## Acoustic and Elastic Wave Fields in Geophysics, Volume 2This 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. |

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### Contents

Principles of geometrical acoustics | 1 |

Dynamics of highfrequency wave fields | 99 |

Basics of Kirchhoff migration | 187 |

Copyright | |

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### Common terms and phrases

accordance with eq acoustic amplitude analytical function assume asymptotic behavior boundary value problem Cauchy theorem characterizes coincides complex amplitude consider const coordinates Correspondingly defined derivative described differential equation diffraction displacement distance eikonal elementary waves equal reflection Fermat's principle follows from eq frequency given by eq head wave Helmholtz equation homogeneous Inasmuch incidence angle incident and reflected incident wave inhomogeneous integral curves integrand interface intersection isochrones latter layer located lower medium normal modes observation point obtain parameter path phase surface phase velocity plane waves point q potential Poynting vector pressure radius record horizon reflected and transmitted reflected wave reflector respect saddle point shown in Fig side of eq sin2 Snell's law solution stationary point Substitution of eqs Suppose Taking into account tangential Taylor series transient waves transmitted waves upper medium vicinity wave field wave propagates z-axis