NMO for Multiple Reflections

In a horizontally-stratified, v(z) medium, multiple reflections can be treated as kinematically-equivalent primaries with the same source-receiver spacing but additional zero-offset traveltime 16#16, as illustrated in Figure . We can write an extension to the NMO equation which flattens multiples to the zero-offset traveltime of the reflector of interest.  

 17#17 (4)

18#18 is the two-way traveltime of a 19#19-order multiple in the top layer. 20#20 is the effective RMS velocity of the equivalent primary shown in the figure. For the simple case of constant velocity v^* in the multiple-generating layer,  

 21#21 (5)

So for the common case of relatively flat reflectors, v(z), and short offsets, equation () should do a reasonable job of flattening water-bottom multiples of any order to the 22#22 of interest, assuming that we pick the water bottom (16#16) and that we know the seismic velocity of water.

 

schem Figure 1 Schematic for NMO of multiples. From the standpoint of NMO, multiples can be treated as pseudo-primaries with the same source-receiver spacing, but with extra zero-offset traveltime 16#16, assuming that the velocity and time-thickness of the multiple layer are known.