Book contents
- Frontmatter
- Contents
- Preface
- Preliminaries
- 1 Introduction
- 2 Basic wave propagation
- 3 Transforms
- 4 Review of continuum mechanics and elastic waves
- 5 Asymptotic ray theory
- 6 Rays at an interface
- 7 Differential systems for stratified media
- 8 Inverse transforms for stratified media
- 9 Canonical signals
- 10 Generalizations of ray theory
- Appendices
- Bibliography
- Author index
- Subject index
2 - Basic wave propagation
Published online by Cambridge University Press: 19 January 2010
- Frontmatter
- Contents
- Preface
- Preliminaries
- 1 Introduction
- 2 Basic wave propagation
- 3 Transforms
- 4 Review of continuum mechanics and elastic waves
- 5 Asymptotic ray theory
- 6 Rays at an interface
- 7 Differential systems for stratified media
- 8 Inverse transforms for stratified media
- 9 Canonical signals
- 10 Generalizations of ray theory
- Appendices
- Bibliography
- Author index
- Subject index
Summary
This introductory chapter introduces the reader to the concepts of seismic waves plane waves, point sources, rays and travel times – without mathematical detail or analysis. Many different types of rays and seismic signals are illustrated, in order to set the scene for the rest of this book. The objective of the book is to provide the mathematical tools to model and understand the signals described in this chapter.
In this chapter, we introduce the basic concepts of wave propagation in a simple, stratified medium. None of the sophisticated mathematics needed to solve for the complete wave response to an impulsive point source in an elastic medium is introduced nor used. Ideas such as Snell's law, reflection and transmission, wavefronts and rays, travel-time curves and related properties, are introduced. The concepts are all straightforward and should be intuitively obvious. Nevertheless many simple questions are left unanswered, e.g. how are the amplitudes of waves found, and what happens when wavefronts are non-planar or singular. These questions will be answered in the rest of this book. This chapter sets the scene and motivates the more detailed investigations that follow.
Plane waves
Plane waves in a homogeneous medium
In this section, we introduce the notation and nomenclature that we are going to use to describe waves. We assume that the reader has a basic knowledge of waves and oscillations, and so understands a simple wave equation with the notation of complex variables used for a solution.
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- Fundamentals of Seismic Wave Propagation , pp. 6 - 57Publisher: Cambridge University PressPrint publication year: 2004
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