Seismic Wave Propagation and Scattering in the Heterogeneous Earth

Seismic waves -- generated both by natural earthquakes and by man-made sources -- have produced an enormous amount of information about the Earth's interior. In classical seismology, the Earth is modeled as a sequence of uniform horizontal layers (or sperical shells) having different elastic properties and one determines these properties from travel times and dispersion of seismic waves. The Earth, however, is not made of horizontally uniform layers, and classic seismic methods can take large-scale inhomogeneities into account. Smaller-scale irregularities, on the other hand, require other methods. Observations of continuous wave trains that follow classic direct S waves, known as coda waves, have shown that there are heterogeneities of random size scattered randomly throughout the layers of the classic seismic model. 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 theory of scattering in acoustic and elastic materials and includes analyses of observations using the theoretical methods developed. Written for advanced undergraduates or beginning graduate students of geophysics or planetary sciences, this book should also be of interest to civil engineers, seismologists, acoustical engineers, and others interested in wave propagation through inhomogeneoud elastic media.

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.- 2.3 Deterministic Imaging Using Seismological Methods.- 2.4 Scattering of High-Frequency Seismic Waves.- 3 Phenomenological Modeling of Coda-Wave Excitation.- 3.1 Single Scattering Models.- 3.2 Multiple Scattering Models.- 3.3 Coda Analysis.- 3.4 Coda-Normalization Method.- 3.5 Related Coda Studies.- 4 Born Approximation for Wave Scattering in Inhomogeneous Media.- 4.1 Scalar Waves.- 4.2 Elastic Vector Waves.- 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.- 5.4 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.- 6.2 Envelope Synthesis in an Infinite Space.- 6.3 Envelope Synthesis in a Half-Space.- 7 Envelope Synthesis Based on the Radiative Transfer Theory: Multiple Scattering Models.- 7.1 Multiple Isotropic Scattering Process for Spherical Source Radiation.- 7.2 Separation of Scattering and Intrinsic Attenuation of S-Waves.- 7.3 Multiple Isotropic Scattering Process for Nonspherical Source Radiation.- 7.4 Multiple Nonisotropic Scattering Process for Spherical Source Radiation.- 7.5 Whole Seismogram Envelope: Isotropic Scattering Including Conversions Between P- and S-Waves.- 8 Diffraction and Broadening of Seismogram Envelopes.- 8.1 Amplitude and Phase Distortions of Scalar Waves.- 8.2 Markov Approximation for Predicting the MS Envelope Due to Diffraction.- 8.3 Observed Broadening of S-Wave Seismogram Envelopes.- 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.