Teisseyre / Takeo / Majewski Earthquake Source Asymmetry, Structural Media and Rotation Effects

1. Auflage 2006
ISBN: 978-3-540-31337-3
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 582 Seiten

This breakthrough book is the first to examine the rotational effects in earthquakes, a revolutionary concept in seismology. Existing models do no yet explain the significant rotational and twisting motions that occur during an earthquake and cause the failure of structures. The rotation and twist effects are investigated and described, and their consequences for designing tall buildings and other important structures are presented. This book will change the way the world views earthquakes.

Autoren/Hrsg.

Teisseyre, Roman

Takeo, Minoru

Majewski, Eugeniusz

Inhaltsverzeichnis

1;Preface;5
2;Contents;9
3;Contributors;19
4;PART I MACROSEISMIC ROTATION EFFECTS AND MICROMOTIONS;24
4.1;1 Development of Earthquake Rotational Effect Study;25
4.1.1;References;31
4.2;2 Sources of Rotation and Twist Motions;33
4.2.1;2.1 Introduction;33
4.2.2;2.2 Elements of the Basic Theory;37
4.2.3;2.3 Recording the Rotation and Twist Motions;40
4.2.4;References;44
4.3;3 Some Examples of Rotation Effects: the Tulbagh Earthquake, South Africa;46
4.3.1;References;49
5;PART II THEORY OF CONTINUA AND FIELDS OF DEFECTS;50
5.1;4 Deviations from Symmetry and Elasticity: Asymmetric Continuum Mechanics;51
5.1.1;4.1 Introduction;51
5.1.2;4.2 Symmetric Stresses: Motion Equations;53
5.1.3;4.3 Thermal Deformations;54
5.1.4;4.4 The Maxwell and Voigt–Kelvin Bodies: Equivalence Theorems;55
5.1.5;4.5 Asymmetric Fields;56
5.1.6;References;60
5.2;5 Degenerated Asymmetric Continuum Theory;62
5.2.1;5.1 Introduction;62
5.2.2;5.2 Transition to Symmetric Tensor of Potentials;68
5.2.3;5.3 Special Case;71
5.2.4;5.4 Conclusions;72
5.2.5;References;74
5.3;6 Continuum with Rotation Nuclei and Defects:;75
5.3.1;6.1 Introduction;75
5.3.2;6.2 Defect Density Fields;78
5.3.3;6.3 Dislocation–Stress Relations;81
5.3.4;6.4 Equations of Motion;82
5.3.5;6.5 Discussion;83
5.3.6;References;84
5.4;7 Towards a Discrete Theory of Defects;85
5.4.1;7.1 Introduction;85
5.4.2;7.2 Towards a Discrete Description;87
5.4.3;7.3 Discrete Weingarten Theorem;89
5.4.4;7.4 Prospects;92
5.4.5;Appendix: Discrete Integration by Parts;93
5.4.6;References;93
5.5;8 Fault Dynamics and Related Radiation;95
5.5.1;8.1 Introduction;95
5.5.2;8.2 Fault and Related Stresses;96
5.5.3;8.3 Evolution Equations for Dislocations and Disclinations;96
5.5.4;8.4 Motion Equations: Fault and Radiation Parts;97
5.5.5;8.5 Discussion;106
5.5.6;References;107
5.6;9 A Review on Friction;108
5.6.1;9.1 Introduction;108
5.6.2;9.2 Stick-Slip Friction of a Granular System. Hysteresis and Precursors;110
5.6.3;9.3 Rock Friction;114
5.6.4;9.4 Laboratory Experiments at High Rates of Slip. The Energy Budget for Tectonic Faulting;119
5.6.5;9.5 Modern Views on Friction. Theoretical Studies;121
5.6.6;9.6 Constitutive Friction Law for the Antisymmetric Stresses;124
5.6.7;9.7 Open Questions;125
5.6.8;References;126
5.7;10 Soliton Physics;129
5.7.1;10.1 Introduction;129
5.7.2;10.2 The Discovery of Solitary Waves;131
5.7.3;10.3 The Korteweg–de Vries Equation;131
5.7.4;10.4 The Modified Korteweg–de Vries Equation;133
5.7.5;10.5 The Kadomtsev–Petviashvili Equation;133
5.7.6;10.6 The Boussinesq Equations;134
5.7.7;10.7 The Doubly Dispersive Equations;135
5.7.8;10.8 The Nonlinear Schrödinger Equation;135
5.7.9;10.9 The Nonlinear Klein–Gordon Equation;136
5.7.10;10.10 The Sine-Gordon Equation;137
5.7.11;10.11 The Inverse Scattering Transform;137
5.7.12;10.12 Rotating Solitons;138
5.7.13;10.13 Discrete Soliton Systems;140
5.7.14;10.14 Conclusions;142
5.7.15;References;143
6;PART III ROTATION MOTIONS, SEISMIC SOURCE MODELS, AND ASYMMETRY OF FRACTURE;145
6.1;11 Rotational Motions Excited by Earthquakes;146
6.1.1;11.1 Introduction;146
6.1.2;11.2 Geometrical Theory of Defects;147
6.1.3;11.3 Formulation of Rotational and Translational Motions Due to Earthquakes;160
6.1.4;11.4 Possibility of Estimating a Rotational Strain Tensor Due to an Earthquake;164
6.1.5;11.5 Conclusions;169
6.1.6;References;170
6.2;12 Ground Rotational Motions Recorded in Near-Source Region of Earthquakes;172
6.2.1;12.1 Introduction;172
6.2.2;12.2 Observational System;173
6.2.3;12.3 Near-Source Ground Rotational Motions;173
6.2.4;12.4 Discussion;176
6.2.5;References;182
6.3;13 Fracture-Band Geometry and Rotation Energy Release;183
6.3.1;13.1 Introduction;183
6.3.2;13.2 Earthquake Dislocation Theory;183
6.3.3;13.3 Earthquake Thermodynamics and Fracture Band Model;185
6.3.4;13.4 Elastic Rotation Energy;187
6.3.5;13.5 Cross-Band Fracturing Model and Rotation Processes;189
6.3.6;13.6 Conclusions;196
6.3.7;References;196
6.4;14 Rotation Motions: Recording and Analysis;198
6.4.1;14.1 Introduction;198
6.4.2;14.2 Examples of Records and Their Preliminary Analysis;199
6.4.3;14.3 Discussion;209
6.4.4;References;210
6.5;15 Glacier Motion: Seismic Events and Rotation/Tilt Phenomena;211
6.5.1;15.1 Introduction;211
6.5.2;15.2 Icequakes;211
6.5.3;15.3 Ice Vibrations;213
6.5.4;15.4 Discussion;226
6.5.5;References;227
6.6;16 Rotational Energy and Angular Momentum of Earthquakes;228
6.6.1;16.1 Introduction;228
6.6.2;16.2 Modelling the Rotational Motions Excited in Earthquake Sources as Rolling Motions;228
6.6.3;16.3 Rolling in the Earthquake Source as Translation and Rotation Combined;229
6.6.4;16.4 The Kinetic Energy of Rolling in the Earthquake Source;230
6.6.5;16.5 Modelling Purely Rotational Motions in the Earthquake Source;232
6.6.6;16.6 The Torque and Angular Momentum of the Earthquake Source;233
6.6.7;16.7 Modelling Rotational Motions in the Earthquake Source as a Turbulence of Grains and Blocks Between Moving Tectonic Plates;234
6.6.8;16.8 Conclusions;236
6.6.9;References;236
6.7;17 Bend-Rotation Wave as a Mechanism of Macroseismic Effects;237
6.7.1;17.1 Introduction;237
6.7.2;17.2 Experimental Data;239
6.7.3;17.3 Field Observations;246
6.7.4;17.4 Conclusions;248
6.7.5;References;249
6.8;18 Solitary Waves in Crustal Faults and their Application to Earthquakes;251
6.8.1;18.1 Introduction;251
6.8.2;18.2 Observational Evidence;252
6.8.3;18.3 Mathematical Model of Deformation Process;253
6.8.4;18.4 Solitary Wave of Fault Activation;255
6.8.5;18.5 Evolution of Waves of Fault Activation;256
6.8.6;18.6 Effect of Periodical Change of Friction in the Fault;257
6.8.7;18.7 Effect of Periodical Change of External Load;258
6.8.8;18.8 Conclusions;261
6.8.9;References;262
6.9;19 Seismic Rotation Waves: Spin and Twist Solitons;264
6.9.1;19.1 Introduction;264
6.9.2;19.2 Modelling the Rotational Motions Excited in Earthquake Sources;265
6.9.3;19.3 Seismic Rotation Waves: PR and SR Waves;266
6.9.4;19.4 The Slow Tectonic Rotation Waves;267
6.9.5;19.5 Hamilton’s Principle;268
6.9.6;19.6 A Rock Medium Modelled as a Nonlinear Micropolar Elastic Continuum;268
6.9.7;19.7 The Nonlinear Field Equations;270
6.9.8;19.8 The Linear Seismic Rotation Waves;270
6.9.9;19.9 The Nonlinear Seismic Rotation Waves;272
6.9.10;19.10 Dispersion Curves and Rotation Solitons;275
6.9.11;19.11 The Seismic Rotation Solitons in the Degenerated Continuum;276
6.9.12;19.12 Conclusions;279
6.9.13;References;280
6.10;20 Earth Rotation, Elasticity and Geodynamics: Earthquake Wave Rotary Model;282
6.10.1;20.1 Introduction;282
6.10.2;20.2 Hypothesis;283
6.10.3;20.3 Stress Field Related to Rotation of Hard Bodies;284
6.10.4;20.4 Interaction Between Seismofocal Blocks;288
6.10.5;20.5 Chain of Blocks: Application to Pacific Margin Seismic Belt;289
6.10.6;20.6 Friction and Irregularities of Block Rotation: Rotation Mechanics of Earthquake Foci;291
6.10.7;20.7 Some Consequences;293
6.10.8;20.8 Conclusions;295
6.10.9;References;296
7;PART IV EFFECTS RELATED TO MEDIUM STRUCTURES AND COMPLEXITY OF WAVE PROPAGATION;299
7.1;21 Seismic Rotation Waves in the Continuum with Nonlinear Microstructure;300
7.1.1;21.1 Introduction;300
7.1.2;21.2 Additivity of Elastic and Self-Parts of Stresses, Microstresses, and Interaction Microforces;301
7.1.3;21.3 The Macroscopic and Microscopic Balance Equations;301
7.1.4;21.4 The Nonlinear Microstructure;305
7.1.5;21.5 Conclusions;306
7.1.6;References;307
7.2;22 Tectonic Solitons Propagating Along the Fault;308
7.2.1;22.1 Introduction;308
7.2.2;22.2 Seismic Waves in the Continuum with Dislocations;308
7.2.3;22.3 Seismic P waves;311
7.2.4;22.4 Splitting the Elastic Distortion Soliton Equation into Seismic and Fault-Related Soliton Equations;312
7.2.5;22.5 Seismic S Waves;313
7.2.6;22.6 Conclusions;315
7.2.7;References;316
7.3;23 Complexity of Rotation Soliton Propagation;317
7.3.1;23.1 Introduction;317
7.3.2;23.2 Preliminary Assumptions;317
7.3.3;23.3 Seismic Rotation Solitons;318
7.3.4;23.4 Conclusions;320
7.3.5;References;321
7.4;24 Micromorphic Continuum with Defects and Taylor–Bishop–Hill Theory for Polycrystals: Anisotropic Propagation of Seismic Waves and the Golebiewska Gauge;322
7.4.1;24.1 Introduction;322
7.4.2;24.2 Micromorphic Continuum with Defects;323
7.4.3;24.3 Taylor–Bishop–Hill Model;325
7.4.4;24.4 Quartz c-axis Preferred Orientation in Quartz Schist;326
7.4.5;24.5 Seismic Anisotropy due to LPO in Deformed Rocks;328
7.4.6;24.6 Discussion;329
7.4.7;24.7 Conclusion;331
7.4.8;References;331
7.5;25 Seismic Ray Theory for Structural Medium based on Kawaguchi and Finsler Geometry;334
7.5.1;25.1 Introduction;334
7.5.2;References;339
7.6;26 From Non-Local to Asymmetric Deformation Field;342
7.6.1;26.1 Introduction;342
7.6.2;26.2 High-Order Spaces and Non-Locality of Deformation;343
7.6.3;26.3 An Interaction Field Between Microscopic and Macroscopic Deformation Fields;344
7.6.4;26.4 Asymmetry and Anholonomity of Deformation;346
7.6.5;26.5 Discussion;347
7.6.6;References;349
7.7;27 Earthquake Hazard in the Valley of Mexico: Entropy, Structure, Complexity;352
7.7.1;27.1 Introduction;352
7.7.2;27.2 Seismology: a Science in Trouble?;353
7.7.3;27.3 Disasters in General, and Mexico City in Particular;354
7.7.4;27.4 A Higher Level of Description;356
7.7.5;27.5 Nonlinearity and Non-Equilibrium Thermodynamics;359
7.7.6;27.6 A Theory of Disasters as Unexpected Events;363
7.7.7;27.7 Disasters and Society;366
7.7.8;References;367
8;PART V SEISMIC ROTATIONAL MOTIONS: RECORDING TECHNIQUES AND DATA ANALYSIS;370
8.1;28 Note on the Historical Rotation Seismographs;371
8.1.1;28.1 Introduction;371
8.1.2;28.2 Electrical Seismograph with Sliding Smoked Paper;375
8.1.3;28.3 Electrical Seismograph with Sliding Smoked Paper – Second Model;378
8.1.4;References;379
8.2;29 Ring Laser Gyroscopes as Rotation Sensors for Seismic Wave Studies;381
8.2.1;29.1 Introduction;381
8.2.2;29.2 Properties of Ring Lasers;383
8.2.3;29.3 Detection of Seismic Signals;389
8.2.4;29.4 GEOsensor;391
8.2.5;References;394
8.3;30 Rotational Motions in Seismology: Theory, Observation, Simulation;395
8.3.1;30.1 Introduction;395
8.3.2;30.2 Fundamental Theory;398
8.3.3;30.3 Rotational Measurements;403
8.3.4;30.4 Observations and Simulations of Rotational Motions;405
8.3.5;30.5 Discussion and Conclusions;411
8.3.6;References;413
8.4;31 Absolute Rotation Measurement Based on the Sagnac Effect;416
8.4.1;31.1 Introduction;416
8.4.2;31.2 Sagnac Effect;416
8.4.3;31.3 Optical Gyroscopes as Systems Utilizing the Sagnac Effect;419
8.4.4;31.4 Fundamental Measurement Limits;422
8.4.5;31.5 Fiber-Optic Rotational Seismometer (FORS);423
8.4.6;31.6 Investigation of the SRE Propagation Velocity;436
8.4.7;31.7 Conclusions;438
8.4.8;References;439
8.5;32 Design of Rotation Seismometer and;442
8.5.1;32.1 Introduction;442
8.5.2;32.2 Design of the Rotation Seismometer;443
8.5.3;32.3 Absolute Rotation Component Amplitudes for Earthquakes Observed at Sites of Different Surface Geological Conditions;447
8.5.4;32.4 Results and Future Scope;452
8.5.5;References;452
8.6;33 Rotation and Twist Motion Recording – Couple Pendulum and Rigid Seismometers System;454
8.6.1;33.1 Introduction;454
8.6.2;33.2 Behaviour of a Pendulum Seismometer During Measurement of Rotations – Static Approach;455
8.6.3;33.3 Measurement of Rotations by a Pair of Seismometers – Influence of Seismic Waves on Signal;457
8.6.4;33.4 Influence of Small Differences in Channel Responses on Rotation Measurement – Dynamic Approach;463
8.6.5;33.5 The Pendulum Seismometer for Measurement of Rotations Alone;468
8.6.6;33.6 Conclusions;472
8.6.7;References;472
8.7;34 Equation of Pendulum Motion Including Rotations and its Implications to the Strong-Ground Motion;474
8.7.1;34.1 Introduction;474
8.7.2;34.2 Theory of the Pendulum;476
8.7.3;34.3 Residual Displacements and what can be Done in Absence of Recorded Rotations (Tilts);479
8.7.4;34.4 Numerical Tests of the Effects of Tilt on Computations of Displacement;482
8.7.5;34.5 Conclusions;485
8.7.6;References;486
8.8;35 Strong Motion Rotation Sensor;489
8.8.1;35.1 Introduction;489
8.8.2;35.2 Experimental Setup;489
8.8.3;35.3 Experimental Records;491
8.8.4;35.4 Conclusions;493
8.8.5;References;494
8.9;36 High-Resolution Wide-Range Tiltmeter: Observations of Earth Free Oscillations Excited by the 26 December 2004 Sumatra -Andaman Earthquake;495
8.9.1;36.1 Introduction;495
8.9.2;36.2 Natural Conditions in the Low Silesian Geophysical Observatory;496
8.9.3;36.3 Principle of Operation of the Long Water-Tube Tiltmeter;497
8.9.4;36.4 The Hydrodynamic System of the Long Water-Tube Tiltmeter;500
8.9.5;36.5 The Optic Module of Interference Gauge of the Water Level Variations Measurements;500
8.9.6;36.6 Determination of the Function of Plumb Line Variations;506
8.9.7;36.7 Determination of tidal wave coefficients on the basis of the long water-tube measurements;514
8.9.8;36.8 Observations of anomalous plumb line variations associated with Earth free oscillations on 26 December 2004;515
8.9.9;36.9 Conclusions;518
8.9.10;References;522
8.10;37 Fiber Optic Sensors for Seismic Monitoring;523
8.10.1;37.1 Introduction;523
8.10.2;37.2 Seismic Monitoring;523
8.10.3;37.3 Sensor/Ground Coupling;525
8.10.4;37.4 Fiber Optic Sensing;525
8.10.5;37.5 Matched Filtering/Antenna Gain;533
8.10.6;37.6 Physical Simulation Results Using STM;540
8.10.7;37.7 Discussion and Summary;544
8.10.8;References;546
9;PART VI ROTATIONS AND ENGINEERING SEISMOLOGY;548
9.1;38 Deriving Seismic Surface Rotations for Engineering Purposes;549
9.1.1;38.1 Introduction and Formulation of the Problem;549
9.1.2;38.2 Spectral Decomposition of Translational;552
9.1.3;Components of Seismic Ground Motion;552
9.1.4;38.3 Rocking from Body Waves Decomposition;553
9.1.5;38.4 Rocking from Surface Waves;559
9.1.6;38.5 Rocking from Spatial Field of Ground Motion;560
9.1.7;38.6 Code Proposals and Approximate Formulae;563
9.1.8;38.7 Application Example: A Slender Tower Under Horizontal-Rocking Excitations;564
9.1.9;38.8 Summary and Conclusions;566
9.1.10;References;567
9.2;39 Effects of Torsional and Rocking Excitations on the Response of Structures;569
9.2.1;39.1 Introduction;569
9.2.2;39.2 Rotational Strong Ground Motion;571
9.2.3;39.3 Recording Rotational Strong Motion;572
9.2.4;39.4 Generation of Synthetic Rotational Motions;573
9.2.5;39.5 Response of Structures;576
9.2.6;References;577