Seismic waves and rays in elastic media / by M.A. Slawinski.

Format:

Book

Author/Creator:

Slawinski, M. A. (Michael A.), 1961-

Series:

Handbook of geophysical exploration. Seismic exploration ; Section I, v. 34.

Handbook of geophysical exploration. Section I, Seismic exploration, 0950-1401 ; v. 34

Language:

English

Subjects (All):

Seismic waves.

Continuum mechanics.

Seismology--Mathematics.

Seismology.

Physical Description:

1 online resource (425 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam ; Boston : Pergamon, 2003.

Language Note:

English

Summary:

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 desc

Contents:

Front Cover; Seismic Waves and Rays in Elastic Media; Copyright Page; Contents; Part I: Elastic continua; Introduction to Part I; Chapter 1. Deformations; 1.1 Notion of continuum; 1.2 Material and spatial descriptions; 1.3 Strain; 1.4 Rotation tensor and rotation vector; Chapter 2. Forces and balance principles; 2.1 Conservation of mass; 2.2 Time derivative of volume integral; 2.3 Stress; 2.4 Balance of linear momentum; 2.5 Stress tensor; 2.6 Cauchy's equations of motion; 2.7 Balance of angular momentum; 2.8 Fundamental equations; Chapter 3. Stress - strain equations

3.1 Formulation of stress-strain equations3.2 Determined system; Chapter 4. Strain energy; 4.1 Strain-energy function; 4.2 Strain-energy function and elasticity-tensor symmetry; 4.3 Stability conditions; 4.4 System of equations for elastic continua; Chapter 5. Material symmetry; 5.1 Orthogonal transformations; 5.2 Transformation of coordinates; 5.3 Condition for material symmetry; 5.4 Point symmetry; 5.5 Generally anisotropic continuum; 5.6 Monoclinic continuum; 5.7 Orthotropic continuum; 5.8 Tetragonal continuum; 5.9 Transversely isotropic continuum; 5.10 Isotropic continuum

Part II: Waves and raysIntroduction to Part II; Chapter 6. Equations of motion: Isotropic homogeneous continua; 6.1 Wave equations; 6.2 Plane waves; 6.3 Displacement potentials; 6.4 Solutions of one-dimensional wave equation; 6.5 Reduced wave equation; 6.6 Extensions of wave equation; Chapter 7. Equations of motion: Anisotropic inhomogeneous continua; 7.1 Formulation of equations; 7.2 Formulation of solutions; 7.3 Eikonal equation; Chapter 8. Hamilton' s ray equations; 8.1 Method of characteristics; 8.2 Time parametrization of characteristic equations

8.3 Example: Ray equations in isotropic inhomogeneous continuaChapter 9. Lagrange's ray equations; 9.1 Transformation of Hamilton's ray equations; 9.2 Relation between p and x; Chapter 10. Christoffel' s equations; 10.1 Explicit form of Christoffel's equations; 10.2 Christoffel's equations and anisotropic continua; 10.3 Phase-slowness surfaces; Chapter 11. Reflection and transmission; 11.1 Angles at interface; 11.2 Amplitudes at interface; Part III: Variational formulation of rays; Introduction to Part III; Chapter 12. Euler's equations; 12.1 Mathematical background

12.2 Formulation of Euler's equation12.3 Beltrami's identity; 12.4 Generalizations of Euler's equation; 12.5 Special cases of Euler's equation; 12.6 First integrals; 12.7 Lagrange's ray equations as Euler's equations; Chapter 13. Fermat's principle; 13.1 Formulation of Fermat ' s principle; 13.2 Illustration of Hamilton's principle; Chapter 14. Ray parameters; 14.1 Traveltime integrals; 14.2 Ray parameters as first integrals; 14.3 Example: Ellipticity and linearity; 14.4 Rays in isotropic continua; 14.5 Lagrange's ray equations in xz-plane

14.6 Conserved quantities and Hamilton's ray equations

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 359-373) and index.

ISBN:

1-281-05395-3

9786611053956

0-08-054089-9

OCLC:

182466538