Acoustics of Layered Media II: Point Sources and Bounded Beams / Edition 2by Leonid M. Brekhovskikh
Pub. Date: 12/03/2010
Publisher: Springer Berlin Heidelberg
Acoustics of Layered Media II presents the theory of sound propagation and reflection of spherical waves and bounded beams in layered media. It is mathematically rigorous but at the same time care is taken that the physical usefulness in applications and the logic of the theory are not hidden. Both moving and stationary media, discretely and continuously layered,… See more details below
Acoustics of Layered Media II presents the theory of sound propagation and reflection of spherical waves and bounded beams in layered media. It is mathematically rigorous but at the same time care is taken that the physical usefulness in applications and the logic of the theory are not hidden. Both moving and stationary media, discretely and continuously layered, including a range-dependent environment, are treated for various types of acoustic wave sources. Detailed appendices provide further background on the mathematical methods.
This second edition reflects the notable recent progress in the field of acoustic wave propagation in inhomogeneous media.
Table of Contents
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.
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