Acoustics of Layered Media II: Point Sources and Bounded Beams

by Leonid M. Brekhovskikh, Oleg A. Godin

Overview

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.

Product Details

ISBN-13:	9783540655923
Publisher:	Springer Berlin Heidelberg
Publication date:	04/28/1999
Series:	Springer Series on Wave Phenomena , #10
Edition description:	Second Edition 1999
Pages:	524
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

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.

Editorial Reviews

"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

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