Acoustics of Layered Media I

Profiles.- 3.6.2 "Compound" Layered Media.- 3.7 Exact Solutions for Media with Continuous Stratification of Sound Velocity, Density, and Flow Velocity.- 3.7.1 Motionless Fluid with Density Stratification.- 3.7.2 Moving Layered Medium.- 4. Plane-Wave Reflection from the Boundaries of Solids.- 4.1 Plane Waves in Elastic Half-Spaces with a Free Boundary.- 4.2 Reflection from Solid-Solid and Solid-Fluid Interfaces.- 4.2.1 Two Elastic Half-Spaces in Contact.- 4.2.2 Sound Wave Reflection from Solid.- 4.2.3 Elastic Wave Reflection from Fluid Half-Space.- 4.3 Reflection from a System of Solid Layers.- 4.3.1 Matrix Propagator.- 4.3.2 Reflection Coefficient of the Sound Wave.- 4.3.3 Scattering Matrix for the Elastic Waves.- 4.3.4 Some Special Cases.- 4.4 Surface and "Leaky" Waves.- 4.4.1 A Simple Example of Surface Waves.- 4.4.2 Rayleigh Wave.- 4.4.3 Stoneley and Other Waves at Fluid-Solid and Solid-Solid Interfaces.- 5. Reflection of Sound Pulses.- 5.1 General Relations. Law of Conservation of Integrated Pulse.- 5.1.1 Integral Representation of Sound Field.- 5.1.2 Conservation of Integrated Pulse.- 5.1.3 Energy Conservation.- 5.2 Change of Pulse Shape upon Total Internal Reflection from a Boundary Between Two Homogeneous Media.- 5.3 Total Reflection of a Pulse in Continuously Layered Media.- 6. Universal Properties of the Plane-Wave Reflection and Transmission Coefficients.- 6.1 Symmetry with Respect to Reversion of the Wave Path.- 6.1.1 Sound Waves in Fluids.- 6.1.2 Elastic Waves in Solids.- 6.2 Analytic Properties.- 6.2.1 Poles of the Reflection and Transmission Coefficients.- 6.2.2 Branch Points.- 6.3 Nonreflecting Layers.- 6.3.1 For Any Fixed Frequency and Angle of Incidence a Reflectionless Layer Exists.- 6.3.2 An Example of a Reflectionless Layer for Arbitrary Angle of Incidence.- 6.3.3 An Example of a Reflectionless Layer for Arbitrary Frequency.- 7. Acoustic Waves in Absorbing Anisotropic Media.- 7.1 Absorption of Sound.- 7.1.1 Waves in Dissipative Fluids.- 7.1.2 Absorption in Solids.- 7.2 Anisotropic Elastic Media. Gulyaev-Bluestein Waves.- 7.2.1 The Christoffel Equation.- 7.2.2 Elastic Waves in Transversally Isotropic Solids. Matrix Exponent.- 7.2.3 Harmonic Waves in Piezocrystals.- 7.3 Elastic Properties of Finely Layered Media.- 7.3.1 Matrix Propagator for Inhomogeneous Solids.- 7.3.2 An Effective Medium.- 7.3.3 The Most Important Special Cases.- 8. Geometrical Acoustics. WKB Approximation.- 8.1 The WKB Approximation and Its Range of Validity.- 8.1.1 Asymptotic Solution of the Wave Equation.- 8.1.2 WKB Approximation's General Conditions of Use.- 8.1.3 Regions of Applicability in Vicinities of Turning Points and Horizons of Resonance Interaction.- 8.2 Physical Meaning of the Approximate Solutions.- 8.2.1 Medium at Rest.- 8.2.2 Moving Medium.- 8.3 Another Approach to the Ray Acoustics Approximation.- 9. The Sound Field in the Case of Turning Horizons and Resonance Interaction with a Flow.- 9.1 Reference Equation Method.- 9.1.1 High-Frequency Solution of the Wave Equation.- 9.1.2 An Estimation of the Asymptotic Solution Accuracy.- 9.1.3 The Simplest Example.- 9.2 Sound Field in the Vicinity of a Turning Point.- 9.3 Reflection from a "Potential Barrier".- 9.3.1 Uniform Asymptotics of the Sound Field.- 9.3.2 Relation to the WKB Approximation.- 9.3.3 Reflection and Transmission Coefficients.- 9.4 Amplification of Sound in an Inhomogeneous Flow.- 9.4.1 Reference Problem.- 9.4.2 General Flow. Well-Separated Horizon of Resonance Interaction and Turning Points.- 9.4.3 General Flow. Arbitrary Separated Horizon of Resonance Interaction and Turning Points.- 9.4.4 Discussion of the Results.- 10. Sound Reflection from a Medium with Arbitrarily Varying Parameters.- 10.1 Differential Equations for Reflection Coefficient and Impedance of a Sound Wave.- 10.1.1 Riccati Equation.- 10.1.2 Two Properties of the Reflection Coefficient in Inhomogeneous Media.- 10.1.3 On Separation of the Wave Field into Direct and Inverse Waves.- 10.2 Reflection from a Thin Inhomogeneous Layer.- 10.2.1 Reduction of the Problem to an Integral Equation.- 10.2.2 Iterative Solution of the Integral Equation.- 10.2.3 Physical Consequences.- 10.3 Method of Successive Approximations for Weakly Reflecting Layers.- 10.3.1 Integral Equation for the Reflection Coefficient.- 10.3.2 The Born Approximation.- 10.3.3 Numerical Example.- 10.4 Reflection at Interfaces in Continuously Layered Media.- 10.4.1 General Approach.- 10.4.2 Sound Reflection at a Weak Interface.- 10.4.3 Ray Interpretation.- References.