Acoustic and Elastic Wave Fields in Geophysics, Part II

by Levshin; Larner; Kaufman

• ISBN13: 9780444506429
• ISBN10: 044450642X
• Format: Hardcover
• Copyright: 2002-10-11
• Publisher: Elsevier Science

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