sato and Fehler (1998), the acceptance of coda waves in the dataset is needed for the acceptance of small-scale seismic heterogeneity of the lithosphere.There are an increasing number of seismologists who accept it, forming the ‘rough earthclub.’ I believe that you are also a member of the rough earth club, judging from theemphasis on the hierarchical heterogeneity of the lithosphere . . .”

xvii

This book starts with theoretical approaches for modeling wave propagation andscattering in randomly inhomogeneous media. Chapter 1 (Margerin) reviews recenttheoretical developments on the weak localization of coda waves: the amplitude ofcoherent back-scattered waves in the vicinity of the source is larger than what predictedfrom the classical radiative transfer theory. For cases where the wavelength is shorter thanthe scale of medium inhomogeneity, the WKBJ approximation is used in Chapter 2(Zheng and Wu) to arrive at a new stochastic theory for the coherence function of logamplitude and phase for waves passing through random media with a depth-dependentbackground velocity structure. As a statistical extension of the phase screen method forthe parabolic wave equation, the Markov approximation is known to be an effectivemethod to predict wave envelopes in randommedia for high-frequency waves. Chapter 3(Sato and Korn) reviews an extension of that approximation for scalar waves to vectorwaves. The newly developed theory reliably predicts envelope broadening and theexcitation of the orthogonal component of motion (the transverse component forP-waves) with increasing travel distance. The validity of the approach is tested bycomparison with sets of wave traces generated by finite differences. Chapter 4 (Kaslilaret al.) discusses the travel time statistics of acoustic waves in random media based ongeometrical optics. They develop a method to estimate the statistical parameters char-acterizing the random media from travel-time fluctuations of reflected and refractedwaves. Chapter 5 (Muller et al.) presents a theory for attenuation and dispersion ofcompressional seismic waves in inhomogeneous, fluid-saturated porous media in theframework of wave propagation in continuous random media. The statistical smoothingmethod treats both intrinsic attenuation due to wave-induced flow and scattering attenu-ation as the redistribution of wave energy in space and time in a unified manner.

The following two chapters treat practical modeling of seismic wave propagationthrough the heterogeneous Earth. Chapter 6 (Shearer and Earle) focuses on the envelopesof teleseismic P waves traveling through the heterogeneous mantle. Envelopes calculatedby using a statistical synthesis based on the Born scattering amplitudes for random elasticmedia are fitted to the observed stacked P wave envelopes. Chapter 7 (Furumura andKennett) presents a scattering slab model for the Pacific plate and the Philippine Seaplate beneath Japan that explains the observed efficient wave-guide for high-frequencyseismic waves in this region. The heterogeneous component of their slab model consistsof an anisotropic random velocity fluctuation with a longer correlation distance in theplate down-dip direction and a much shorter correlation distance across the platethickness. Precise numerical simulations well explain the frequency selective wavepropagation effect.

The following two chapters treat laboratory experiment and scaling issues in boreholesurveys. Chapter 8 (Nishizawa and Fukushima) presents laboratory experiments ofultrasonic wave propagation through heterogeneous rock samples by using a laserDoppler vibrometer. Variations in travel times, fluctuations of amplitude, phase, andparticle-motion, as well as envelope formation are examined with respect to the statisti-cal properties of random heterogeneities of rock in the range of millimeters. Chapter 9(Cheng) reviews the latest technologies in down-hole seismic measurements: acousticlogging, cross well seismic and vertical seismic profiling. They cover a frequency rangefrom about 10 kHz down to about 10 Hz, and can investigate heterogeneity in the Earthfrom a scale of 10 s of centimeters to 100 s of meters. This chapter contains a discussionof the scale over which the various methods can resolve heterogeneity.

xviii PREFACE

The following chapters treat various types of observations and analyses of coda waves.Chapter 10 (Yoshimoto and Jin) presents the general characteristics of coda waves oflocal earthquakes and theoretical models based on the radiative transfer theory.This chapter discusses the nonuniform distribution of coda energy in tectonically activeregions. The measurement of coda attenuation is focused especially as a useful toolfor monitoring the temporal change in physical parameters in the curst. Chapter 11(Nishigami and Matsumoto) presents the inversion of coda wave envelopes of localearthquakes for the spatial distribution of scattering strength in the crust. The idea isbased of the assumption that the lapse-time dependent residual of individual codaenvelope from a smooth master curve reflects the spatial variation of scattering strength.Applying this method to data retrieved in the San Andreas Fault system, they show agood correlation between sub-parallel active faults and relatively stronger scatteringzones in the crust. This chapter also has a discussion about slant stacking of seismicarray waveform data for the energy evaluation under the assumption of a single scatteringmodel. Chapter 12 (Phillips et al.) develops a calibration technique to estimate the sourcespectra from the spectra of Lg and Sn coda waves of local earthquakes. Applying thesetechniques to records registered at stations across central and eastern Asia, they deter-mine the regional variation of coda attenuation and apparent stress of earthquakes.Chapter 13 (Del Pezzo) reviews scattering studies in various volcanic regimes. Insome cases, the frequency dependence of coda attenuation in volcanoes is found to beless than that measured in nonvolcanic areas. According to the multiple lapse timewindow analysis of the data, scattering loss dominates over intrinsic loss with increasingfrequency because of strong heterogeneity in volcanoes. Different from the aboveenvelope analyses, Chapter 14 (Poupinet et al.) focuses on the phase information ofcoda waves and presents a cross-correlation (-spectrum) moving window technique ofcoda waves of local earthquake doublets for monitoring the temporal change inthe velocity structure of the crust. This technique is tested by earthquake doubletseismograms registered by a digital seismic network with a high time precision.This chapter also presents a technique that creates “virtual doublets” from the correlationof long seismic noise sequences.

The last two chapters treat earthquake strong motions and source models. Chapter 15(Nakahara) presents a seismogram envelope inversion for short-period seismic energyradiation from an earthquake fault. The basic idea is to use the envelope Green functionderived from the multiple isotropic scattering model for short period S-waves to invertfor the spatial variation in radiation from a fault. This chapter compiles the characteristicsof short-period seismic energy radiation from moderate to large earthquakes. Chapter 16(Lavallee) presents an earthquake source model based on the assumption that the slipdistribution obeys a Levy law. This model predicts that the sum of these amplitudesobserved at a given distance from the sources will also be distributed according to aLevy law.

The text is written for graduate students, scientists, and engineers of geophysics,physics, acoustics, civil engineering, environmental sciences, geology, and planetarysciences. A glossary of special terms relevant to the study of scattering of waves inrandom media is placed at the end of this book. For further understanding, there aremonographs that treat medium heterogeneity and wave scattering as follows:Chandrasekhar (1960) is a classic text for radiative transfer theory in scattering media.Ishimaru (1978) and Rytov et al. (1987) offer advanced mathematical tools for the studyof wave propagation in random media and a link between wave theory and the radiative

xixPREFACE

transfer theory. Shapiro and Hubral (1999) puts special focus on wave propagationthrough stratified random media focusing on 1D problems. Goff and Holliger (2002)summarizes observations of crustal heterogeneity. Sato and Fehler (1998) reviewsseismological observation facts and mathematical models of scattering phenomenaespecially focusing on short period seismic waves and small-scale heterogeneity.

We thank the following scientists for their careful reviews of different chapters: JoeAndrews, Nirenda Biswas, Daniel Burns, Arthur C.H. Cheng, Vernon F. Cormier,Edoardo Del Pezzo, Karl Ellefsen, William L. Ellsworth, Alexander A. Gusev, DavidHigdon, Lianjie Huang, Ludek Klimes, Michael Korn, Yury A. Kravtsov, LudovicMargerin, Gary Mavko, Steve McNutt, Tobias Muller, Takeshi Nishimura, MasakazuOhtake, Lenya Rhyzik, Steve Roecker, Tatsuhiko Saito, Sergei Shapiro, Roel Snieder,Anna Tramelli, Kasper Van Wijk, Ulrich Wegler, Kazuo Yoshimoto, and Yuehua Zeng.

We thank the IASPEI, in particular the ex-president E. Robert Engdahl, the Secretary-General, Peter Suhadolc, the chairman of the Commission on Seismological Observationand Interpretation, Dmitry Storchak, and the current president, Zhongliang Wu for theirsupport during this book project.

This book also owes a lot to Renata Dmowska, the editor of the series “Advances inGeophysics.” We thank her for her continuous encouragement and help for the editingwork.

Haruo Sato and Michael C. FehlerJune 7, 2008

References

Aki, K. (1969). Analysis of seismic coda of local earthquakes as scattered waves. J. Geophys. Res.74, 615–631.

Aki, K. (2003). Seismology of Earthquake and Volcano Prediction. pp. 1–219. NIED and YIES,

Tsukuba.

Chandrasekhar, S. (1960). Radiative Transfer. Dover, New York.

Goff, J.A., Holliger, K. (2002). Heterogeneity in the Crust and Upper Mantle – Nature, Scaling andSeismic Properties. Kluwer Academic/Plenum Publishers, Dorderecht, The Netherlands.

Ishimaru, A. (1978). Wave Propagation and Scattering in Random Media. Academic, San Diego.

Rytov, S.M., Kravtsov, Y.A., Tatarskii, V.I. (1987). Wave propagation through random media. InPrinciples of Statistical Radio Physics, vol. 4, Springer-Verlag, Berlin.

Shapiro, S.A., Hubral, P. (1999). Elastic Waves in Random Media—Fundamentals of SeismicStratigraphic Filtering. Springer-Verlag, Berlin.

Sato, H., Fehler, M.C. (1998). Seismic Wave Propagation and Scattering in the HeterogeneousEarth. Springer-Verlag, New York.

Wu, R.S., Maupin, V. (2007). Advances in wave propagation in heterogeneous earth. In Advancesin Geophysics (Series Ed., R. Dmowska), vol. 48, Academic Press, San Diego.

xx PREFACE

advances in geophysicszisin.geophys.tohoku.ac.jp/~sato/satohp2012/books_and...advances in geophysics...

Documents