Total time required for seismic wave to travel through the rock towards the seismic receiver:
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T^2T_x = T^2_0 +\int_0^{L_x} \frac{4 x^2dl}{V^2_{rms}}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, where is
a lateral offset between the seismic source and seismic receiver,
– trajectory of reflection wave from seismic source @ LaTeX Math Inline |
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body | (x = 0, \, y = 0, \, z = 0) |
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and seismic receiver @ LaTeX Math Inline |
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body | (x, \, y = 0, \, z = 0) |
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body | dl = \sqrt{dx^2 + dy^2 + dz^3} |
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is differential element of the distance along the reflection travel trajectory, is p-wave velocity of rocks found at travel point .
In relatively simple geological structures the travel time can be approximated by a Dix equation:
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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),
– average
p-wave speed through velocity through the reflecting travel distance between the seismic source and seismic sensor:
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