In the field of the oil exploration, the research is focused on the fracture detection in recent years. The difficulty is how to determine the orientation of the crack. To solve this problem, the relationship between the wave equations and the orientation of the crack should be determined. Unfortunately, the existing wave equations cannot completely reveal these relations. This paper studies the fractured media with arbitrary azimuthal angles. The convolution integral is solved incrementally, and then the corresponding time-domain wave equations are presented. The wave equations may be solved to model the wave propagation in the azimuthally anisotropic and viscoelastic media and to reveal the mechanisms of seismic multi-wave propagation in fractured media.