Fundamentals of Seismic Wave Propagation

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.