Seismology and Structure of the Earth: Treatise on Geophysics

Cover......Page 1
Editor-in-Chief......Page 2
Volume Editors......Page 3
Preface......Page 4
1.01 Overview......Page 7
Developments from the Late Nineteenth Century until the Early 1950s......Page 8
Developments from 1950s through the Early 1980s......Page 12
From 1980 to Present: The Era of Tomography and Broadband Digital Seismic Networks......Page 18
Current Issues in Global Tomography......Page 24
References......Page 31
Relevant Website......Page 35
Introduction......Page 36
Hamilton’s Principle and the Equations of Motion......Page 37
The Generalized Spherical Harmonics......Page 42
The Green’s Function for the Spherically Symmetric Earth......Page 45
Numerical Solution......Page 50
Elastic Displacement as a Sum over Modes......Page 57
The Normal Mode Spectrum......Page 58
Normal Modes and Theoretical Seismograms in Three-Dimensional Earth Models......Page 63
Concluding Discussion......Page 68
References......Page 69
Free Oscillations......Page 71
What We See in Seismograms - The Basics......Page 73
Modes of a Spherically Symmetric Earth......Page 75
Mode splitting......Page 77
Mode coupling......Page 81
Measuring Mode Observables......Page 85
Multiplet stripping and degenerate mode frequencies......Page 86
Singlet and receiver stripping......Page 89
Retrieving the splitting matrix with iterative spectral fitting......Page 90
Observed mode coupling......Page 92
Example of a Mode Application: IC Rotation......Page 95
Example of a Mode Application: Earth’s Hum......Page 96
Standing Waves and Traveling Waves......Page 98
The Measurement of Fundamental Mode Dispersion......Page 102
Group velocity......Page 105
Phase velocity......Page 107
Time variable filtering......Page 110
Other Surface Wave Observables......Page 111
Higher mode dispersion and waveform modeling......Page 113
Love waves and overtones......Page 117
Surface Waves and Structure at Depth......Page 118
Concluding Remarks......Page 121
References......Page 122
Relevant Website......Page 129
Introduction......Page 130
Intuitive Approach......Page 133
Elastodynamic Equations and Wave Equations......Page 134
Rays and Wave Fronts......Page 135
Variational Approaches of Ray Tracing......Page 136
Transport Equation......Page 137
Acoustic and Elastic Ray Theory......Page 138
Paraxial Ray Theory......Page 139
Ray Tracing Tools......Page 140
Boundary Conditions, Continuity, Reflection/\rTransmission Coefficients......Page 141
WKBJ summation......Page 142
Gaussian beam summation......Page 144
Coherent-state transformation technique......Page 145
Geometrical Theory of Diffraction......Page 146
Ray+Born/Rytov Formulation......Page 147
Ray+Kirchhoff Approximation......Page 148
Finite Frequency Effects on Ray Functions......Page 150
Conclusion......Page 151
References......Page 153
Introduction......Page 159
Elastic Velocities and Polarizations......Page 161
Common Structural Effects on Waveforms......Page 163
Deep-Earth Structural Problems......Page 166
Modeling Algorithms and Codes......Page 167
Reflectivity......Page 168
WKBJ-Maslov......Page 170
Full-Wave Theory and Integration in Complex p Plane......Page 172
DRT and Gaussian Beams......Page 173
Modal Methods......Page 174
Numerical Methods......Page 175
Homogeneous Layers Separated by Curved or Tilted Boundaries......Page 178
General 3-D Models......Page 179
Instrument and Source......Page 180
Far-Field Source Time Function......Page 181
Frequency-Dependent Ray Theory......Page 183
Attenuation......Page 184
Anisotropy......Page 185
Scattering......Page 186
References......Page 187
Relevant Websites......Page 191
Introduction......Page 192
The Challenge......Page 193
Equation of Motion......Page 195
Finite Difference Method......Page 197
Pseudospectral Method......Page 198
Weak Implementations......Page 200
Rayleigh-Ritz Method......Page 201
Coupled mode method......Page 202
Direct solution method......Page 203
Finite Element Method......Page 204
Spectral Element Method......Page 207
Discussion and Conclusions......Page 211
References......Page 214
Introduction......Page 219
Geometrical Preliminaries......Page 220
Modal Decomposition......Page 222
Receiver Functions and the Property of Minimum Phase......Page 224
Improved Teleseismic P Green’s Functions......Page 225
Teleseismic S Green’s Functions......Page 227
Deconvolution,  Stacking,\r and Array Processing......Page 228
Least-Squares Optimization......Page 229
Monte Carlo Inversion......Page 230
Born Inversion and Classic (Delay-and-Sum) Studies......Page 231
Multidimensional Inversion......Page 235
Beyond the Born Approximation......Page 238
The Inverse-Scattering Series......Page 239
Transmission to Reflection......Page 240
Conclusions......Page 242
References......Page 243
Introduction......Page 247
Vertical-Incidence and Wide-Angle Seismology......Page 248
Reflection Seismology......Page 250
The CMP Method in Reflection Seismology......Page 253
Migration......Page 255
Back-Propagation Operators......Page 256
Reflection Seismology Examples......Page 258
Refraction/Wide-Angle Seismology......Page 260
Wide-Angle Seismology Experiments......Page 261
Model Dimension......Page 263
Forward Modeling......Page 264
Traveltime Inversion and Tomography: Theory and Practical Issues......Page 265
Traveltime Inversion and Tomography: Algorithms......Page 270
S-Waves, Density, Attenuation,\rand Anisotropy......Page 272
Fine-Scale Heterogeneities......Page 273
Model Assessment......Page 274
Wide-Angle Migration......Page 276
Wavefield Inversion......Page 277
Wavefield Inversion Examples......Page 279
Future Directions......Page 280
References......Page 283
Relevant Website......Page 288
Introduction......Page 289
Basic General Theory......Page 290
Different Parametrizations of the Elastic Coefficients......Page 292
Ray Theory......Page 294
Surface Waves and Normal Modes......Page 296
Crustal Anisotropy......Page 301
Origin of Upper-Mantle Anisotropy......Page 302
Traveltime Residuals and Lithospheric Anisotropy......Page 304
SKS Waves and Upper-Mantle Anisotropy......Page 306
P and S Waves and Subduction Zones......Page 308
Surface Waves and Upper Mantle......Page 309
Polarization of Surface Waves......Page 311
Converted Waves and Lithospheric Anisotropy......Page 312
PKP Waves and the Inner Core......Page 314
References......Page 315
Introduction to Seismic Tomography......Page 322
Data Types in Seismic Tomography......Page 324
Body Waves......Page 326
Surface Waves......Page 327
Normal Modes......Page 328
Waveforms......Page 329
Cells, Nodes,\rand Basis Functions......Page 330
Irregular Cell and Adaptive Mesh Methods......Page 333
Linear versus Nonlinear Solutions......Page 335
Generalized inverse and damped least-squares solutions......Page 337
Occam’s inversion and Bayesian methods......Page 339
Hypocenter-Structure Coupling......Page 340
Static (Station) Corrections Revisited......Page 341
Double-Difference Tomography......Page 342
Data Coverage......Page 343
Model Resolution Analysis......Page 347
Hypothesis Testing......Page 349
Future Directions......Page 352
References......Page 353
Introduction, Purpose, and Scope......Page 360
Geology, Tectonics, and Earth History......Page 363
Active-Source Data......Page 365
Seismic refraction/wide-angle reflection profiles......Page 367
Seismic reflection profiles......Page 368
Passive-Source Data......Page 369
Receiver Functions......Page 371
Vp-Vs relations and poisson’s ratio......Page 372
Seismic anisotropy and the uppermost mantle......Page 373
Gravity Anomalies......Page 374
Aeromagnetics......Page 375
Heat Flow Data......Page 378
Structure of Oceanic Crust and Passive Margins......Page 379
Typical Oceanic Crust......Page 380
Oceanic Plateaux and Volcanic Provinces......Page 383
Ocean Trenches and Subduction Zones......Page 386
Passive Continental Margins......Page 387
Principal Crustal Types......Page 388
Global Crustal Models......Page 393
The Crystalline Crust and Uppermost Mantle......Page 394
Discussion and Conclusions......Page 396
References......Page 397
Depth Extent of Anomalous Structure......Page 417
Form of Shallow Upwelling and Onset of Melting......Page 418
Flow in the Mantle......Page 421
General Seismic Structure of the Oceanic Crust......Page 422
Fast-to-Superfast-Spreading Ridge Crustal Structure......Page 424
Intermediate Spreading Rate Ridge Crustal Structure......Page 428
Slow-Spreading Ridge Crustal Structure......Page 430
Ultraslow-Spreading Ridge Crustal Structure......Page 434
References......Page 435
Origin of the Hot-Spot Concept......Page 442
Potential Significance of Hot Spots......Page 448
Large Igneous Provinces......Page 449
Aseismic Ridges......Page 452
Superswells......Page 453
Mid-Plate Volcanic Chains and Clusters......Page 455
Orientation and Age......Page 456
Depth and Subsidence......Page 457
Geoid Height......Page 458
Elastic Plate Thickness......Page 459
Heat Flow......Page 460
Sedimentary Structures......Page 464
Volcanic Crust and Underplating......Page 465
Mantle Lithosphere......Page 469
Emerging View on Geophysical Structure of Hot Spots and Swells......Page 470
References......Page 471
1.14 Crust and Lithospheric Structure - Natural Source Portable Array Studies of Continental Lithosphere......Page 476
Introduction......Page 477
Instrumentation......Page 479
Field Installations and Data Acquisition......Page 481
Body wave tomography......Page 482
Surface wave tomography......Page 483
Discontinuity imaging......Page 484
Methodological Weaknesses and Caveats......Page 486
Snake River Plain/Yellowstone and Wyoming Craton......Page 488
Southern Rocky Mountain region......Page 489
Rio Grande Rift and Colorado Plateau......Page 490
Great Basin......Page 494
Crustal structure......Page 495
Seismic structure of uppermost mantle......Page 496
Continental Margin Subduction Zones......Page 498
Andean studies......Page 499
Alaska......Page 505
Kamchatka......Page 507
Central and Eastern North America......Page 508
Australia......Page 511
Archean Cratons......Page 514
Mantle tomographic images......Page 516
Crustal thickness and Moho structure beneath southern Africa......Page 517
Passive Array Studies of Other Cratons......Page 520
Seismic Constraints on Composition and Temperature of the Continental Lithosphere......Page 521
Discussion......Page 522
References......Page 523
Relevant Websites......Page 528
Introduction - Regional Geologic/Tectonic Setting of the Central Europe......Page 529
A New Generation of Long-Range Seismic Experiments......Page 531
Characteristics of the Seismic Wave Fields along Profiles for Different Tectonic Provinces (Terranes)......Page 533
Examples of 2-D and 3-D Modeling of the Earth’s Crust and Lower Lithosphere......Page 537
POLONAISE’97 Crustal and Lithospheric Models (Profiles P4 and P1)......Page 538
SUDETES 2003 Crustal Model (Profile S02)......Page 541
CELEBRATION 2000 Crustal Models CEL05 and CEL01......Page 542
Example of 3-D Tomographic Modeling......Page 545
Geotectonic Models of the TESZ and the Transition from the EEC to the Carpathians and the Pannonian Basin......Page 546
POLONAISE’97 Area......Page 548
CELEBRATION 2000 Area......Page 549
Summary......Page 551
References......Page 552
Introduction......Page 555
First-Order Perturbation Theory......Page 556
Effect of Anisotropic Heterogeneities on Normal Modes and Surface Waves......Page 558
Comparison between Surface Wave Anisotropy and SKS Splitting Data......Page 560
Data space: d......Page 561
Finite-frequency effects......Page 563
Inverse Problem......Page 564
Isotropic and Anisotropic Images of the Upper Mantle......Page 567
Geodynamic Applications......Page 569
Oceanic Plates......Page 570
Continents......Page 572
Velocity and Anisotropy in the Transition Zone......Page 573
Appendix 1: Effect of Anisotropy on Surface Waves in the Plane-Layered Medium......Page 575
Love Waves......Page 577
Rayleigh Waves......Page 578
References......Page 580
Relevant Websites......Page 585
Glossary......Page 586
Introduction......Page 587
Global Transition Zone Structure......Page 589
Japan......Page 592
Andes......Page 593
Additional observations......Page 594
North America......Page 595
Oceans......Page 596
520 discontinuity......Page 597
Summary of the Upper-Mantle Transition Zone......Page 598
The Gutenberg Discontinuity......Page 599
The Lehmann Discontinuity......Page 603
Summary of the Lehmann Discontinuity......Page 604
Conclusions......Page 605
References......Page 606
Glossary......Page 614
Lower Mantle and DPrime Basic Structural Attributes......Page 615
Mineralogical Structure......Page 616
Body-Wave Traveltime and Slowness Constraints......Page 617
Surface-Wave/Normal-Mode Constraints......Page 618
Attenuation Structure......Page 619
Seismic Tomography......Page 620
Dynamical Structures......Page 622
Large-Scale Seismic Velocity Attributes......Page 625
Thermal Boundary Layer Aspect......Page 626
DPrime Discontinuities......Page 627
Seismic Wave Triplications......Page 628
Phase Change in Perovskite......Page 629
Large Low-Shear-Velocity Provinces......Page 631
Seismic Velocity Properties......Page 632
Seismic Phases Used for Detection......Page 634
Partial Melting and Chemical Anomalies......Page 635
Lower-Mantle Anisotropy......Page 636
Mineralogical/Dynamical Implications......Page 637
Scattering in DPrime......Page 638
Conclusions......Page 639
References......Page 640
1.19 Deep Earth Structure - The Earth’s Cores......Page 650
Indirect Evidences for the Existence of a Core,\rand Historical Controversies......Page 651
The Seismological Detection of the Liquid Core and Inner Core......Page 652
Body-Wave Seismology: The Core Phases......Page 653
Free Oscillations......Page 654
Radial Structure of the Core in Global Earth Models......Page 656
The topography of the CMB......Page 658
The Inner Core Boundary......Page 659
The Main Questions Relative to Liquid Core Structure......Page 660
The Stratification at the Top of the Liquid Core......Page 661
The Attenuation in the Liquid Core......Page 662
Evidence for anisotropy in P-velocity......Page 663
Depth dependence of the anisotropy......Page 664
Origin of the anisotropy......Page 666
Lateral Heterogeneities inside the Inner Core......Page 667
Attenuation in the Inner Core......Page 668
The apparent incompatibility of body wave and normal mode results......Page 670
The anisotropy in attenuation......Page 672
S-Waves and the Rigidity of the Inner Core......Page 673
Tracking the Drift of a Heterogeneity along a Stable Seismic Path......Page 674
Discussion......Page 677
Summary of the Results......Page 680
The Open Questions, the Future Challenges,\rthe Data for the Future......Page 681
References......Page 682
Introduction......Page 689
Single-Scattering Theory and Random Media......Page 690
Q notation and definitions......Page 691
Finite Difference Calculations and the Energy Flux Model......Page 692
Multiple-Scattering Theories......Page 694
Scattering Observations......Page 697
S Coda......Page 698
P Coda......Page 700
Pdiff Coda......Page 703
PP and P’P’ Precursors......Page 704
PKP Precursors......Page 706
PKKP Precursors and PKKPX......Page 709
PKiKP and PKP Coda and Inner-Core Scattering......Page 711
Other Phases......Page 713
Discussion......Page 714
References......Page 715
1.21 Deep Earth Structure – Q of the Earth from Crust to Core......Page 724
Frequency Dependence of Q......Page 725
Early Studies......Page 727
1-D Global Mantle Q Models......Page 728
Attenuation in the Inner Core......Page 731
Hemispherical variations......Page 732
Early studies......Page 733
Anelasticity and focusing......Page 735
Current status......Page 737
Global Body-Wave Studies......Page 738
Multiple ScS Studies......Page 740
Other Body-Wave Studies......Page 742
Q or Attenuation Determinations for Seismic Waves in the Crust......Page 744
Spectral decay methods in which source effects cancel – Regional phases......Page 745
Spectral decay methods in which source effects cancel – Fundamental-mode surface waves......Page 746
Spectral decay methods for which assumptions are made about the source spectrum – Regional phases......Page 748
Tomographic Mapping of Crustal Q......Page 750
QLgC, QLg, and Q tomography in regions of Eurasia......Page 753
QLgC, QLg, and P/S tomography in North America......Page 757
Variation of crustal Q with time......Page 758
Conclusions......Page 759
References......Page 760
Relevant Website......Page 767
Introduction......Page 768
Overview......Page 770
One-Dimensional Lattice Dynamics and the Continuum Limit......Page 771
Experimental Methods......Page 772
3-D Lattice Dynamics: Polarization and Anisotropy......Page 773
Nontrivial Crystal Structures,\rOptic Modes, and Thermodynamics......Page 777
Influence of Pressure and Temperature on the Elastic Constants......Page 781
Composites Theory......Page 783
Attenuation and Dispersion......Page 786
Scaling......Page 789
Uncertainties......Page 790
Implications for Inversions......Page 792
References......Page 793
Introduction......Page 797
Convection-Related Surface Observations......Page 799
Evidence for Mantle Flow in Correlations between Internal Structure and Surface Gravity Anomalies......Page 801
Governing equations......Page 803
Spectral treatment of the mantle flow equations......Page 806
Internal boundary conditions......Page 807
Boundary conditions at Earth’s solid surface......Page 809
Boundary conditions at CMB......Page 811
Determining viscous flow Green functions......Page 812
Incorporating tectonic plates as a surface boundary condition......Page 813
Geodynamic Response Functions for the Mantle......Page 816
Depth Dependence of Mantle Viscosity......Page 817
Modeling Geodynamic Observables with Seismic Tomography......Page 821
Seismic Heterogeneity Models......Page 822
Mantle Density Anomalies......Page 823
Predicted Tectonic Plate Motions......Page 826
Predicted Free-Air Gravity Anomalies......Page 828
Predicted Dynamic Surface Topography......Page 829
Predicted CMB Topography......Page 835
Tomography-Based Geodynamic Inferences of Compositional Heterogeneity......Page 838
Constraints from Mineral Physics......Page 839
Compositional Density Anomalies Inferred from Joint Shear- and Bulk-Sound Tomography......Page 841
Compositional Density Anomalies Inferred from \'Hot’ and\r\'Cold’ Mantle Heterogeneity......Page 842
Diffuse Mid-Mantle Compositional Horizon......Page 844
Concluding Remarks......Page 845
References......Page 846