Table Of Content• •
Roman Teisseyre Minoru Takeo Eugeniusz Majewski
Earthquake Source Asymmetry, Structural Media and
Rotation Effects
Roman Teisseyre
Minoru Takeo
Eugeniusz Majewski
(Eds.)
Earthquake
Source Asymmetry,
Structural Media
and Rotation Effects
With 223 Figures
EDITORS:
PROFESSOR ROMAN TEISSEYRE
ASSOCIATE PROFESSOR EUGENIUSZ MAJEWSKI
INSTITUTE OF GEOPHYSICS,
POLISH ACADEMY OF SCIENCES
UL. KS. JANUSZA 64
01-452 WARSAW
POLAND
PROFESSOR MINORU TAKEO
EARTHQUAKE RESEARCH INSTITUTE
UNIVERSITY OF TOKYO
1-1 YAYOI 1-CHOME, BUNKYO-KU
TOKYO 113 0032
JAPAN
E-mail: [email protected]
[email protected]
[email protected]
ISBN 10 3-540-31336-2 Springer Berlin Heidelberg New York
ISBN 13 978-3-540-31336-6 Springer Berlin Heidelberg New York
Library of Congress Control Number: 2006922187
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Preface
When thinking, at the beginning of the new century, on our horizons in
seismology, we might return to the old question related to the seismic rota-
tion effects and waves. Seismology, with its spectacular achievements (cid:16)
instrumentation, data processing, seismic tomography and source process
theories – remains practically confined to linear ideal elasticity (isotropic
or anisotropic). Numerous renown seismologists have tried to go beyond
this horizon. As concerns rotation waves, such attempts were inspired by
numerous macroscopic observations pointing out the rotation effects, often
observed on the ground surface. However, this problem has been appar-
ently closed by Mallet in 1862, who gave the following explanation: rota-
tions of a body on the surface are due to a sequence of impacts of different
seismic phases emerging under different angles. Later on, in 1937, Ima-
mura underlined an influence of different inertia moments of an inflicted
body. Thus, the surface rotation effects – rotation of some objects on the
ground surface – were explained as being caused by the consecutive incli-
nations and recovery of these objects to the vertical, when hit by the inci-
dent seismic body or surface waves. The final position of the object could
become slightly twisted in comparison to its former place; the differences
between the inertia tensor moments of the object and/or its attachment (as
related to friction resistance of binding) to the ground surface play an im-
portant role.
At that time, seismic observations were not accurate enough to detect
any rotation waves; moreover, from the point of view of ideal elasticity –
such waves shall not be observed at all, because rotation motion, even if
generated in a seismic source, shall be immediately attenuated. Of course,
there remains the displacement rotation component, which differs from
zero for shear motion, but in an ideal isotropic elastic body this component
attains very small values.
Perhaps some new, but rather isolated, attempts to record the rotation
waves were undertaken again in relation to these theoretical predictions.
However, most of them failed again because the instrumental tools were
not powerful enough.
In the second half of last century, we have observed a spectacular de-
velopment of mechanics of continua including defects, granular structure
and other deviations from the ideal linear elasticity. Special interests were
VI
concentrated on the micropolar and micromorphic continua. In such elastic
continua, the real rotations can be accompanied by another kind of axial
motion – the twist-bend motion.
We must stress that seismologists share different opinions on the nature
of rotation waves. Perhaps, still the majority believes that such rotation
motions are not related to inner rotations but are directly related to rotation
of displacement field which may reach much higher magnitudes in materi-
als with an internal structure than in homogeneous layers; considering
damages in the high buildings, there are many examples indicating enor-
mous increase of rotation effects caused by consecutive impacts of seismic
body and surface waves.
The rotation and twist motions are parts of the microdisplacement mo-
tion as related to the tensor of microstrain which appears in the generalized
continua. In ideal elasticity, any rotation motion is reduced to the dis-
placement vector rotation components, while the twist motion is related to
the non-diagonal strain components. In our Monograph, both approaches
are discussed.
In the last years, new types of the very sensitive rotation seismographs
and the laser/fiber ring interferometers (ring laser gyroscopes and fiber op-
tic gyros), based on the Sagnac principle, opened new abilities of recording
techniques.
Real media deviate from the ideal elasticity mainly due to defect content
and granular structure; such media will be further called the structured
continua. At the same time, some theoretical papers have recently ap-
peared pointing out that the values of the displacement rotation compo-
nents may be much higher than those predicted by the ideal elastic theory.
In both cases, anisotropy shall be also included.
However, apart of the rotation of displacements, in the structured media
there may also appear true rotation motions, as independent deformation
features. These rotation motions are part of the deformation and rotation
tensors, which includes rotation, twist and compression/dilatation motions;
together with the displacement vector, these motions form a complete de-
formation pattern.
The theory of structured continua enhanced our interest in the microdis-
placement motions. The microdisplacement fields are produced by the
asymmetric pattern of the faulting and friction motions. The slip friction
process causes rotation of adjacent grains and any deviations from symme-
try lead to a non-zero net rotation motion. Here, we point out the major
feature of earthquakes revealed in faulting along the main fault plane. This
is the main asymmetry feature of earthquake processes. We may admit that
generation of real rotation and twist motions in a source zone is a real fact.
However, there remains an open question whether such fields can propa-
VII
gate far from a source or are quickly attenuated when reaching a more con-
solidated elastic zone. Probably we should confine our considerations to
the near-field effects only.
However, we shall again take into account the fact that body and surface
seismic waves, when entering a near-surface region, which is characterized
by the more complex structure features, may give rise to conjugated mi-
crodisplacement motions; hence, rotation and twist waves may again ap-
pear due to interaction of the incident seismic waves with the complex fea-
tures of a near-surface zone. The theories of micropolar and micromorphic
media predict some relation between the displacement derivatives and the
microdisplacements.
Such considerations inspired us to write a comprehension monograph
which may open a new insight into seismological observations and studies.
We decided that a subject of such a monograph shall be broad, covering
many aspects, beginning from the historical observations, through modern
sensors detecting different types of seismic motions, to the advanced theo-
ries and models giving us a better insight into the complexity pattern of
earthquake source processes. Among other things, further studies on soli-
ton solutions for the events generated in a confined source zone may im-
prove the fracture band models, as introduced by some authors participat-
ing in the present task. Also, more attention shall be paid to the anisotropy
pattern related to the earthquake source zone.
At last, we shall turn to questions related to the earthquake engineering
problems which may arise even due to small rotation motions; the whole
problem started because in many cases some twist deformations have been
observed on ground surface. And now we shall also examine whether the
true rotation or twist motions, however small, can influence some struc-
tures senstive to moment of momentum impact.
The book covers, thus, many subjects, enlightened from different points
of view, as presented by the individual authors; we tried to collect the in-
dividual contributions in such a way as to create a possibly complete cov-
erage of the discussed subjects.
At the end of these considerations, it seems suitable to give a very brief
outline of the content of the present Monograph. It is divided into the fol-
lowing six parts:
Part I. MACROSEISMIC ROTATION EFFECTS AND MICROMOTIONS.
We discuss the possible causes of the rotation motions and effects in the
Earth’s interior and on its surface; also we recall some descriptions of the
rotation-like damages caused by the historical earthquakes.
Part II. THEORY OF CONTINUA AND FIELDS OF DEFECTS. We pre-
sent the asymmetric theory of continuous media with defects and anti-
VIII
symmetric strains and stresses (as equivalent to the stress moments and re-
lated conservation law for moment of momentum); the included introduc-
tion to the soliton physics has a particular meaning for the fracturing proc-
esses.
Part III. ROTATION MOTIONS, SEISMIC SOURCE MODELS, AND
ASYMMETRY OF FRACTURE. We discuss a rotation counterpart in the
fracturing process and the related energy release, we approach the prob-
lems of complex fracturing and flow phenomena and we face the problems
of analysis of the complex seismic motions; further, we present different
approaches to fracturing processes and the associated rotation motions in
the seismic active regions.
Part IV. EFFECTS RELATED TO MEDIUM STRUCTURES AND
COMPLEXITY OF WAVE PROPAGATION. We present some new ap-
proaches to the complexity of deformations in the structured and micro-
morphic media; the non-Riemannian description of deformations is in-
cluded.
Part V. SEISMIC ROTATIONAL MOTIONS: RECORDING TECHNIQUES
AND DATA ANALYSIS. Starting with a historical note, we include the de-
scriptions of some modern measuring systems for rotation, twist and tilt
motions, we discuss the gained observations and recordings and we give
their tentative analysis.
Part VI. ROTATIONS AND ENGINEERING SEISMOLOGY. We end our
Monograph with the problems of the earthquake engineering and strong
motions which include the rotation and tilt impacts on high buildings.
Acknowledgement. I would like to express my great thankfulness to
the editors of the camera-ready PDF form of manuscripts, Mrs Anna
Dziembowska, Mrs Maria Wernik and their staff, for their devoted and la-
borious work.
Roman Teisseyre
IX
Contents
PART I MACROSEISMIC ROTATION EFFECTS AND
MICROMOTIONS....................................................................................1
1 Development of Earthquake Rotational Effect Study
Jan T. Kozák............................................................................................3
2 Sources of Rotation and Twist Motions
Roman Teisseyre, Jan T. Kozák.............................................................11
2.1 Introduction...............................................................................11
2.2 Elements of the Basic Theory....................................................15
2.3 Recording the Rotation and Twist Motions...............................18
3 Some Examples of Rotation Effects: the Tulbagh Earthquake,
South Africa
Gerhard Graham, Andrzej Kijko...........................................................25
PART II THEORY OF CONTINUA AND FIELDS OF DEFECTS29
4 Deviations from Symmetry and Elasticity: Asymmetric
Continuum Mechanics
Roman Teisseyre, Wojciech Boraty(cid:276)ski.................................................31
4.1 Introduction...............................................................................31
4.2 Symmetric Stresses: Motion Equations.....................................33
4.3 Thermal Deformations...............................................................34
4.4 The Maxwell and Voigt–Kelvin Bodies: Equivalence
Theorems...................................................................................35
4.5 Asymmetric Fields.....................................................................36
5 Degenerated Asymmetric Continuum Theory
Roman Teisseyre, Mariusz Bia(cid:225)ecki, Marek Górski...............................43
5.1 Introduction...............................................................................43
5.2 Transition to Symmetric Tensor of Potentials...........................49
5.3 Special Case...............................................................................52
5.4 Conclusions...............................................................................53
X
6 Continuum with Rotation Nuclei and Defects: Dislocation
and Disclination Densities
Wojciech Boraty(cid:276)ski, Roman Teisseyre.................................................57
6.1 Introduction...............................................................................57
6.2 Defect Density Fields................................................................60
6.3 Dislocation–Stress Relations.....................................................63
6.4 Equations of Motion..................................................................64
6.5 Discussion..................................................................................65
7 Towards a Discrete Theory of Defects
Mariusz Bia(cid:225)ecki....................................................................................67
7.1 Introduction...............................................................................67
7.2 Towards a Discrete Description................................................69
7.3 Discrete Weingarten Theorem...................................................71
7.4 Prospects....................................................................................74
Appendix: Discrete Integration by Parts..........................................75
8 Fault Dynamics and Related Radiation
Wojciech Boraty(cid:276)ski, Roman Teisseyre.................................................77
8.1 Introduction...............................................................................77
8.2 Fault and Related Stresses.........................................................78
8.3 Evolution Equations for Dislocations and Disclinations...........78
8.4 Motion Equations: Fault and Radiation Parts............................79
8.5 Discussion..................................................................................88
9 A Review on Friction
Panayiotis Varotsos, Mary Lazaridou...................................................91
9.1 Introduction...............................................................................91
9.2 Stick-Slip Friction of a Granular System. Hysteresis
and Precursors...........................................................................93
9.3 Rock Friction.............................................................................97
9.4 Laboratory Experiments at High Rates of Slip. The Energy
Budget for Tectonic Faulting...................................................102
9.5 Modern Views on Friction. Theoretical Studies......................104
9.6 Constitutive Friction Law for the Antisymmetric Stresses......107
9.7 Open Questions.......................................................................108
10 Soliton Physics
Eugeniusz Majewski...........................................................................113
10.1 Introduction...........................................................................113
10.2 The Discovery of Solitary Waves..........................................115
10.3 The Korteweg–de Vries Equation.........................................115
XI
10.4 The Modified Korteweg–de Vries Equation..........................117
10.5 The Kadomtsev–Petviashvili Equation..................................117
10.6 The Boussinesq Equations.....................................................118
10.7 The Doubly Dispersive Equations.........................................119
10.8 The Nonlinear Schrödinger Equation....................................119
10.9 The Nonlinear Klein–Gordon Equation.................................120
10.10 The Sine-Gordon Equation..................................................121
10.11 The Inverse Scattering Transform.......................................121
10.12 Rotating Solitons.................................................................122
10.13 Discrete Soliton Systems.....................................................124
10.14 Conclusions.........................................................................126
PART III ROTATION MOTIONS, SEISMIC SOURCE
MODELS, AND ASYMMETRY OF FRACTURE ..........................129
11 Rotational Motions Excited by Earthquakes
Minoru Takeo.....................................................................................131
11.1 Introduction...........................................................................131
11.2 Geometrical Theory of Defects.............................................132
11.3 Formulation of Rotational and Translational Motions
Due to Earthquakes................................................................145
11.4 Possibility of Estimating a Rotational Strain Tensor
Due to an Earthquake............................................................149
11.5 Conclusions...........................................................................154
12 Ground Rotational Motions Recorded in Near-Source Region
of Earthquakes
Minoru Takeo.....................................................................................157
12.1 Introduction...........................................................................157
12.2 Observational System............................................................158
12.3 Near-Source Ground Rotational Motions..............................158
12.4 Discussion..............................................................................161
13 Fracture-Band Geometry and Rotation Energy Release
Roman Teisseyre, Marek Górski, Krzysztof P. Teisseyre..................169
13.1 Introduction...........................................................................169
13.2 Earthquake Dislocation Theory.............................................169
13.3 Earthquake Thermodynamics and Fracture Band Model......171
13.4 Elastic Rotation Energy.........................................................173
13.5 Cross-Band Fracturing Model and Rotation Processes.........175
13.6 Conclusions...........................................................................182
