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

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

where 

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body \{ x, \, y, \, z \}

 is cartesian coordinates in 3D space with 

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body x

-axis aligned between seismic source and seismic sensor, 

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body y

-axis is traversal to 

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body x

-axis and 

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body z

-axis is oriented towards Earth centre, 

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body x

 is a lateral offset between the seismic source and seismic receiver,

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body l(x,y,z)

 – trajectory of reflection wave from seismic source @ 

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body (x = 0, \, y = 0, \, z = 0)

 and seismic receiver @ 

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body (x, \, y = 0, \, z = 0)

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body dl = \sqrt{dx^2 + dy^2 + dz^3}

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

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body V_p(l)

 is p-wave velocity of rocks found at travel point 

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body l

.

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

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

where

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body T^2_0

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

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body V_{rms}

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

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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 

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body V_p(t_i)

 is p-wave velocity of rocks found at travel time 

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body t_i

, 

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body \delta t_i

 is travel time through the rock element of thickness 

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body \delta h_i

 in tghe rock element found at travel time 

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body t_i

.