9780444506429

Acoustic and Elastic Wave Fields in Geophysics, Part II

by ; ;
  • ISBN13:

    9780444506429

  • ISBN10:

    044450642X

  • Format: Hardcover
  • Copyright: 2002-10-11
  • Publisher: Elsevier Science
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Summary

This book is a continuation of 'Acoustic and Elastic Wave Fields in Geophysics, Part I' published in 2000. The second volume is dedicated to propagation of linear plane, spherical and cylindrical acoustic waves in different media. Chapter 1 is devoted to principles of geometric acoustic in plane wave approximation. The eikonal and transport equations are derived. Ray tracing and wavefront construction techniques are explained. Chapter 2 deals with dynamic properties of wave fields. The behavior of pressure and displacements amplitudes in zero approximation is analysed in two ways: using Poynting vector and solving the transport equation. This chapter contains several examples related to shadow zones and caustics. In Chapter 3 using the results of analysis of high-frequency wave kinematics and dynamics some fundamental aspects of Kirchhoff migration are described. Chapters 4 and 5 are devoted to propagation of plane waves in media with flat boundaries in the case of normal and oblique incidence. Special attention is paid to the case when an incident angle exceeds the critical angles. Formation of normal modes in the waveguide is discussed. Chapter 6 deals with a spherical wave reflection and refraction. The steepest descent method is introduced to describe the behavior of reflected, transmitted, head and evanescent waves. In Chapter 7 propagation of stationary and transient waves in a waveguide formed by a flat layer with low velocity are investigated. Normal modes and waves related to the branch points of integrands under consideration are studied. Dispersive properties of normal modes are discussed. Chapter 8 describes wave propagation inside cylinder in acoustic media. Several appendices are added to help the reader understand different aspects of mathematics used in the book.

Table of Contents

Introduction vii
List of Symbols
xi
Principles of geometrical acoustics
1(98)
Transition to high-frequency acoustics
1(30)
Reflected waves in media with plane interfaces
31(15)
Head waves in media with plane interfaces
46(19)
Wavefront construction and ray tracing
65(21)
Fermat's principle and ray equations
86(13)
Dynamics of high-frequency wave fields
99(88)
Orientation of Poynting vector and rays at high-frequency spectrum
101(6)
Amplitude A0 along a ray
107(24)
Reflected and transmitted waves in presence of boundary
131(23)
Wave field near caustic
154(18)
Fresnel volume and physical meaning of ray
172(15)
Basics of Kirchhoff migration
187(52)
Time fields and reconstruction of reflector
187(12)
Principles of Kirchoff migration
199(40)
Plane waves in layered media (normal incidence)
239(34)
Waves in media with a single planar interface
239(10)
Normal incidence of plane wave in horizontally layered media
249(24)
Plane waves in layered media (oblique incidence)
273(94)
Reflection and transmission of plane wave
273(12)
Reflection and refraction of sinusoidal waves
285(12)
Distribution of energy between reflected and transmitted waves
297(9)
Reflection and transmission of transient plane wave
306(10)
Reflection and transmission of inhomogeneous plane waves
316(4)
Oblique incidence of plane waves in media with two interfaces
320(11)
Wave propagation in waveguides
331(13)
Waves in media with continuously changing velocity
344(23)
Spherical waves in the presence of horizontal interface
367(84)
Spherical source in a half-space with a free or rigid surface
367(11)
Spherical source in medium with plane boundary (general case)
378(8)
Analysis of wave fields by the stationary phase method
386(19)
Head wave and integration along branch cuts
405(12)
Wave and near zones
417(3)
Wave asymptotics and the steepest descent method
420(31)
Propagation of waves inside a layer
451(46)
Acoustic potential of elementary source located inside a layer
451(6)
Expansion of integrands in series
457(3)
Integration along branch cuts and around poles
460(9)
Normal modes
469(8)
Asymptotic behavior of waves related to potential U
477(5)
Transient waves inside a layer
482(5)
Evaluation of normal modes
487(10)
Acoustic potential in medium with a cylindrical interface
497(22)
Solution of the boundary value problem
497(10)
Normal modes inside the cylinder
507(7)
Head wave in borehole
514(5)
Appendices 519(94)
Appendix A. Functions of complex variables
519(36)
Appendix B. Hilbert transform
555(6)
Appendix C. The saddle point method
561(18)
Appendix D. Differential equations
579(34)
References 613(2)
Index 615

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