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.
Introduction. List of symbols. 1. Principles of geometrical acoustics. Transition of high-frequency acoustics. Reflected waves in media with plane interfaces. Head waves in media with plane interfaces. Wavefront construction and ray tracing. Fermat's principle and ray equations. 2. Dynamics of high-frequency wave fields. Orientation of Poynting vector and rays at high-frequency spectrum. Amplitude A0 along a ray. Reflected and transmitted waves in presence of boundary. Wave field near caustic. Fresnel volume and physical meaning of ray. 3. Basics of Kirchhoff migration. Time fields and reconstruction of reflector. Principles of Kirchhoff migration. 4. Plane waves in layered media (normal incidence). Waves in media with a single planar interface. Normal incidence of plane wave in horizontally layered media. 5. Plane waves in layered media (oblique incidence). Reflection and transmission of plane wave. Reflection and refraction of sinusoidal waves. Distribution of energy between reflected and transmitted waves. Reflection and transmission of transient plane wave. Reflection and transmission of inhomogeneous plane waves. Oblique incidence of plane waves in media with two interfaces. Wave propagation in waveguides. Waves in media with continuously changing velocity. 6. Spherical waves in the presence of horizontal interface. Spherical source in a half-space with a free or rigid surface. Spherical source in medium with plane boundary (general case). Analysis of wave fields by the stationary phase method. Head wave and integration along branch cuts. Wave and near zones. Wave asymptotics and the steepest descent method. 7. Propagation of waves inside a layer. Acoustic potential of elementary source located inside a layer. Expansion of integrands in series. Integration along branch cuts and around poles. Normal modes. Asymptotic behavior of waves related to potential U. Transient waves inside a layer. Evaluation of normal modes. 8. Acoustic potential in medium with a cylindrical interface. Solution of the boundary value problem. Normal modes inside the cylinder. Head wave in borehole. Appendices. Appendix A. Functions of complex variables. Appendix B. Hilbert transform. Appendix C. The saddle point method. Appendix D. Different equations. References. Index.
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