Refraction along a layer

Abstract High-frequency geometric ray theory is used to investigate the refracted arrival from a high-speed layer embedded in an infinite medium. The effect of changing the layer thickness to dominant wavelength ratio (E/lambda d ) and the range to depth ratio (rho /H) is analyzed for a point compressional source. The results approximate the exact solution when E/lambda d or = 1. The theory predicts shingling and shows that it is range-limited. Factors which improve the resolution between reflected arrivals increase the range over which shingling occurs. As the range increases, the traveltime curves for all the multiply reflected rays which cross the layer the same number of times in the shear mode approach the same asymptote (regardless of the number of crossings in the compressional mode). When the layer is thick compared to the dominant wavelength, the refracted arrival may consist of a series of events separated by equal time intervals. Each event is produced by the superposition of reflected waves which cross the layer the same number of times in the shear mode. Because the head waves decay like (rho /H) (super -2) , the reflected waves predominate at large ranges.