Resonance theory of elastic head waves in layered media. I. A fluid layer bottomed by an infinite solid

Abstract

In the conventional theory of elastic wave in layered media, the head wave is believed to be the ‘‘critically refracted arrival.’’ However, there are many difficulties which remain unsettled. In order to clarify these questions, the corresponding boundary value problem is re-treated by the standing wave method, in which the path of integration in the wave-number plane is uniquely determined by the boundary conditions. It is found that the critical refraction does not exist. The physical mechanism of the head wave is shown to be a mode of resonance, and is a nonlinear effect of the elastic wave equation. The property of the head wave is discussed in detail. Some predictions are compared with observations.