## Acoustic and Elastic Wave Fields in Geophysics, Volume 1This book is dedicated to basic physical principles of the propagation of acoustic and elastic waves. It consists of two volumes. The first volume includes 8 chapters and extended Appendices explaining mathematical aspects of discussed problems. The first chapter is devoted to Newton's laws, which, along with Hooke's law, govern the behavior of acoustic and elastic waves. Basic concepts of mechanics are used in deriving equations which describe wave phenomena. The second and third chapters deal with free and forced vibrations as well as wave propagation in one dimension along the system of elementary masses and springs which emulates the simplest elastic medium. In addition, shear waves propagation along a finite and infinite string are discussed. In chapter 4 the system of equations describing compressional waves is derived. The concepts of the density of the energy carried by waves, the energy flux, and the Poynting vector are introduced. Chapter 5 is dedicated to propagation of spherical, cylindrical, and plane waves in homogeneous media, both in time and frequency domains. Chapter 6 deals with interference and diffraction. The treatment is based on Helmholtz and Kirchhoff formulae. The detailed discussion of Fresnel's and Huygens's principles is presented. In Chapter 7 the effects of interference of waves with close wave numbers and frequencies are considered. Concepts such as the wave group, the group velocity, and the stationary phase important for understanding propagation of dispersive waves are introduced. The final chapter of the first volume is devoted to the principles of geometrical acoustics in inhomogeneous media. |

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### Contents

Newtons laws and parlide motion | 1 |

Free and forced vibrations | 21 |

Propagation | 49 |

Copyright | |

27 other sections not shown

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accordance with eq acoustic angle arbitrary assume becomes smaller behavior boundary conditions boundary value problem center of mass characterizes complex amplitude complex number component compression compressional wave consider const constant Correspondingly curl decrease defined deformation density derivative describe diffraction displacement distance elementary volume equal to zero external force flux follows from eq force F frequency grad group velocity homogeneous medium Hooke's law Huygens principle increase inside the volume instant integral interface interval latter located magnitude motion move Newton's second law observation point obtain parameter particle phase surface phase velocity position Poynting vector reflected wave respect scalar potential screen shown in Fig side of eq sinusoidal function sinusoidal waves Snell's law solution spring superposition Suppose Taking into account unit vector vector field wave equation wave field wave length wave number wave propagation x-axis zone