Reflection-point smear for dipping reflectors

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Problem

Assume a reflector 2000 m beneath the midpoint and a dip of $ 20^{\circ } $ with constant over-burden velocity. How much does the reflecting point move between members of the common-midpoint set for offsets of 0, 500, 1000, 1500, and 2000 m?

Background

Equation (4.11e) gives the shift in the reflecting point $ \Delta L $ in terms of the dip $ \xi $, slant depth $ h_{c} $, and offset 2s:


$ {\begin{aligned}\Delta L=(s^{2}/2h_{c}){\rm {\;sin\;}}2\xi .\end{aligned}} $ (8.2a)

Solution

Because $ \sin 2\xi =\sin 40^{\circ }=0.64 $, equation (8.2a) becomes

$ {\begin{aligned}\Delta L=0.16\times 10^{-3}s^{2}{\mbox{m}}.\end{aligned}} $

Thus, we get the following values of $ \Delta L $ for the various offsets:

$ {\begin{aligned}{\hbox{Offset}}(2s)&\rightarrow &0&500&1000&1500&2000m,\\{\hbox{Shift}}(\Delta L)&\rightarrow &0&40&160&360&640m.\end{aligned}} $

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Reflection-point smear for dipping reflectors