Seismic Waves and Rays in Elastic Media

Seismic Waves and Rays in Elastic Media

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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.Since, in the variational approach to ray theory, either time or distance constitutes the single variable, the stationarity conditions are a ... 10 The theory of the calculus of variations originated with the statement of Johannes Bernoulli, who, in 1696, posed the problem to ... a#39;interested readers might refer to Born, M., and Wolf, E., (1999) Principles of optics (7th edition): Cambridge University Press, p. xxvi.

Title:Seismic Waves and Rays in Elastic Media
Author: Michael A. Slawinski
Publisher:Elsevier - 2003

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