Description 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.
Contents
I. Elastic continua. Introduction to Part I. 1. Deformations. 2. Forces and balance principles. 3. Stress-strain equations.
4. Strain energy. 5. Material symmetry.
II. Waves and rays. Introduction to Part II. 6. Equations of motion: Isotopic
homogeneous continua. 7. Equations of motion: Anisotropic inhomogeneous continua. 8. Hamilton's ray equations. 9. Lagrange's ray equations.
10. Christoffel's equations. 11. Reflection and transmission.
III. Variational formulation of rays. Introduction to
Part III. 12. Euler's equations. 13. Fermat's principle. 14. Ray parameters.
IV. Appendices. Introduction to Part IV.
A. Euler's homogenous-function theorem. B. Legendre's transformation. C. List of symbols. Bibliography. Index. About the author.
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