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layered media Previous: Waves in layered media   Consider two
halfspaces (deep ocean on top of earth, for example). If a wave
of unit amplitude is incident onto the boundary, there is a
transmitted wave of amplitude t and a reflected wave of
amplitude c as depicted in Figure 1.  Figure 1 Waves incident,
reflected c, and transmitted t at an interface.  A very simple
relationship exists between t and c. The wave amplitudes have a
physical meaning of something like pressure, material
displacement, traction, or tangential electric or magnetic
fields. These physical variables must be the same value on
either side of the boundary. This means the transmitted wave
must equal the sum of the incident plus reflected waves. t & = &
1 + c \\ t' & = & 1 + c'\end{eqnarray} (1)  The reflection
coefficient c may be positive or negative so the transmission
coefficient t may be greater than unity. It may seem surprising
that t can be greater than unity. This does