Publisher Summary This chapter focuses on elastic wave propagation in stratified media. The development of the theory of elastic wave propagation in stratified media has been strongly influenced by the problems of seismic wave propagation and the nature of the seismograms recorded from earthquakes. For purely analytic developments of elastic wave propagation, the level of manageable algebraic complexity is reached in a model with one or two uniform layers overlying a uniform half space. This chapter shows how the excitation of elastic waves, within a horizontally stratified structure, can be conveniently developed in terms of reflection and transmission matrices. This procedure has allowed the construction of the full response of the medium or approximations with desired properties so that theoretical seismograms may be calculated for realistic distributions of elastic parameters. Although this development has been for isotropic media, nearly all the results apply directly to the case of full anisotropy if 3 × 3 reflection and transmission matrices allowing coupling between all wave types are employed. This development of the wavefield for both source and receiver within the stratification may be used for other classes of wave propagation.

Some Problems of Geodynamics

Seismic Wave Propagation in Stratified Media

An explanation in terms of the thermal evolution of thickened continental lithosphere is offered to explain the transition, in the late Tertiary to Quaternary, from north-south compression to east-west extension in the strain rate field of the Tibetan Plateau. The lower part of the lithosphere consists of a thermal boundary layer which, when thickened by horizontal shortening, is colder and denser than its surroundings. Convective instability of the thickened thermal boundary layer and its replacement by hot asthenosphere would rapidly raise the surface elevation and gravitational potential energy of the overlying part of the lithosphere. The convective instability would happen in a time brief compared with the collision time scale but would only occur after there had already been substantial thickening of the lithosphere. The increase in surface height and of potential energy are sufficient for east-west extension to replace north-south compression as the dominant feature of the stress field.

Extension during continental convergence, with application to the Tibetan Plateau

Research into ultrasonic NDE techniques for the inspection of multilayered structures relies strongly on the use of modeling tools which calculate dispersion curves and reflection and transmission spectra. These predictions are essential to enable the best inspection strategies to be identified and their sensitivities to be evaluated. General purpose multilayer modeling tools may be developed from a number of matrix formulations which have evolved in the latter half of this century and there is now a formidable number of publications on the subject. This paper presents a review of the main developments of the matrix techniques, and their use in response and modal models, with emphasis on ultrasonics applications. >

Matrix techniques for modeling ultrasonic waves in multilayered media

The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvenic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvenic-type, oscillations arise only in high density (strictly, low Alfven velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.

Wave propagation in a magnetic cylinder

Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.

Some Problems of Geodynamics

Citations

Seismic Wave Propagation in Stratified Media

Extension during continental convergence, with application to the Tibetan Plateau

Matrix techniques for modeling ultrasonic waves in multilayered media

Wave propagation in a magnetic cylinder

Ultrasonic Guided Waves in Solid Media

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