However, ART has several failings, including an inability to model wave effects such as caustics, diffractions, and (for zero-order theory) head waves. First-order theory correctly models head waves. Theories such as those of edge waves (Klem-Musatov and Aisenberg, 1985), which is used in geophysics, and the electrical-engineering theory UAT (uniform asymptotic theory of edge diffraction, Lewis and Boersma, 1969) handle diffraction to some extent. Furthermore, there is at times a large sensitivity to small variations in the definition of the model.
The built-in assumption is that the signal is infinite-frequency. Indeed, the ray theory solution is exact only for infinitely high frequency, but it generally agrees reasonably well with finite frequency experimental data, provided that the properties of the continuum do not vary significantly within the wavelength of the signal. The ratio between a significant length scale of change of properties within the continuum and the wavelength of the signal must be much greater than one.
Also, in terms of differential geometry, a ray is a traveltime geodesic, i.e. a path of stationary traveltime and, quite often but not always, minimum traveltime. Some differential geometry reviewed in Arnold (1989) and Schutz (1980) can be used to study such geodesics, since geodesics are a classical part of both the calculus of variations (e.g., Weinstock, 1974) and differential geometry.