Seismic Wave Propagation and Scattering in the Heterogeneous Earth

This book focuses on recent developments in the area of seismic wave propagation and scattering through the randomly heterogeneous structure of the Earth, with emphasis on the lithosphere. The presentation combines information from many sources to present a coherent introduction to the threory of scattering in acoustic and elastic materials and includesanalyses of observations using the theoretical methods developed.

1 Introduction.- 2 Heterogeneity in the Lithosphere.- 2.1 Geological Evidence.- 2.2 Well-Logs.- 2.2.1 Velocity Inhomogeneity Revealed by Well-Logs.- 2.2.2 Autocorrelation Function and Power Spectral Density Function.- 2.3 Deterministic Imaging Using Seismological Methods.- 2.3.1 Velocity Tomography.- 2.3.2 Refraction Surveys.- 2.3.3 Reflection Surveys.- 2.4 Scattering of High-Frequency Seismic Waves.- 2.4.1 S-Coda Waves.- 2.4.2 Three-Component Seismogram Envelopes.- 2.4.3 Broadening of S-Wave Seismogram Envelopes.- 3 Phenomenological Modeling of Coda-Wave Excitation.- 3.1 Single Scattering Models.- 3.1.1 Single Backscattering Model for a Common Source and Receiver Location.- 3.1.2 Single Isotropic Scattering Model for General Source and Receiver Locations.- 3.2 Multiple Scattering Models.- 3.2.1 Diffusion Model.- 3.2.2 Energy-Flux Model.- 3.2.3 Simulations of Coda-Wave Excitation.- 3.3 Coda Analysis.- 3.3.1 Coda-Excitation Measurements.- 3.3.2 Coda-Attenuation Measurements.- 3.3.3 Temporal Change in Coda Characteristics.- 3.4 Coda-Normalization Method.- 3.4.1 Site Amplification Measurements.- 3.4.2 Source Radiation Measurements.- 3.4.3 Attenuation Measurements.- 3.5 Related Coda Studies.- 3.5.1 S-Coda Anomalies.- 3.5.2 Teleseismic P-Coda.- 3.5.3 Lg and Lg-Coda.- 4 Born Approximation for Wave Scattering in Inhomogeneous Media.- 4.1 Scalar Waves.- 4.1.1 Born Approximation for a Localized Velocity Inhomogeneity.- 4.1.2 Scattering by Distributed Velocity Inhomogeneities.- 4.2 Elastic Vector Waves.- 4.2.1 Born Approximation for a Localized Elastic Inhomogeneity.- 4.2.2 Reduction of Independent Medium Fluctuations Using Birch’s Law.- 4.2.3 Scattering by Distributed Elastic Inhomogeneities.- 5 Attenuation of High-Frequency Seismic Waves.- 5.1 Attenuation in the Lithosphere.- 5.2 Intrinsic Attenuation Mechanisms.- 5.3 Scattering Attenuation Due to Distributed Random Inhomogeneities.- 5.3.1 Use of the Born Approximation for Estimating Scattering Attenuation of Scalar Waves.- 5.3.2 Use of the Born Approximation for Estimating Scattering Attenuation of Elastic Vector Waves.- 5.4 Scattering Attenuation Due to Distributed Cracks and Cavities.- 5.5 Power-Law Decay of Maximum Amplitude with Travel Distance.- 6 Synthesis of Three-Component Seismogram Envelopes for Earthquakes Using Scattering Amplitudes from the Born Approximation.- 6.1 Earthquake Source.- 6.1.1 Point Shear-Dislocation.- 6.1.2 Omega-Square Model for the Source Spectrum.- 6.2 Envelope Synthesis in an Infinite Space.- 6.2.1 Geometry of Source and Receiver.- 6.2.2 Power Spectral Density of Velocity Wavefield at the Receiver.- 6.2.3 Numerical Simulations.- 6.3 Envelope Synthesis in a Half-Space.- 6.3.1 Effects of the Free Surface.- 6.3.2 Numerical Simulations.- 6.3.3. Crustal Inhomogeneity in the Nikko Area, Northern Kanto, Japan.- 7 Envelope Synthesis Based on the Radiative Transfer Theory: Multiple Scattering Models.- 7.1 Multiple Isotropic Scattering Process for Spherical Source Radiation.- 7.1.1 Three-Dimensional Case.- 7.1.2 One- and Two-Dimensional Cases.- 7.1.3 Nonuniform Distribution of Scatterers.- 7.2 Separation of Scattering and Intrinsic Attenuation of S-Waves.- 7.2.1 Seismic Albedo.- 7.2.2 Multiple Lapse-Time Window Analysis.- 7.3 Multiple Isotropic Scattering Process for Nonspherical Source Radiation.- 7.3.1 Formulation.- 7.3.2 Simulation for a Point Shear-Dislocation Source.- 7.3.3 Using the Radiative Transfer Theory to Invert for the High-Frequency Radiation from an Earthquake.- 7.4 Multiple Nonisotropic Scattering Process for Spherical Source Radiation.- 7.4.1 Formulation.- 7.4.2 Simulation.- 7.5 Whole Seismogram Envelope: Isotropic Scattering Including Conversions Between P- and S-Waves.- 7.5.1 Formulation.- 7.5.2 Analytical Representation of the Single Scattering Term.- 7.5.3 Time Trace of the Total Energy Density.- 8 Diffraction and Broadening of Seismogram Envelopes.- 8.1 Amplitude and Phase Distortions of Scalar Waves.- 8.1.1 Parabolic Wave Equation.- 8.1.2 Transverse Correlations of Amplitude and Phase Fluctuations.- 8.1.3 Measurements of Amplitude and Phase Fluctuations.- 8.2 Markov Approximation for Predicting the MS Envelope Due to Diffraction.- 8.2.1 Coherent Wavefield.- 8.2.2 Mutual Coherence Function.- 8.2.3 Two-Frequency Mutual Coherence Function.- 8.2.4 Master Equation for Quasi-Monochromatic Waves.- 8.2.5 MS Envelope.- 8.3 Observed Broadening of S-Wave Seismogram Envelopes.- 8.3.1 Envelope Broadening Observed in Kanto, Japan.- 8.3.2 Differences of Random Inhomogeneities across the Volcanic Front in the Kanto-Tokai District, Japan.- 8.4 Split-Step Fourier Method for Modeling Wave Propagation Through an Inhomogeneous Medium.- 9 Summary and Epilogue.- 9.1 Summary of Methods and Observations.- 9.2 Future Developments.- Glossary of Symbols.- References.