Waves in layered media

  The gravitational stratification of the earth arouses our interest in layered media. There are many kinds of waves that can exist. Here we study waves without assuming knowledge of physics and differential equations. We use only assumptions about the general principles of delay, continuity, and energy conservation. The results are directly applicable to sound waves, water waves, light in thin films, normal incident elastic waves of both pressure and shear type, electromagnetic waves, transmission lines, and electrical ladder networks. This chapter seems to concern itself only with vertically incident waves. Actually, with certain precautions, the theory here applies to the set of all waves with a fixed Snell parameter $p=\sin\theta/v$.

A lengthier version of this chapter appears in chapter 8 in my book Fundamental of Geophysical Data Processing (FGDP) (available on the web). The lengthier web version also presents the solution to the more practical problem, to deduce the reflection coefficients given the observed waves.