Total time required for seismic wave to travel through the rock towards the seismic receiver:

T_x = \int_0^{L_x}  \frac{dl}{V_p(l)}

where 

 is cartesian coordinates in 3D space with -axis aligned between seismic source and seismic sensor, -axis is traversal to -axis and -axis is oriented towards Earth centre, 

 is a lateral offset between the seismic source and seismic receiver

 – trajectory of reflection wave from seismic source @  and seismic receiver @ 

 is differential element of the distance along the reflection travel trajectory,

 is p-wave velocity of rocks found at travel point .


Two Way Time Illustration


In relatively simple geological structures the travel time can be approximated by a Dix equation:

T^2_x = T^2_0 + \frac{4 x^2}{V^2_{rms}}

where  is reflection time at zero offset (which means the normal incident wave reflection):

T_0 = 2 \cdot \int_0^H \ \frac{\delta z}{V_p(z)}

where  is the depth of the reflecting boundary,

 – average p-wave velocity through the reflecting travel distance  between the seismic source and seismic receiver:

V^2_{rms} = \frac{\sum_i^N  V_p^2(t_i) \, \delta t_i}{\sum_i^N \delta t_i}= \frac{\sum_i^N  V_p(t_i) \, \delta h_i}{\sum_i^N \frac{\delta h_i}{V_p(t_i)}}

where 

 is p-wave velocity of rocks found at travel time 

 is travel time through the rock element of thickness  in tghe rock element found at travel time .