Non-geometrical waves-are there any? An asymptotic description of some ‘non-geometrical’ phenomena in seismic wave propagation

Abstract

S U M M A R YA review of a number of asymptotic studies of the so called 'non-geometrical' phenomena in seismic wave propagation is presented. The results concerning high frequency asymptotics fall into two groups. Some phenomena are described by a slightly modified ray method or by considering higher order approximations. They are the much spoken of S*-waves, the effect of wave tunnelling through a higher velocity layer and the low frequency depolarization of P-, S-, Love and Rayleigh waves described by the first-order asymptotic approximation. Description of phenomena of the other group requires boundary layer techniques. These phenomena are: generation of S-waves by a pressure centre due to velocity and density gradients or due to weak anisotropy as well as depolarization at caustics and in penumbra.

On applying complex rays to calculation of scalar “Nongeometric” waves

“…Formulas (5.7)-(5.8) are consistant with known results (see, for example, [9]) obtained by other methods. Formula (5.7) does not contain singular terms as y0 -~ 0.…”

“…The standard version of the ray method cannot be applied here, but using the reciprocity principle yields an optical-geometric expansion by applying a sufficiently simple procedure that does not demand an explicit solution. One can find its description and also references to earlier investigations in papers [8][9]. Here we give a more direct approach to the problem of discription of the wave P*.…”

Ray Tracing in Elastic and Viscoelastic Media

“…In elasticity and acoustics they have found numerous applications in modelling evanescent waves asssociated with caustics (e.g., HANYGA and SEREDYŃ -SKA, 1991;HANYGA and HELLE, 1990;HANYGA, 1993) and ''non-geometric'' S* waves (BABICH and KISELEV, 1989), in convex body diffraction (CHAPMAN et al, 1998a), edge diffraction (HANYGA, 1993;CHAPMAN et al, 1998b) and in modelling directional sources (FELSEN, 1982;NORRIS and HANSEN, 1995). A global study of complex ray fields can be found in WHITE and PEDERSEN (1981).…”

10.1007/s11446-008-1012-0

“…The resulting infinite series are of an asymptotic nature. Typically, the leading term of the ray series describes the standard polarization of the corresponding local plane wave, while the correction term contains an anomalous polarization component which is missing in the standard plane wave [6]. In applications, the wave fields are conveniently modeled using two-term [7] (two-component [8]) representations comprising the sum of the leading term of the asymptotics and the anomalously polarized part of the first correction term.…”