Conceptually, dynamic ray tracing can be divided into two steps. The first step is the same as geometric ray tracing, from which we get raypaths and traveltimes along the raypaths. These raypaths are called ``central ray''. The second step is to estimate traveltime, amplitude, and phase-shift in the vicinity of each central ray. In other words, each central ray represents a 3-D ``ray tube''.

The feature that ray tracings are high-frequency approximation requires that the variation of velocity should be smooth enough within one wavelength. Therefore, smoothing the model is necessary to make the model more ``ray valid''. Furthermore, smoothing the model can make ray tracing more like band-limited solutions Biondi (1992).

There are many references on the theory of dynamic ray tracing Cervený et al. (1982); Cervený and Psencik (1983); Cervený (1985, 1987). In order to make this paper complete, we give a brief version of the dynamic ray tracing theory by skipping the deductions.

11/11/1997