ACOUSTIC AND ELASTIC WAVE FIELDS IN GEOPHYSICS, PART I, 37
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By A.A. Kaufman, Department of Geophysics, Colorado School of Mines, Golden, CO, USA A.L. Levshin, Department of Physics, University of Colorado, Boulder, CO 80390, USA
Description This 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.
Contents
Introduction. List of Symbols. Newton's laws and parlide motion. Newton's laws. Motion of system of particles.
Free
and forced vibrations. Hooke's law of springs. Free vibrations of the system: mass-spring. Forced vibrations of the system:
mass-spring. Principles of measuring vibrations.
Propagation. Propagation of waves along a system of masses and springs.
Solution of 1-D wave equation. Boundar conditions. Transversal waves in a spring.
Basic equations for dilatational waves.
Introduction. Wave phenomena in gas and fluid. Wave equation and boundary conditions for dilatational waves. The kinetic and potential
energy of the wave flux of the energy Poynting vector. Boundary value problem. Theorem of uniqueness. Gravitational waves in a fluid.
Waves in homogeneous medium. Spherical waves from an elementary source. Cylindrical waves from linear source in homogenous
medium. Plane waves in homogeneous medium.
Interference and diffration. Superposition of waves in an uniform medium,
caused by a system of primary sources. Helmholtz formula. Kirchhoff diffration theory. Fraunhofer and Fresnel diffration. Helmholtz -
Kirchhoff formula. Huygens - Fresnel principles. Relationship of potential with initial conditions. Poisson's formula. Transition and
transportation equations.
Superposition of sinusoidal waves with different frequencies and wave lengths. Wave group:
Phase and group velocities. Superposition of sinussoidal waves and the method of stationary phase.
Principles of geometrical
acoustics. Introduction. Rays and their general features. Behaviour of rays when velocity is a function of one cartesian coordinate.
Behaviour of rays when velocity is a function of one coordintae r. Rays near interfaces. Time fields.
Appendices.
Vector algebra. Scalar field and gradient. Vector fields. Complex numbers. Linear ordinary differential equations with constant coefficients.
Fourier series. Fourier integral. Duhamel integral.
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