Q of the Earth: Global, Regional, and Laboratory Studies

489 Pages·1999·14.639 MB·English

by  Brian J. Mitchell, Barbara Romanowicz (auth.), Brian J. Mitchell, Barbara Romanowicz (eds.)

Q of the Earth: Global,
Regional, and Laboratory
Studies
Edited by
Brian J. Mitchell
Barbara Romanowicz
1999 Springer Basel AG
Reprint from Pageoph
(PAGEOPH), Volume 153 (1998), Nos. 2/3/4
The Editors:
Brian J. Mitchell Barbara Romanowicz
Department of Earth and Atmospheric Sciences Department of Geology and Geophysics
Saint Louis University University of California, Berkeley
St. Louis, Missouri 63103 Berkeley, California 94720
USA USA
A CIP catalogue record for this book is available from the Library of Congress, Washington
D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
Q of the earth : global, regional, and laboratory studies /
ed. by Brian J. Mitchell ; Barbara Romanowicz. -Basel ; Boston; Berlin:
Birkhăuser 1999
(Pageoph topical volumes)
ISBN 978-3-7643-6049-8 ISBN 978-3-0348-8711-3 (eBook)
DOI 10.1007/978-3-0348-8711-3
This work is subject to copyright. AlI rights are reserved, whether the whole or part of the
material is concerned, specificalIy the rights of translation, reprinting, re-use of illustrations,
broadcasting, reproduction on microfilms Of in other ways, and storage in data banks. For any
kind ofuse whatsoever, permission from the copyright owner must be obtained.
© 1999 Springer Basel AG
Originally published by Birkhauser Verlag in 1999
Printed on acid-free paper produced from chlorine-free pulp
ISBN 978-3-7643-6049-8
987654321
Contents
235 Introduction, B. J. Mitchell, B. Romanowicz
Part I: Global and Mantle Studies
239 A Dislocation Model of Seismic Wave Attenuation and Micro-creep in the
Earth: Harold Jeffreys and the Rheology of the Solid Earth, S. Karato
257 Attenuation Tomography of the Earth's Mantle: A Review of Current
Status, B. Romanowicz
273 High-frequency P- and S-wave Attenuation in the Earth, Z. A. Der
311 2-D Image of Seismic Attenuation beneath the Deep Seismic Sounding
Profile "Quartz," Russia,/. B. Morozov, E. A. Morozova, S. B. Smithson and
L. N. Solodilov
345 Attenuation of Broadband P and S Waves in Tonga: Observations of
Frequency Dependent Q, M. P. Flanagan and D. A. Wiens
377 Three-dimensional Mapping of Magma Source and Transport Regions from
Seismic Data: The Mantle Wedge beneath Northeastern Japan, H. Sato,
K. Muro and A. Hasegawa
399 Comparison between Time-domain and Frequency-domain Measurement
Techniques for Mantle Shear-wave Attenuation, J. Bhattacharyya
419 A Model to Study the Bias on Q Estimates Obtained by Applying the Rise
Time Method to Earthquake Data, S. de Lorenzo
Part II: Crustal Studies
441 Seismic-frequency Laboratory Measurements of Shear Mode Viscoelasticity
in Crustal Rocks II: Thermally Stressed Quartzite and Granite, C. Lu and 1.
Jackson
475 A Summary of Attenuation Measurements from Borehole Recordings of
Earthquakes: The 10 Hz Transition Problem, R. E. Abercrombie
489 Frequency-dependent Attenuation of High-frequency P and S Waves in the
Upper Crust in Western Nagano, Japan, K. Yoshimoto, H. Sato, Y. lio,
H. /to, T. Ohm ina to and M. Ohtake
503 Seismic Velocity and Q Structure of the Middle Eastern Crust and Upper
Mantle from Surface-wave Dispersion and Attenuation, L. Cong and B. J.
Mitchell
539 Seismic Attenuation Computed from GLIMPCE Reflection Data and Com
parison with Refraction Results, M. P. Matheney and R. L. Nowack
563 Lg Coda Q and its Relation to the Geology and Tectonics of the Middle
East, L. Cong and B. J. Mitchell
587 Lg Coda Q Variations across South America and their Relation to Crustal
Evolution, J. L. de Souza and B. J. Mitchell
613 Regional Variation of Lg Coda Q in the Continental United States and its
Relation to Crustal Structure and Evolution, S. Baqer and B. 1. Mitchell
639 Lg Coda Q in Australia and its Relation to Crustal Structure and Evolution,
B. J. Mitchell, S. Baqer, A. Akinci and L. Cong
655 Lg Coda Q and its Relation to the Structure and Evolution of Continents:
A Global Perspective, B. J. Mitchell and L. Cong
665 Comparison of Seismic Body Wave and Coda Wave Measures of Q,
G. Sarker and G. A. Abers
685 Estimation of the Intrinsic Absorption and Scattering Attenuation in North
eastern Venezuela (Southeastern Caribbean) Using Coda Waves, A. Ugalde,
L. G. Pujades, J. A. Canas and A. Villasenor
703 Intrinsic and Scattering Seismic Attenuation in W. Greece, G.-A. Tselentis
713 Coda Q Estimates in the Koyna Region, India, S. C. Gupta, S. S. Teotia,
S. S. Rai, and N. Gautam
© Birkhliuser Verlag, Basel, 1998
Pure appl. geophys. 153 (1998) 235-236 I
0033-4553/98/040235-02 $ 1.50 + 0.20/0 Pure and Applied Geophysics
Introduction
In tenns of its possible contribution to our understanding of the earth, few areas
of seismological study have posed as many difficulties as that of seismic wave
attenuation, or Q. Many surface-wave seismologists have measured amplitudes at
two seismic stations along the same great-circle path from an earthquake and
found, even after correcting for instrumental factors, that the amplitude of a
particular phase is larger at the more distant station. Similarly, body-wave seismol
ogists have long been aware of the severe effect that velocity gradients and
low-velocity zones can have on wave amplitudes. Awareness that such effects can
completely swamp those of anelasticity has, undoubtedly, deterred many investiga
tors from pursuing research on seismic-wave attenuation.
In recent years, however, improved instrument deployment and methodologies,
as well as the availability of digital data from well-calibrated instruments have
spurred progress in obtaining reliable measurements of Q in the earth. In addition,
improved laboratory measurements of Q in the seismic frequency band, improved
theoretical models, and increasing knowledge of factors that contribute to Q have
generated increased interest in this area.
Despite the difficulties inherent in the study of Q, it is a compelling field of
endeavor. For a practical point of view, knowledge of Q is important for magnitude
detennination; for predicting ground motion and using that knowledge to design
buildings, bridges, dams and other structures; and for monitoring compliance with
nuclear test ban treaties. Knowledge of Q is also important in determining aspects
of earth structure that are not easily amenable to study using only seismic velocities.
It has long been known that Q is sensitive to temperature, movement of solid-state
defects, partial melt, and fluid content to a much greater degree than are seismic
velocities. For these reasons, reliable knowledge of the distribution of Q in the earth
should provide new insights on its internal structure and evolution.
We therefore think that it is timely to compile a special volume on Q that
addresses pertinent issues from a variety of perspectives. Part I of this volume
emphasizes global and mantle studies of Q. It includes papers pertaining to a
dislocation model for seismic wave attenuation and creep (Karato); the state of
global Q tomography (Romanowicz); on teleseismic body waves, both observa
tional results (Der, Morozov et at.) and methodology (Bhattacharyya, de Lorenzo);
and on subduction zones (Sato et at., Flanagan and Wiens).
Part II emphasizes the crust and includes studies that cover a broad range of
scales and distances. These include papers on laboratory studies of crustal rock (Lu
236 Introduction Pure app!. geophys.,
and Jackson); surface waves (Cong and Mitchell) and Lg coda (Cong and Mitchell,
de Souza and Mitchell, Baqer and Mitchell, Mitchell et at.) over distances of 100 to
1000 or more km; on regional body waves (Sarker and Albers, Tselentis, Ugalde et
at., Gupta); on refraction and reflection surveys (Matheny and Nowack), and on
bore hole experiments (Abercrombie, Yoshimoto et al.). This diversity of papers
illustrates the wealth of questions that can be probed in the field of seismic wave
attenuation, and of the oft-required need for novel experimental and theoretical
approaches.
We hope that this volume will generate an enhanced appreciation of the
difficulties inherent in the study of Q, of the diverse approaches that are required
for making progress, and of the promise that Q studies hold for obtaining new and
intriguing information about the earth. It is an exciting and multi-faceted discipline
that will require the diligent efforts of researchers in observational and theoretical
aspects of both seismology and material properties. We believe that observations
from global observatories, as well as from controlled experiments on the earth's
surface, in bore holes, and laboratory samples, as well as evolving theoretical
insights, will continue to contribute to our understanding of the Q distribution in
the earth and the factors that control that distribution. Moreover, because mantle
Q is intimately related to creep and crustal Q appears to be strongly affected by
tectonic and orogenic activity, knowledge of its distribution promises to provide
new knowledge regarding mantle flow, plate movement, and crustal deformation in
the earth.
Brian J. Mitchell
Department of Earth and Atmospheric Sciences
Saint Louis University
St. Louis, Missouri 63103
USA
and
Barbara Romanowicz
Department of Geology and Geophysics
University of California, Berkeley
Berkeley, California
USA
Part I
Global and Mantle Studies
© Birkhauser Verlag, Basel, 1998
Pure appl. geophys. 153 (1998) 239-256 I
0033-4553/98/040239-18 $ 1.50 + 0.20/0 Pure and Applied Geophysics
A Dislocation Model of Seismic Wave Attenuation and
Micro-creep in the Earth: Harold Jeffreys and the Rheology of the
Solid Earth
SHUN-ICHIRO KARATOI
Abstract-A microphysical model of seismic wave attenuation is developed to provide a physical
basis to interpret temperature and frequency dependence of seismic wave attenuation. The model is
based on the dynamics of dislocation motion in minerals with a high Peierls stress. It is proposed that
most of seismic wave attenuation occurs through the migration of geometrical kinks (micro-glide) and/or
nucleation/migration of an isolated pair of kinks (Bordoni peak), whereas the long-term plastic
deformation involves the continuing nucleation and migration of kinks (macro-glide). Kink migration is
much easier than kink nucleation, and this provides a natural explanation for the vast difference in
dislocation mobility between seismic and geological time scales. The frequency and temperature
dependences of attenuation depend on the geometry and dynamics of dislocation motion both of which
affect the distribution of relaxation times. The distribution of relaxation times is largely controlled by the
distribution in distance between pinning points of dislocations, L, and the observed frequency depen
dence of Q, Q ex w', is shown to require a distribution function of P(L) ex L -m with m = 4 - 2cx. The
activation energy of Q-l in minerals with a high Peierls stress corresponds to that for kink nucleation
and is similar to that of long-term creep. The observed large lateral variation in Q-l strongly suggests
that the Q-l in the mantle is frequency dependent. Micro-deformation with high dislocation mobility
will (temporarily) cease when all the geometrical kinks are exhausted. For a typical dislocation density
of ~ 108 m -2, transient creep with small viscosity related to seismic wave attenuation will persist up to
the strain of ~ 10-6, thus even a small strain (~1O-6 - 10-4) process such as post-glacial rebound is
only marginally affected by this type of anelastic relaxation. At longer time scales continuing nucleation
of kinks becomes important and enables indefinitely large strain, steady-state creep, causing viscous
behavior.
Key words: Seismic wave attenuation, dislocations, geometrical kinks, transient creep, Peierls stress,
Bordoni peak, Maxwell time.
Introduction
Understanding the physical mechanisms of an elasticity is important in a number
of geophysical problems. For example, interpretation of radial and lateral variation
of seismic wave attenuation (e.g., WIDMER et al., 1991; MITCHELL, 1995;
1 University of Minnesota, Department of Geology and Geophysics, Minneapolis, MN 55455,
U.S.A. E-mail: [email protected], Fax: [phone]
240 Shun-ichiro Karato Pure app\. geophys.,
ROMANOWICZ, 1994; DUREK and EKSTROM, 1996) III terms of geodynamic
parameters (such as temperature) requires a physically sound model for the
temperature and frequency dependence of attenuation. Interpretation of the distri
bution of seismic wave velocity also needs to consider the effects of attenuation and
resultant velocity dispersion (e.g., KANAMORI and ANDERSON, 1977; KARATO,
1993). Although some microscopic models of dislocation mechanisms have been
proposed, for example by GUEGUEN and MERCIER (1973) and MINSTER and
ANDERSON (1981), they either fail to explain some of the key parameters such as
the activation energy or are inadequate in explaining the origin of the wide
distribution of relaxation times implied by the observed frequency dependence. For
example, both of these authors assumed that glide motion of dislocations is
significantly easier than climb motion and that the former controls seismic wave
attenuation and the latter long-term creep. Such a notion is introduced from
metallurgy but is not justified for silicate minerals for several reasons. First, such a
model would imply that the activation energy of Q-I should be significantly smaller
than that of creep. Although such seems to be the case for metals (e.g., FANTOZZI
et at., 1982) and MgO (GETTING et al., 1997), the activation energy of Q-I is
similar to that of creep in olivine (for a review see KARA TO and SPETZLER, 1990).
Second, the notion of easy dislocation glide is not supported for silicates where
glide is difficult because of high Peierls stresses. For example, GOETZE (1978)
showed that creep in olivine can be explained by a glide-controlled model under
certain conditions.
Another potentially important application of seismic wave attenuation is the
inference of earth's long-term rheology. Because both seismic wave attenuation and
long-term rheology involve viscous motion of crystalline defects, some link between
them may exist. For example, if the earth behaves like a Maxwell body, then Q-I
is directly linked to viscosity by Q-I = M / OJ 11 where M: elastic modulus, 11:
viscosity and OJ: frequency. However, the earth's mantle does not behave like a
Maxwell body, but the frequency dependence of Q-I is Q-I oc OJ-" with 0 < IX < 1
in the seismic frequency range (ANDERSON and MINSTER, 1979; SIPKIN and
JORDAN, 1979; ANDERSON and GIVEN, 1982; ULUG and BERCKHEMER, 1984).
Such behavior corresponds to transient creep, namely s ~ t" and i; ~ 11 -I ~ t" - 1
where s: strain, i;: strain-rate and t: time. Therefore, if such a frequency dependence
is extrapolated to much lower frequencies (i.e., longer time scales), one would
predict a significantly larger viscosity for long-term deformation than for shorter
term deformation. Such an attempt was made by JEFFREYS (1958, 1976) and
ANDERSON and MINSTER (1979) to infer the viscosity relevant to mantle convec
tion and to post-glacial rebound, respectively. JEFFREYS (1958, 1976), in particular,
predicted very high viscosities at geological time scales and rejected the convection
hypothesis on that ground. Although we now recognize that the earth's mantle can
plastically deform at geological time scales by solid state creep, the relationship
between long-term creep and seismic wave attenuation has been unclear, and
Vol. 153, 1998 A Dislocation Model of Seismic Wave Attenuation 241
therefore there has not been any clear theoretical basis on which to go beyond
JEFFREYS (KARATO and SPETZLER, 1990). A physically sound model to link Q-I
with long-term rheology is clearly needed.
Any model of seismic wave attenuation must be consistent with seismological
and experimental observations of internal friction and with the microscopic physics
of minerals. Both experimental observations on olivine and MgO and theoretical
models suggest that mechanisms involving dislocation motion are most likely to be
responsible for seismic wave attenuation (GUEGUEN et al., 1989; KARATO and
SPETZLER, 1990; JACKSON et al., 1992; GETTING et al., 1997), although grain
boundary mechanisms may be important for fine-grained materials (TAN et al.,
1997; LAKKI et aI., 1998). Experimental evidence for dislocation mechanisms is well
established, however theoretical background of nonelastic relaxation has not been
well-understood. One of the most difficult issues is to explain the vast difference in
dislocation mobility required to cause attenuation at seismic frequencies and that
responsible for long-term deformation. A related issue is to explain observed rather
weak frequency dependence of Q over a wide frequency range. Furthermore, the
observed difference in activation energies of Q-I in olivine and in MgO must be
explained by a microscopic model.
The purpose of this paper is thus to develop a microscopic model of seismic
wave attenuation which is consistent with the properties of dislocations in silicates.
In particular, I will emphasize the consequence of a high Peierls stress, which gives
rise to an important distinction between the migration of geometrical kinks
(WUTHRICH, 1975; SEEGER and WUTHRICH, 1976) and the nucleation of a pair of
kinks (the Bordoni peak; ENGELKE, 1969a,b; FANTOZZI et al., 1982). It is shown
that this model provides a clear physical picture for the frequency dependence and
activation energy of Q-I, and also allows us to estimate the limit of extrapolation
of nonelastic properties obtained from Q-I to longer-term phenomena.
Theory
1. General Considerations
Dislocations can cause a wide range of nonelastic behavior of solids (for review
see FANTOZZI et al., 1982; HIRTH and LOTHE, 1982; KARATO and SPETZLER,
1990). At short time scales, micro-motion of dislocations between pinning points
causes anelastic behavior. Pinning can occur by various mechanisms including the
presence of jogs on screw dislocations and nodes caused by mutual interaction of
dislocations and the interaction of dislocations with impurities or vacancies (e.g.,
HIRTH and LOTHE, 1982). Evidence of some of them are shown in Figure 1. At
longer time scales continuous motion of dislocations becomes possible and vis
coelastic behavior occurs. A simple phenomenological model to describe these