text: # Suppressing multiples by NMO differences
  
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  Series Geophysical References Series Problems in Exploration Seismology and their Solutions Lloyd P. Geldart and Robert E. Sheriff 6 181 - 220 http://dx.doi.org/10.1190/1.9781560801733 ISBN 9781560801153 SEG Online Store
  
  ## Problem 6.11
  
  A primary and a multiple each arrive at 0.600 s at ${\displaystyle x=0}$; their stacking velocities are 1800 and 1500 m/s, respectively. Calculate the residual NMO (after NMO correction for the primary velocity) for offsets of 300 ${\displaystyle n}$, where ${\displaystyle n=1,2,...}$. What is the shortest offset that will give good multiple suppression for a wavelet with a 50-ms dominant period?
  
  ### Solution
  
  The distance to the primary reflector is ${\displaystyle (0.600\times 1800)/2=540\ {\rm {m}}}$ and to the reflector responsible for the multiple, assuming it is simply a double bounce, is ${\displaystyle (0.600\times 1500)/4=225\ {\rm {m}}}$. NMO is given by equation (4.1c), ${\displaystyle \Delta t_{\rm {NMO}}=x^{2}/2V^{2}t_{0}}$. We obtain the following values for the moveouts:
  
   Offset 300 m 600 m 900 m Primary NMO 0.023 s 0.093 s 0.208 s Multiple NMO 0.033 s 0.133 s 0.300 s NMO Difference 0.010 s 0.040 s 0.092 s
  
  Multiple suppression should be maximum when the NMO difference approximates half the wavelet period so that some of the traces are out-of-phase, which is achieved at offset ${\displaystyle x}$ where
  
  {\displaystyle {\begin{aligned}x^{2}/1.200\times 1500^{2}-x^{2}/1.200\times \;1800^{2}\;=0.050,\;x=660\ {\rm {m}}.\end{aligned}}}