The attributes of a wavefront

Multiple arrivals may reach a subsurface point. Whereas some arrivals are identifiable by the kinematics of seismic waves, other arrivals have to be identified by the dynamics of seismic waves. Therefore, the attributes of a wavefront should include both the kinematic parameters and the dynamic parameters of seismic waves.

The local ray-tracing method uses five wavefront attributes in the process of wavefront propagation. They are

$${\bf \eta}=\{\tau,\ (u,w),\ \gamma,\ R,\ J\},$$ (3)

where $\tau$ is the traveltime for a wave to propagate from a surface point to a subsurface point, $(u,w)=(\tau_x,\tau_z)$ is the traveltime-gradient vector that points to the direction of the wave propagation at the subsurface point, $\gamma$ is the take-off angle of the ray connecting the surface point and the subsurface point, R is the curvature radius of the wavefront at the subsurface point, and finally, J is the geometrical spreading factor (see its definition in Cervený, 1981b) at the subsurface point. Among these attributes, $\tau$, (u,w) and $\gamma$ are related to the kinematics of wave propagation, whereas R and J are related to the dynamics.