MULTIPLE SEPARATION

NMO correction makes separation of the multiple energy from primary energy straightforward. Primary events in NMO-corrected gathers are flat and map to the zero slowness, p=0s/km, slice of model space. The energy in the rest of the model is multiple energy and can easily be isolated by windowing out all slices with slowness greater than zero. This isolated multiple energy can be forward modeled and subtracted from the original NMO-corrected data or the primary energy can be forward modeled directly from the zero slowness slice. The NMO approach avoids the somewhat difficult approach taken by Holden and Biondi (1996) of applying a time-offset dependent mute to inverted data without NMO correction. A potential drawback to the NMO approach is that primary events in NMO-corrected gathers may not always be flat. This may be compensated for if there is prior knowledge of the primary event shape. In this respect the NMO method may not be as robust as the method of applying a time-offset dependent mute to inverted data without NMO correction

The multiple filtering results are displayed in figure . These results were obtained by simply windowing the zero slowness slice of each inversion result displayed in figures , + , and then forward modeling. The windowing of the primary events in the model2 case involved three slowness slices due to the negative dips present on the primaries. Like the primaries, the multiples will have a component of very nearly zero slowness at the nearest offset. This energy will map into the zero slowness panel with the primaries. This energy appears as stubs at the near offsets of the results in figure . The reflecting boundary conditions contribute to the amplitude of these stubs.

 

fwdprime
Figure 10 Result of beam stack multiple suppression. Left: model1 estimated primaries, Center: model2 estimated primaries, Right: model3 estimated primaries.

 

diffbs
Figure 11 Energy difference of original primaries and result of beam stack multiple suppression.

 

prtprime
Figure 12 Results of PRT multiple suppression method. Left: model1 estimated primaries, Center: model2 estimated primaries, Right: model3 estimated primaries.

 

diffprt
Figure 13 Energy difference of original primaries and result of PRT multiple suppression.

 

prttrans
Figure 14 PRT transform space. Left: model1, Center: model2, Right: model3

I have prepared results of the PRT multiple suppression method as a comparison. The estimated primaries of the NMO-corrected data using the PRT multiple suppression method are displayed in figure . The PRT transform of the NMO-corrected data are displayed in figure . Multiple energy is obviously present in all three results in figure , the most notable cases are the distinct strong multiple ghosts present with the estimated primaries of model1 and model2. These ghosts are caused by the inability of the PRT to compactly represent the significantly non-parabolic multiples in PRT transform space such that the masking procedure can not separate the primary from the multiple energy. Examination of figure reveals that multiple energy spreads over a large region of the PRT transform space and is probably not properly isolated by the masking procedure associated with the PRT method.

The difference between the estimated primaries from each method and the original multiple-free primaries appear in figure for the beam stack method and in figure for the PRT method. The PRT method leaves a significant amount of multiple energy in the multiple suppressed results for all three cases at all times and offsets, where as the beam stack method contains multiple energy only at the near offsets. Increasing the sampling of the slowness parameter or range of the slowness parameters of the PRT transform does not change the PRT result significantly.