More numerical experiments in high frequency edge diffraction theory
P. F. Daley
Formulae related to the diffraction of seismic waves by linear edges in elastodynamic media, based on an extension of the high frequency, zero order Asymptotic Ray Theory (ART) formulation are presented. Theoretical aspects of the problem have been minimized, as these have been developed in numerous notable works. The intention here is to present the basic methodology for numerical implementation into synthetic seismogram software.
Schematics indicating relevant details such as the shadow boundary and the boundary ray are have been included. The identification of the boundary ray is required as the argument of the diffraction coefficient is dependent on the angle between the shadow boundary ray and the diffracted ray or equivalently the difference between the diffracted and direct arrival times. The direct geometrical arrival does not exist in the shadow region and its travel time is required to determine the argument of the diffraction coefficient which is done within the context of analytic continuation and the aforementioned limits of minimal theoretical discussion.
A basic problem is considered to give a brief overview of the theory of edge diffractions. The geometry of this problem involves a wedge embedded in a halfspace in a manner such that the plane of incidence is the plane and the wedge is such that its leading edge is perpendicular to this plane, i.e., parallel to the y axis. Both the source and receivers are located in the plane.