Head-wave coefficients in anisotropic media

Reflections and transmissions from interfaces can generate headwaves. Although the kinematic properties of head waves are modelled simply using ray concepts, the dynamic properties require an extension of ray theory or the use of wave theory. Head waves are important in exploration and crustal seismology as they indicate the existence of an interface and the velocity of the generating wave. Head waves have been described in the literature for isotropic media but the extension to anisotropic media seems to be lacking. The expressions for the head-wave coefficients using ray concepts or wave theory differ, and their equality is not obvious. This paper extends the theory for head-wave coefficients to anisotropic media using both ray theory and wave theory, and generalizes the proof of equality of the two methods. Simple numerical examples confirm this equality and indicate how the head-wave results can be calculated in anisotropic media and included in a ray tracing algorithm.