Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Books Cited -- 1 Simple Wave Solutions -- Synopsis -- 1.1 Model Equations -- 1.1.1 One-Dimensional Models -- 1.1.2 Two-Dimensional Models -- 1.1.3 Displacement Potentials -- 1.1.4 Energy Relations -- 1.2 The Fourier and Laplace Transforms -- 1.3 A Wave Is Not a Vibration -- 1.4 Dispersive Propagation -- 1.4.1 An Isolated Interaction -- 1.4.2 Periodic Structures -- References -- 2 Kinematical Descriptions of Waves -- Synopsis -- 2.1 Time-Dependent Plane Waves -- 2.2 Time-Harmonic Plane Waves -- 2.3 Plane-Wave or Angular-Spectrum Representations -- 2.3.1 A Gaussian Beam -- 2.3.2 An Angular-Spectrum Representation of a Spherical Wave -- 2.3.3 An Angular-Spectrum Representation of a Cylindrical Wave -- 2.4 Asymptotic Ray Expansion -- 2.4.1 Compressional Wave -- 2.4.2 Shear Wave -- Appendix: Spherical and Cylindrical Waves -- References -- 3 Reflection, Refraction, and Interfacial Waves -- Synopsis -- 3.1 Reflection of a Compressional Plane Wave -- 3.1.1 Phase Matching -- 3.1.2 Reflection Coefficients -- 3.2 Reflection and Refraction -- 3.3 Critical Refraction and Interfacial Waves -- 3.4 The Rayleigh Wave -- 3.4.1 The Time-Harmonic Wave -- 3.4.2 Transient Wave -- 3.4.3 The Rayleigh Function -- 3.4.4 Branch Cuts -- References -- 4 Green's Tensor and Integral Representations -- Synopsis -- 4.1 Introduction -- 4.2 Reciprocity -- 4.3 Green's Tensor -- 4.3.1 Notes -- 4.4 Principle of Limiting Absorption -- 4.5 Integral Representation: A Source Problem -- 4.5.1 Notes -- 4.6 Integral Representation: A Scattering Problem -- 4.6.1 Notes -- 4.7 Uniqueness in an Unbounded Region -- 4.7.1 No Edges -- 4.7.2 Edge Conditions -- 4.7.3 An Inner Expansion -- 4.8 Scattering From an Elastic Inclusion in a Fluid -- References -- 5 Radiation and Diffraction -- Synopsis.

5.1 Antiplane Radiation into a Half-Space -- 5.1.1 The Transforms -- 5.1.2 Inversion -- 5.2 Buried Harmonic Line of Compression I -- 5.3 Asymptotic Approximation of Integrals -- 5.3.1 Watson's Lemma -- 5.3.2 Method of Steepest Descents -- The Steepest Descents Contour -- An Isolated First-Order Saddle Point -- 5.3.3 Stationary Phase Approximation -- 5.4 Buried Harmonic Line of Compression II -- 5.4.1 The Complex Plane -- 5.4.2 The Scattered Compressional Wave -- 5.4.3 The Scattered Shear Wave -- 5.5 Diffraction of an Antiplane Shear Wave at an Edge -- 5.5.1 Formulation -- 5.5.2 Wiener-Hopf Solution -- 5.5.3 Description of the Scattered Wavefield -- 5.6 Matched Asymptotic Expansion Study -- Appendix: The Fresnel Integral -- References -- 6 Guided Waves and Dispersion -- Synopsis -- 6.1 Harmonic Waves in a Closed Waveguide -- 6.1.1 Partial Waves and the Transverse Resonance Principle -- 6.1.2 Dispersion Relation: A Closed Waveguide -- 6.2 Harmonic Waves in an Open Waveguide -- 6.2.1 Partial Wave Analysis -- 6.2.2 Dispersion Relation: An Open Waveguide -- 6.3 Excitation of a Closed Waveguide -- 6.3.1 Harmonic Excitation -- 6.3.2 Transient Excitation -- 6.4 Harmonically Excited Waves in an Open Waveguide -- 6.4.1 The Wavefield in the Layer -- 6.4.2 The Wavefield in the Half-Space -- 6.4.3 Leaky Waves -- 6.5 A Laterally Inhomogeneous, Closed Waveguide -- 6.6 Dispersion and Group Velocity -- 6.6.1 Causes of Dispersion -- 6.6.2 The Propagation of Information -- 6.6.3 The Propagation of Angular Frequencies -- A Signaling Problem -- A Kinematic Theory -- A Kinetic Theory -- References -- Index.