The Amplitude-Distance Curves for Waves Reflected at a Plane Interface for Different Frequency Ranges

Summary The amplitude-distance curves for compressional waves reflected at a plane interface between two elastic half-spaces differ quite appreciably for different frequency ranges (in the case of a symmetrical point-source). At some distances from the source, the amplitude-distance curves deviate considerably from those computed by the methods of the geometric ray theory even at very high frequency. At lower frequencies the characteristic shape of the amplitude-distance curves implied by the geometric ray theory may be completely changed. A whole series of models of the interface was examined numerically. The results presented were obtained by exact numerical integrations along suitably chosen contours of integration in the complex plane, which suppress the oscillatory character of the integrand. The method can be generalized virtually without difficulties to cover also the more general types of seismic waves propagating in a layered medium.