Corpsular straight trajectories versus rays in layered media

Abstract

An alternative approach to rays for determining the wave motion in horizontally stratified layered medium is presented. Rays obey Snell's law and are bending towards or away from the normal when crossing an interface. We show how by squaring the propagation velocities and scaling interface depth the rays are stretched so as to move along straight lines when crossing the interface. We chose to call it corpsular straight trajectory as it is closely related to Newton's Corpuscular Theory of wave motion. We show that this new concept is useful in transforming two or fully three spatial dimensions wave fields as function of time to many simple essentially one dimensional problems. It may provide a new look on the dichotomy of particles versus waves. Its potential lies on the massive parallelism that can be obtained by solving the various corpsular trajectories emitted from the source in a plurality of directions as separate quasi one dimensional problems. The summation of these individual solutions yields the three dimensional solution of the wave equation.