Abstract The preceding lessons have shown the very fundamental and important role played by the relationship existing between the slope of the time-distance curve (dt/dx) of a seismic “event” and the emergence angle of the corresponding wave. There is yet another concept of equal importance in the study of “geometrical acoustics,” to coin a phrase, which we shall now introduce. Consider a moving plane wave front which assumes the successive positions of the members of a family of parallel planes. Let its velocity of propagation in the medium be VI. Now suppose that this medium is bounded by a plane surface, called the interface, on the other side of which is a medium in which the velocity of propagation is V 2 , different from VI.

Abstract A fundamental result in the mathematical discussion of wave propagation is the concept known as Fermat*#x0027;s Principle . Stated for our purposes, it runs somewhat like this: The study of the propagation of waves may be reduced to the study of wave paths which are defined as the paths along which the travel-times are minimal. We proceed to expand on this subject. Consider a moving wave front. Corresponding to it is a family of wave paths (see Lesson No.1). Choose any two points lying on anyone of these wave paths. Of all possible paths joining those two points, the wave path is that for which the travel-time is least. In other words, the travel-time along any other path (within suitable limits) joining those two points would be greater than along the wave path .

Abstract Reflection seismology is the science of examining the earth’s interior through the analysis of mechanical waves. Seismic waves are bent, reflected, refracted, diffracted, and scattered. The emitted signal is weakened by these effects as well as geometric spreading and attenuation. Seismic waves are generated by controlled sources and travel through fluids, solids, and porous solids. In this chapter, we consider those properties of waves that do not depend on the kind of material supporting the wave propagation. For example, Snell’s law is a general property of wave motion but differs in detail between reflection of acoustic and elastic waves. In this chapter, when considering a general property such as Snell’s law, we will discuss the scalar (acoustic) wave case.