Numerical experiments in high frequency diffraction theory
P. F. Daley
Formulae for diffraction theory in elastodynamic media, based on the high frequency Asymptotic Ray Theory (ART) formulation are presented. The original papers and texts from which the formulae used here were obtained are highly mathematical, and the progression from theory to the development of associated software is not a straightforward endeavour. This paper addresses the diffraction of seismic waves by linear edges, employing an extension of zero order asymptotic ray theory. This extension is obtained through the implementation of the boundary layer method. To provide some initial insight into this problem for the elastodynamic case, a few simple models were chosen for analysis. The motivation for this was to establish a basis for the extension of diffraction theory to more complicated and realistic geological structures. Program packages, based on ART, dealing with these structure types are common in seismic modeling software packages. However, at present their use is limited, with a few exceptions, to modeling of only reflected seismic response recorded at the earth's surface, or vertical seismic profile (VSP) arrays as a result of some form of point source media excitation. The inclusion of diffracted arrivals in these packages would produce more realistic synthetic traces, enhancing their usefulness.
Also discussed is how complicated seismic diffracting structures may be divided into a configuration consisting of several linear edge components so that the total diffracted response from the more complicated structure is the sum of these individual linear edge building blocks.