Tests on the SEG/EAGE Salt data set

The Salt Model C3-NA data set simulates a narrow-azimuth marine acquisition with 8 streamers recorded on an area about one quarter of the whole model. The maximum absolute offset is about 2,600 m and the maximum cross-line offset between the sources and the outer streamers is ${\rm \pm140~m}$.The in-line direction is East-West, corresponding to the approximate North-South direction in the model as displayed in Figure . Notice that the Figure displays the model rotated with respect to its ``true'' orientation; that is, the ``true North'' of the model points to the West of the Figure.

The fault plane indicated as ``Fault A'' in Figure  is a good reflector for testing methods of partial stacking, in particular where it cuts through the salt body and creates a high-reflectivity interface between the top of the salt and the sediments above. Figure  shows an example of in-line section through the velocity model. In this section ``Fault A'' is in the top-right corner; the shallower part of the fault cuts through sediments, while the deeper part coincides with the top of the salt. The section in Figure  is approximately located as the in-line vertical section displayed in Figure . Notice that the vertical/horizontal aspect ratio is not preserved in Figure  and thus the fault appears to be dipping at a steeper angle with respect to the in-line direction than its true dip of about $40^\circ$.

At the North-East corner of the recording area the reflections from the fault-plane are free from interferences with the salt body, and thus can be used for comparing DMO and AMO in a horizontally layered medium. However, towards the center of the model the fault-plane reflections move rapidly under the ``shadow'' of the salt body, and therefore they are useful for comparing the sensitivity of DMO and AMO to NMO-velocity conflicts.

The tests compare the results of three methods for transforming prestack data after NMO and before partial stacking: a) simple binning with spatial interpolation, b) AMO and c) DMO. All the data within the 2-2.5 km offset range were transformed using these three methods. No inverse NMO was applied after the transformation. To enable the analysis of the moveouts along the offset axis after the application of DMO and AMO, the results are organized in pseudo-offset cubes with a narrow-offset ranges of 100 m.

 

Vel-sec Figure 2 In-line vertical section through the interval velocity model.

 

Vel-1D Figure 3 Typical vertical velocity profile in the area of study.

 

All-XYs Figure 4 CMP gathers after NMO and the application of: (a) Binning, (b) AMO, and (c) DMO. The fault-plane reflection is at about 2.2 s.

The AMO and DMO operators have similar implementations. They use the same anti-aliasing method and the same temporal and spatial interpolations. For the test data set, the computational times were also comparable. By optimizing the spatial sampling of the AMO operator, it should be possible to obtain an even faster, but as accurate, AMO implementation ().