Ray Tracing for Seismic Surface Waves

Abstract

Summary Hamilton’s wave theory is used to study the effect on seismic surface wave propagation of lateral variations in the composition of the crust and mantle. For cases with small lateral variations the distortion of the propagation paths from the great circle paths is determined by a perturbation method. Moreover, surface wave paths from the Mid-Atlantic Ridge toward the NORSAR and LASA arrays are computed by numerical integration of the ray equations. The computed wave paths agree well with existing observations. The model of the surface wave velocity distribution used in this study cannot, however, explain all the observed multipathing effects. Studies by several authors have shown that the lateral variations in the structure of the Earth’s crust and upper mantle may lead to large distortions of the propagation paths for seismic surface waves. Notably among these works are the works by Evernden (1953, 1954) and the works by Capon (1970, 1971). These works show that surface waves are refracted or reflected at the continental margins and at major geological structures. The oceanic ridge systems are an example to the latter. Estimates of the propagation path for surface waves are presented in the work cited above. Apart from this and a study by Julian (1972) little has been done in order to compute the propagation paths for surface waves. In various branches of Physics, Hamilton’s wave theory (or the eikonal approximation) has successfully been used to study wave propagation in heterogeneous media. Within the theory of seismic surface waves the method has received less attention although the applicability of it has been demonstrated in an elegant study by Backus (1962). The application of this theory to surface wave propagation in cases with lateral variation in the structure of the crust and upper mantle deserves more exploration. A fundamental assumption in Hamilton’s wave theory is that the physical parameters which are important for the wave propagation vary only by a small fraction of their values over a distance comparable to a wavelength. The theory has therefore very misleadingly been referred to as a short wavelength approximation. The propagation of seismic surface waves are for example fundamentally effected by the value of the physical parameters in a surface layer with thickness comparable to the wavelength. Therefore the lateral variations of the parameters describing the wave motion may be smaller for long waves than for short waves. This is confirmed by the observations