# Reflection-point smear for dipping reflectors

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Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 8 253 - 294 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store

## Problem

Assume a reflector 2000 m beneath the midpoint and a dip of ${\displaystyle 20^{\circ }}$ 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 ${\displaystyle \Delta L}$ in terms of the dip ${\displaystyle \xi }$, slant depth ${\displaystyle h_{c}}$, and offset 2s:

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

### Solution

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

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

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

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