Ray Tracing in Arbitrarily Heterogeneous Media
MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB
Pagination or Media Count:
The study of lateral variations of earth structure has been stimulated recently by several factors, especially the theory of plate tectonics and the increasing use of large seismic arrays. The extension of seismic ray theory to two and three dimensional structures is thus of great practical importance. The problem of ray tracing in a generally heterogeneous medium is treated, using the calculus of variations and Fermats principle of stationary time. The solution is expressed in terms of a system of five simultaneous first order differential equations giving the variation with time of the position and direction of motion of a point on a ray in terms of the wave speed and its spatial derivatives in the medium. If the earth model has certain symmetry properties, then constants of the motion along each ray can be found which simplify the calculations. The propagation of surface waves on an earth with geographical variations can be treated by a simplified special case of the method presented here.