Time relationships in the earth's interior

The following obvious equation relates the traveltimes along the ray paths to source and geophone, t_s and t_g, to the given total traveltime t_sg:

 

t_s + t_g = t_sg . (7)

We can also state two more equations to account for the fact that the three ray paths, namely the zero-offset, source, and geophone ray paths, end at the same point in depth (R):  

$$\tau(p_0,t_0) = \tau(p_s,t_s) = \tau(p_g,t_g) ,$$ (8)

where $\tau(p,t)$ is the table of vertical traveltimes.