...
is a lateral offset between the
seismic source and and seismic receiver, – trajectory of reflection wave from
seismic source @ source @ LaTeX Math Inline |
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body | (x = 0, \, y = 0, \, z = 0) |
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and
seismic receiver @ receiver @ LaTeX Math Inline |
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body | (x, \, y = 0, \, z = 0) |
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is
p-wave velocity of rocks found at travel point
.
Image Added
In relatively simple geological structures the travel time can be approximated by a Dix equation:
LaTeX Math Block |
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T^2_x = T^2_0 + \frac{4 x^2}{V^2_{rms}} |
where where
is reflection time at zero offset (which means the normal incident wave reflection)
: LaTeX Math Block |
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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 and seismic sensorreceiver:
LaTeX Math Block |
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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)}} |
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