Acoustics of Layered Media II

"The two books are characterized by scholasticity in the analytical treatment. The analysis is rigorous and complete. This could be attributed to the 'Russian school' where both authors belong to, offering an excellent framework for the study of problems of Mathematical Physics. ...In general, the books are considered valuable for researchers interested in the mathematical modeling of wave phenomena as they provide the readers with a comprehensive coverage of practically all the analytical aspects of the forward problem of acoustic wave propagation. In addition, throughout the books, they will meet many references to non-standard issues, as the propogation in moving media and energy conservation." Michael Taroudakis, Acustica United with Acta Acus, 2000/86/6

• 1. Reflection and Refraction of Spherical Waves.- 2. Reflection of Bounded Wave Beams.- 3. The Lateral Wave.- 4. Exact Theory of the Sound Field in Inhomogeneous Moving Media.- 5. High Frequency Sound Fields.- 6. The Field at and near a Caustic.- 7. Wave Propagation in a Range Dependent Waveguide.- 8. Energy Conservation and Reciprocity for Waves in Three-Dimensionally Inhomogeneous Moving Media.- Appendix A. The Reference Integrals Method.- A.1 The Method of Steepest Descent.- A.1.1 Integrals over an Infinite Contour.- A.1.2 Integrals over Semi-infinite Contours.- A.1.3 Integrals with Finite Limits.- A.1.4 The Contribution of Branch Points.- A.1.5 Integrals with Saddle Points of Higher Orders.- A.1.6 Several Saddle Points.- A.1.7 Concluding Remarks.- A.2 Integrals over a Real Variable.- A.2.1 Asymptotics of Laplace Integrals.- A.2.2 Stationary Phase Method. Asymptotics of Fourier Integrals.- A.2.3 Asymptotics of Multiple Fourier Integrals.- A.2.4 Asymptotics of Multiple Laplace Integrals.- A.2.5 Contributions of Critical Points on a Boundary.- A.3 Uniform Asymptotics of Integrals.- A.3.1 The Concept of Uniform Asymptotics.- A.3.2 A Pole and a Simple Stationary Point.- A.3.3 A Single Simple Stationary Point and a Branch Point.- A.3.4 Semi-infinite Contours.- A.3.5 Other Cases.- A.3.6 Concluding Remarks.- Appendix B. Differential Equations of Coupled-Mode Propagation in Fluids with Sloping Boundaries and Interfaces.- B.1 Derivation of the Differential Equations for Mode Coupling.- B.2 Mode-Coupling Coefficients in Terms of Environmental Gradients.- B.3 Energy Conservation and Symmetry of the Mode Coupling Coefficients.- B.4 Convergence of Normal Mode Expansions and its Implications on the Mode-Coupling Equations: Two Examples.- Appendix C. Reciprocity and Energy Conservation Within the Parabolic Approximation.- C.1 Definitions and Basic Relationships.- C.1.1 Range-Independent One-Way Wave Equations.- C.1.2 Equivalence of Reciprocity and Energy Conservation.- C.2 Energy Conserving and Reciprocal One-Way Wave Equation.- C.3 Generalized Claerbout PE (GCPE).- C.3.1 GCPE Derivation.- C.3.2 Local Reciprocity and Energy Balance Relations.- C.3.3 Media with Interfaces.- C.4 Comparison of Different One-Way Approximations.- C.5 Conclusion.- References.