Refraction arrivals along a thin elastic plate surrounded by a fluid medium

An asymptotic solution is derived for the first arrival of significant amplitude and low frequency, which is refracted along a thin high-velocity plate surrounded by a fluid medium. This first arrival travels with approximately the velocity of a longitudinal plate wave in the refracting layer. The shape of the signal depends upon the contrast (in density and elastic constants) between the plate and the fluid as well as upon the distance (in units of plate thickness) that the signal has been refracted along the plate. Solutions in closed form are given. For the case of moderate contrast or large distance, we treat the problem of a point and of a line source in the fluid emitting a step (or δ) pressure pulse. The refracted signal is approximately a gaussian curve (or its derivative). For the case of large contrast and moderate distance, we treat the problem of a line source in the fluid emitting a step pressure pulse. The refracted signal is described by an Airy function. For intermediate cases, the refracted signal for the line or for the point source is given in the form of an integral, which must be evaluated numerically. Because of the relatively simple nature of the results, interesting features of the signal are readily derived. In an appendix, we discuss briefly a thin high-velocity plate shallowly submerged in a liquid half-space. The low-frequency refracted signal from a step pressure line source is described by an Airy function for all cases of contrast.