4.7.2 Aftershocks, 277
4.7.3 Earthquake probabilities, 278
Further reading, 282
Problems, 282
5 Seismology and Plate Tectonics, 286
5.1 Introduction, 286
5.2 Plate kinematics, 290
5.2.1 Relative plate motions, 290
5.2.2 Global plate motions, 293
5.2.3 Space-based geodesy, 295
5.2.4 Absolute plate motions, 296
5.3 Spreading centers, 298
5.3.1 Geometry of ridges and transforms, 298
5.3.2 Evolution of the oceanic lithosphere, 299
5.3.3 Ridge and transform earthquakes and
processes, 305
5.4 Subduction zones, 307
5.4.1 Thermal models of subduction, 308
5.4.2 Earthquakes in subducting slabs, 312
5.4.3 Interplate trench earthquakes, 321
5.5 Oceanic intraplate earthquakes and tectonics, 326
5.5.1 Locations of oceanic intraplate seismicity, 326
5.5.2 Forces and stresses in the oceanic lithosphere, 328
5.5.3 Constraints on mantle viscosity, 331
5.6 Continental earthquakes and tectonics, 333
5.6.1 Continental plate boundary zones, 334
5.6.2 Seismic, aseismic, transient, and
permanent deformation, 339
5.6.3 Continental intraplate earthquakes, 342
5.7 Faulting and deformation in the earth, 346
5.7.1 Rheology, 346
5.7.2 Rock fracture and friction, 348
5.7.3 Ductile flow, 355
5.7.4 Strength of the lithosphere, 357
5.7.5 Earthquakes and rock friction, 359
5.7.6 Earthquakes and regional deformation, 364
Further reading, 366
Problems, 367
6 Seismograms as Signals, 369
6.1 Introduction, 369
6.2 Fourier analysis, 369
6.2.1 Fourier series, 369
6.2.2 Complex Fourier series, 371
6.2.3 Fourier transforms, 372
6.2.4 Properties of Fourier transforms, 374
6.2.5 Delta functions, 375
6.3 Linear systems, 377
6.3.1 Basic model, 377
6.3.2 Convolution and deconvolution modeling, 379
6.3.3 Finite length signals, 380
6.3.4 Correlation, 383
6.4 Discrete time series and transforms, 385
6.4.1 Sampling of continuous data, 385
Contents vii
6.4.2 The discrete Fourier transform, 387
6.4.3 Properties of DFTs, 389
6.4.4 The fast Fourier transform (FFT), 389
6.4.5 Digital convolution, 390
6.5 Stacking, 391
6.5.1 Random errors, 392
6.5.2 Stacking examples, 395
6.6 Seismometers and seismological networks, 398
6.6.1 Introduction, 398
6.6.2 The damped harmonic oscillator, 398
6.6.3 Earth noise, 400
6.6.4 Seismometers and seismographs, 400
6.6.5 Digital recording, 405
6.6.6 Types of networks, 407
6.6.7 Global networks, 407
6.6.8 Arrays, 409
6.6.9 Regional networks, 410
Further reading, 412
Problems, 412
7 Inverse Problems, 415
7.1 Introduction, 415
7.2 Earthquake location, 416
7.2.1 Theory, 416
7.2.2 Earthquake location for a homogeneous
medium, 419
7.2.3 Errors, 420
7.2.4 Earthquake location for more complex
geometries, 422
7.3 Travel time tomography, 424
7.3.1 Theory, 424
7.3.2 Generalized inverse, 426
7.3.3 Properties of the generalized inverse
solution, 427
7.3.4 Variants of the solution, 429
7.3.5 Examples, 430
7.4 Stratified earth structure, 434
7.4.1 Earth structure from normal modes, 434
7.4.2 Parameter and data space inversions, 436
7.4.3 Features of the solutions, 437
7.5 Inverting for plate motions, 439
7.5.1 Method, 439
7.5.2 Testing the results with χ 2 and
F-ratio tests, 440
Further reading, 441
Problems, 442
Appendix: Mathematical and
Computational Background, 443
A.1 Introduction, 443
A.2 Complex numbers, 443
A.3 Scalars and vectors, 445
A.3.1 Definitions, 445
A.3.2 Elementary vector operations, 446
A.3.3 Scalar products, 446
4.7.3 Earthquake probabilities, 278
Further reading, 282
Problems, 282
5 Seismology and Plate Tectonics, 286
5.1 Introduction, 286
5.2 Plate kinematics, 290
5.2.1 Relative plate motions, 290
5.2.2 Global plate motions, 293
5.2.3 Space-based geodesy, 295
5.2.4 Absolute plate motions, 296
5.3 Spreading centers, 298
5.3.1 Geometry of ridges and transforms, 298
5.3.2 Evolution of the oceanic lithosphere, 299
5.3.3 Ridge and transform earthquakes and
processes, 305
5.4 Subduction zones, 307
5.4.1 Thermal models of subduction, 308
5.4.2 Earthquakes in subducting slabs, 312
5.4.3 Interplate trench earthquakes, 321
5.5 Oceanic intraplate earthquakes and tectonics, 326
5.5.1 Locations of oceanic intraplate seismicity, 326
5.5.2 Forces and stresses in the oceanic lithosphere, 328
5.5.3 Constraints on mantle viscosity, 331
5.6 Continental earthquakes and tectonics, 333
5.6.1 Continental plate boundary zones, 334
5.6.2 Seismic, aseismic, transient, and
permanent deformation, 339
5.6.3 Continental intraplate earthquakes, 342
5.7 Faulting and deformation in the earth, 346
5.7.1 Rheology, 346
5.7.2 Rock fracture and friction, 348
5.7.3 Ductile flow, 355
5.7.4 Strength of the lithosphere, 357
5.7.5 Earthquakes and rock friction, 359
5.7.6 Earthquakes and regional deformation, 364
Further reading, 366
Problems, 367
6 Seismograms as Signals, 369
6.1 Introduction, 369
6.2 Fourier analysis, 369
6.2.1 Fourier series, 369
6.2.2 Complex Fourier series, 371
6.2.3 Fourier transforms, 372
6.2.4 Properties of Fourier transforms, 374
6.2.5 Delta functions, 375
6.3 Linear systems, 377
6.3.1 Basic model, 377
6.3.2 Convolution and deconvolution modeling, 379
6.3.3 Finite length signals, 380
6.3.4 Correlation, 383
6.4 Discrete time series and transforms, 385
6.4.1 Sampling of continuous data, 385
Contents vii
6.4.2 The discrete Fourier transform, 387
6.4.3 Properties of DFTs, 389
6.4.4 The fast Fourier transform (FFT), 389
6.4.5 Digital convolution, 390
6.5 Stacking, 391
6.5.1 Random errors, 392
6.5.2 Stacking examples, 395
6.6 Seismometers and seismological networks, 398
6.6.1 Introduction, 398
6.6.2 The damped harmonic oscillator, 398
6.6.3 Earth noise, 400
6.6.4 Seismometers and seismographs, 400
6.6.5 Digital recording, 405
6.6.6 Types of networks, 407
6.6.7 Global networks, 407
6.6.8 Arrays, 409
6.6.9 Regional networks, 410
Further reading, 412
Problems, 412
7 Inverse Problems, 415
7.1 Introduction, 415
7.2 Earthquake location, 416
7.2.1 Theory, 416
7.2.2 Earthquake location for a homogeneous
medium, 419
7.2.3 Errors, 420
7.2.4 Earthquake location for more complex
geometries, 422
7.3 Travel time tomography, 424
7.3.1 Theory, 424
7.3.2 Generalized inverse, 426
7.3.3 Properties of the generalized inverse
solution, 427
7.3.4 Variants of the solution, 429
7.3.5 Examples, 430
7.4 Stratified earth structure, 434
7.4.1 Earth structure from normal modes, 434
7.4.2 Parameter and data space inversions, 436
7.4.3 Features of the solutions, 437
7.5 Inverting for plate motions, 439
7.5.1 Method, 439
7.5.2 Testing the results with χ 2 and
F-ratio tests, 440
Further reading, 441
Problems, 442
Appendix: Mathematical and
Computational Background, 443
A.1 Introduction, 443
A.2 Complex numbers, 443
A.3 Scalars and vectors, 445
A.3.1 Definitions, 445
A.3.2 Elementary vector operations, 446
A.3.3 Scalar products, 446