Seismic Waves and Rays in Elastic Media (Seismic Exploration Series): Handbook of Geophysical Exploration, Vol. 34
This book seeks to explore seismic phenomena in elastic media and emphasizes the interdependence of mathematical formulation and physical meaning. The purpose of this title - which is intended for senior undergraduate and graduate students as well as scientists interested in quantitative seismology - is to use aspects of continuum mechanics, wave theory and ray theory to describe phenomena resulting from the propagation of waves.\ The book is divided into three parts: Elastic continua, Waves...
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This book seeks to explore seismic phenomena in elastic media and emphasizes the interdependence of mathematical formulation and physical meaning. The purpose of this title - which is intended for senior undergraduate and graduate students as well as scientists interested in quantitative seismology - is to use aspects of continuum mechanics, wave theory and ray theory to describe phenomena resulting from the propagation of waves.The book is divided into three parts: Elastic continua, Waves and rays, and Variational formulation of rays. In Part I, continuum mechanics are used to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such material. In Part II, these equations are used to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, the high-frequency approximation is used and establishes the concept of a ray. In Part III, it is shown that in elastic continua a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary travel time.
IElastic continua1Introduction to Part I31Deformations72Forces and balance principles333Stress-strain equations614Strain energy695Material symmetry85IIWaves and rays125Introduction to Part II1276Equations of motion: Isotropic homogeneous continua1297Equations of motion: Anisotropic inhomogeneous continua1638Hamilton's ray equations1739Lagrange's ray equations19710Christoffel's equations21711Reflection and transmission245IIIVariational formulation of rays265Introduction to Part III26712Euler's equations26913Fermat's principle29314Ray parameters319IVAppendices337Introduction to Part IV339AEuler's homogeneous-function theorem341BLegendre's transformation347CList of symbols355Bibliography359Index374About the author401
\ From the Publisher"The purpose of this title...is to use aspects of continuum mechanics, wave theory, and ray theory to describe phenomena resulting from the propagation of waves." \ -M.A. Slawinski, FIRST BREAK, Volume 23\ \
