Title: Applications of normal coordinate theory to very low frequency propagation
Abstract: In the linear theory of waves the use of exact mode theory is particularly indicated at low frequencies because the ray and WKB approximations are often invalid. This paper focuses on the normal coordinate technique, which uses mode amplitudes as generalized coordinates. This approach has the attraction of completely bypassing the need for a radiation condition, leading directly to travelling impulsive and transient solutions. It also automatically provides correct integral transform representations of the solution when the field operators or boundary conditions are nonstandard, e.g., not of the Sturm-Liouville type; the only restriction here is that such conditions must be conservative. These features are illustrated by the solution of an impulsive point source solution for a rigid surface with microroughness, a situation in which it has been shown (Biot, 1968) that the effect of roughness can be represented by non-standard types of boundary condition applied to a plane surface. The method of normal coordinates leads here to simple, closed form solutions.