Seismology and Structure of the Earth : Treatise on Geophysics

Seismology and Structure of the Earth focuses on theory and applications of seismology strictly as related to our understanding of the Earth’s interior structure. This volume provides an overview of the status of geophysics and is divided into three parts. Part I is devoted to various aspects of seismic wave propagation theory, data analysis and inversion methods, and documents the increasingly important role of numerical computational methods. Part II addresses the internal structure from the crust to the core, considering elastic, anelastic and anisotropic views of the Earth at global and regional scales. And, Part III reviews mineral physics and geodynamics to further progress in the understanding of Earth's internal dynamics and of the forces that drive plate tectonics by combining constraints from different disciplines. Self-contained volume starts with an overview of the subject then explores each topic with in depth detail Extensive reference lists and cross references with other volumes to facilitate further research Full-color figures and tables support the text and aid in understanding Content suited for both the expert and non-expert 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/ Transmission 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, 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, and 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, and 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, and 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, the 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, Optic 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 'Cold’ Mantle Heterogeneity......Page 842 Diffuse Mid-Mantle Compositional Horizon......Page 844 Concluding Remarks......Page 845 References......Page 846 Treatise on Geophysics: Seismology and Structure of the Earth, Volume 1, provides a comprehensive review of the state of knowledge on the Earths structure and earthquakes. It addresses various aspects of structural seismology and its applications to other fields of Earth sciences. The book is organized into four parts. The first part principally covers theoretical developments and seismic data analysis techniques from the end of the nineteenth century until the present, with the main emphasis on the development of instrumentation and its deployment. The second part reviews the status of knowledge on the structure of the Earths shallow layers, starting with a global review of the Earth's crustal structure. The third part focuses on the Earth's deep structure, divided into its main units: the upper mantle, the transition zone and upper-mantle discontinuities, the D region at the base of the mantle, and the Earth's core. The fourth part comprises two chapters which discuss constraints on Earth structure from fields other than seismology: mineral physics and geodynamics. Self-contained volume starts with an overview of the subject then explores each topic with in depth detail Extensive reference lists and cross references with other volumes to facilitate further research Full-color figures and tables support the text and aid in understanding Content suited for both the expert and non-expert