Earthquake Source Asymmetry, Structural Media and Rotation Effects (eBook)

Preface 5
Contents 9
Contributors 19
PART I MACROSEISMIC ROTATION EFFECTS AND MICROMOTIONS 24
1 Development of Earthquake Rotational Effect Study 25
References 31
2 Sources of Rotation and Twist Motions 33
2.1 Introduction 33
2.2 Elements of the Basic Theory 37
2.3 Recording the Rotation and Twist Motions 40
References 44
3 Some Examples of Rotation Effects: the Tulbagh Earthquake, South Africa 46
References 49
PART II THEORY OF CONTINUA AND FIELDS OF DEFECTS 50
4 Deviations from Symmetry and Elasticity: Asymmetric Continuum Mechanics 51
4.1 Introduction 51
4.2 Symmetric Stresses: Motion Equations 53
4.3 Thermal Deformations 54
4.4 The Maxwell and Voigt–Kelvin Bodies: Equivalence Theorems 55
4.5 Asymmetric Fields 56
References 60
5 Degenerated Asymmetric Continuum Theory 62
5.1 Introduction 62
5.2 Transition to Symmetric Tensor of Potentials 68
5.3 Special Case 71
5.4 Conclusions 72
References 74
6 Continuum with Rotation Nuclei and Defects: 75
6.1 Introduction 75
6.2 Defect Density Fields 78
6.3 Dislocation–Stress Relations 81
6.4 Equations of Motion 82
6.5 Discussion 83
References 84
7 Towards a Discrete Theory of Defects 85
7.1 Introduction 85
7.2 Towards a Discrete Description 87
7.3 Discrete Weingarten Theorem 89
7.4 Prospects 92
Appendix: Discrete Integration by Parts 93
References 93
8 Fault Dynamics and Related Radiation 95
8.1 Introduction 95
8.2 Fault and Related Stresses 96
8.3 Evolution Equations for Dislocations and Disclinations 96
8.4 Motion Equations: Fault and Radiation Parts 97
8.5 Discussion 106
References 107
9 A Review on Friction 108
9.1 Introduction 108
9.2 Stick-Slip Friction of a Granular System. Hysteresis and Precursors 110
9.3 Rock Friction 114
9.4 Laboratory Experiments at High Rates of Slip. The Energy Budget for Tectonic Faulting 119
9.5 Modern Views on Friction. Theoretical Studies 121
9.6 Constitutive Friction Law for the Antisymmetric Stresses 124
9.7 Open Questions 125
References 126
10 Soliton Physics 129
10.1 Introduction 129
10.2 The Discovery of Solitary Waves 131
10.3 The Korteweg–de Vries Equation 131
10.4 The Modified Korteweg–de Vries Equation 133
10.5 The Kadomtsev–Petviashvili Equation 133
10.6 The Boussinesq Equations 134
10.7 The Doubly Dispersive Equations 135
10.8 The Nonlinear Schrödinger Equation 135
10.9 The Nonlinear Klein–Gordon Equation 136
10.10 The Sine-Gordon Equation 137
10.11 The Inverse Scattering Transform 137
10.12 Rotating Solitons 138
10.13 Discrete Soliton Systems 140
10.14 Conclusions 142
References 143
PART III ROTATION MOTIONS, SEISMIC SOURCE MODELS, AND ASYMMETRY OF FRACTURE 145
11 Rotational Motions Excited by Earthquakes 146
11.1 Introduction 146
11.2 Geometrical Theory of Defects 147
11.3 Formulation of Rotational and Translational Motions Due to Earthquakes 160
11.4 Possibility of Estimating a Rotational Strain Tensor Due to an Earthquake 164
11.5 Conclusions 169
References 170
12 Ground Rotational Motions Recorded in Near-Source Region of Earthquakes 172
12.1 Introduction 172
12.2 Observational System 173
12.3 Near-Source Ground Rotational Motions 173
12.4 Discussion 176
References 182
13 Fracture-Band Geometry and Rotation Energy Release 183
13.1 Introduction 183
13.2 Earthquake Dislocation Theory 183
13.3 Earthquake Thermodynamics and Fracture Band Model 185
13.4 Elastic Rotation Energy 187
13.5 Cross-Band Fracturing Model and Rotation Processes 189
13.6 Conclusions 196
References 196
14 Rotation Motions: Recording and Analysis 198
14.1 Introduction 198
14.2 Examples of Records and Their Preliminary Analysis 199
14.3 Discussion 209
References 210
15 Glacier Motion: Seismic Events and Rotation/Tilt Phenomena 211
15.1 Introduction 211
15.2 Icequakes 211
15.3 Ice Vibrations 213
15.4 Discussion 226
References 227
16 Rotational Energy and Angular Momentum of Earthquakes 228
16.1 Introduction 228
16.2 Modelling the Rotational Motions Excited in Earthquake Sources as Rolling Motions 228
16.3 Rolling in the Earthquake Source as Translation and Rotation Combined 229
16.4 The Kinetic Energy of Rolling in the Earthquake Source 230
16.5 Modelling Purely Rotational Motions in the Earthquake Source 232
16.6 The Torque and Angular Momentum of the Earthquake Source 233
16.7 Modelling Rotational Motions in the Earthquake Source as a Turbulence of Grains and Blocks Between Moving Tectonic Plates 234
16.8 Conclusions 236
References 236
17 Bend-Rotation Wave as a Mechanism of Macroseismic Effects 237
17.1 Introduction 237
17.2 Experimental Data 239
17.3 Field Observations 246
17.4 Conclusions 248
References 249
18 Solitary Waves in Crustal Faults and their Application to Earthquakes 251
18.1 Introduction 251
18.2 Observational Evidence 252
18.3 Mathematical Model of Deformation Process 253
18.4 Solitary Wave of Fault Activation 255
18.5 Evolution of Waves of Fault Activation 256
18.6 Effect of Periodical Change of Friction in the Fault 257
18.7 Effect of Periodical Change of External Load 258
18.8 Conclusions 261
References 262
19 Seismic Rotation Waves: Spin and Twist Solitons 264
19.1 Introduction 264
19.2 Modelling the Rotational Motions Excited in Earthquake Sources 265
19.3 Seismic Rotation Waves: PR and SR Waves 266
19.4 The Slow Tectonic Rotation Waves 267
19.5 Hamilton’s Principle 268
19.6 A Rock Medium Modelled as a Nonlinear Micropolar Elastic Continuum 268
19.7 The Nonlinear Field Equations 270
19.8 The Linear Seismic Rotation Waves 270
19.9 The Nonlinear Seismic Rotation Waves 272
19.10 Dispersion Curves and Rotation Solitons 275
19.11 The Seismic Rotation Solitons in the Degenerated Continuum 276
19.12 Conclusions 279
References 280
20 Earth Rotation, Elasticity and Geodynamics: Earthquake Wave Rotary Model 282
20.1 Introduction 282
20.2 Hypothesis 283
20.3 Stress Field Related to Rotation of Hard Bodies 284
20.4 Interaction Between Seismofocal Blocks 288
20.5 Chain of Blocks: Application to Pacific Margin Seismic Belt 289
20.6 Friction and Irregularities of Block Rotation: Rotation Mechanics of Earthquake Foci 291
20.7 Some Consequences 293
20.8 Conclusions 295
References 296
PART IV EFFECTS RELATED TO MEDIUM STRUCTURES AND COMPLEXITY OF WAVE PROPAGATION 299
21 Seismic Rotation Waves in the Continuum with Nonlinear Microstructure 300
21.1 Introduction 300
21.2 Additivity of Elastic and Self-Parts of Stresses, Microstresses, and Interaction Microforces 301
21.3 The Macroscopic and Microscopic Balance Equations 301
21.4 The Nonlinear Microstructure 305
21.5 Conclusions 306
References 307
22 Tectonic Solitons Propagating Along the Fault 308
22.1 Introduction 308
22.2 Seismic Waves in the Continuum with Dislocations 308
22.3 Seismic P waves 311
22.4 Splitting the Elastic Distortion Soliton Equation into Seismic and Fault-Related Soliton Equations 312
22.5 Seismic S Waves 313
22.6 Conclusions 315
References 316
23 Complexity of Rotation Soliton Propagation 317
23.1 Introduction 317
23.2 Preliminary Assumptions 317
23.3 Seismic Rotation Solitons 318
23.4 Conclusions 320
References 321
24 Micromorphic Continuum with Defects and Taylor–Bishop–Hill Theory for Polycrystals: Anisotropic Propagation of Seismic Waves and the Golebiewska Gauge 322
24.1 Introduction 322
24.2 Micromorphic Continuum with Defects 323
24.3 Taylor–Bishop–Hill Model 325
24.4 Quartz c-axis Preferred Orientation in Quartz Schist 326
24.5 Seismic Anisotropy due to LPO in Deformed Rocks 328
24.6 Discussion 329
24.7 Conclusion 331
References 331
25 Seismic Ray Theory for Structural Medium based on Kawaguchi and Finsler Geometry 334
25.1 Introduction 334
References 339
26 From Non-Local to Asymmetric Deformation Field 342
26.1 Introduction 342
26.2 High-Order Spaces and Non-Locality of Deformation 343
26.3 An Interaction Field Between Microscopic and Macroscopic Deformation Fields 344
26.4 Asymmetry and Anholonomity of Deformation 346
26.5 Discussion 347
References 349
27 Earthquake Hazard in the Valley of Mexico: Entropy, Structure, Complexity 352
27.1 Introduction 352
27.2 Seismology: a Science in Trouble? 353
27.3 Disasters in General, and Mexico City in Particular 354
27.4 A Higher Level of Description 356
27.5 Nonlinearity and Non-Equilibrium Thermodynamics 359
27.6 A Theory of Disasters as Unexpected Events 363
27.7 Disasters and Society 366
References 367
PART V SEISMIC ROTATIONAL MOTIONS: RECORDING TECHNIQUES AND DATA ANALYSIS 370
28 Note on the Historical Rotation Seismographs 371
28.1 Introduction 371
28.2 Electrical Seismograph with Sliding Smoked Paper 375
28.3 Electrical Seismograph with Sliding Smoked Paper – Second Model 378
References 379
29 Ring Laser Gyroscopes as Rotation Sensors for Seismic Wave Studies 381
29.1 Introduction 381
29.2 Properties of Ring Lasers 383
29.3 Detection of Seismic Signals 389
29.4 GEOsensor 391
References 394
30 Rotational Motions in Seismology: Theory, Observation, Simulation 395
30.1 Introduction 395
30.2 Fundamental Theory 398
30.3 Rotational Measurements 403
30.4 Observations and Simulations of Rotational Motions 405
30.5 Discussion and Conclusions 411
References 413
31 Absolute Rotation Measurement Based on the Sagnac Effect 416
31.1 Introduction 416
31.2 Sagnac Effect 416
31.3 Optical Gyroscopes as Systems Utilizing the Sagnac Effect 419
31.4 Fundamental Measurement Limits 422
31.5 Fiber-Optic Rotational Seismometer (FORS) 423
31.6 Investigation of the SRE Propagation Velocity 436
31.7 Conclusions 438
References 439
32 Design of Rotation Seismometer and 442
32.1 Introduction 442
32.2 Design of the Rotation Seismometer 443
32.3 Absolute Rotation Component Amplitudes for Earthquakes Observed at Sites of Different Surface Geological Conditions 447
32.4 Results and Future Scope 452
References 452
33 Rotation and Twist Motion Recording – Couple Pendulum and Rigid Seismometers System 454
33.1 Introduction 454
33.2 Behaviour of a Pendulum Seismometer During Measurement of Rotations – Static Approach 455
33.3 Measurement of Rotations by a Pair of Seismometers – Influence of Seismic Waves on Signal 457
33.4 Influence of Small Differences in Channel Responses on Rotation Measurement – Dynamic Approach 463
33.5 The Pendulum Seismometer for Measurement of Rotations Alone 468
33.6 Conclusions 472
References 472
34 Equation of Pendulum Motion Including Rotations and its Implications to the Strong-Ground Motion 474
34.1 Introduction 474
34.2 Theory of the Pendulum 476
34.3 Residual Displacements and what can be Done in Absence of Recorded Rotations (Tilts) 479
34.4 Numerical Tests of the Effects of Tilt on Computations of Displacement 482
34.5 Conclusions 485
References 486
35 Strong Motion Rotation Sensor 489
35.1 Introduction 489
35.2 Experimental Setup 489
35.3 Experimental Records 491
35.4 Conclusions 493
References 494
36 High-Resolution Wide-Range Tiltmeter: Observations of Earth Free Oscillations Excited by the 26 December 2004 Sumatra -Andaman Earthquake 495
36.1 Introduction 495
36.2 Natural Conditions in the Low Silesian Geophysical Observatory 496
36.3 Principle of Operation of the Long Water-Tube Tiltmeter 497
36.4 The Hydrodynamic System of the Long Water-Tube Tiltmeter 500
36.5 The Optic Module of Interference Gauge of the Water Level Variations Measurements 500
36.6 Determination of the Function of Plumb Line Variations 506
36.7 Determination of tidal wave coefficients on the basis of the long water-tube measurements 514
36.8 Observations of anomalous plumb line variations associated with Earth free oscillations on 26 December 2004 515
36.9 Conclusions 518
References 522
37 Fiber Optic Sensors for Seismic Monitoring 523
37.1 Introduction 523
37.2 Seismic Monitoring 523
37.3 Sensor/Ground Coupling 525
37.4 Fiber Optic Sensing 525
37.5 Matched Filtering/Antenna Gain 533
37.6 Physical Simulation Results Using STM 540
37.7 Discussion and Summary 544
References 546
PART VI ROTATIONS AND ENGINEERING SEISMOLOGY 548
38 Deriving Seismic Surface Rotations for Engineering Purposes 549
38.1 Introduction and Formulation of the Problem 549
38.2 Spectral Decomposition of Translational 552
Components of Seismic Ground Motion 552
38.3 Rocking from Body Waves Decomposition 553
38.4 Rocking from Surface Waves 559
38.5 Rocking from Spatial Field of Ground Motion 560
38.6 Code Proposals and Approximate Formulae 563
38.7 Application Example: A Slender Tower Under Horizontal-Rocking Excitations 564
38.8 Summary and Conclusions 566
References 567
39 Effects of Torsional and Rocking Excitations on the Response of Structures 569
39.1 Introduction 569
39.2 Rotational Strong Ground Motion 571
39.3 Recording Rotational Strong Motion 572
39.4 Generation of Synthetic Rotational Motions 573
39.5 Response of Structures 576
References 577