The first model is a diffractor situated at a depth of 600 meters.
The velocity used is 2000 m/s and the number of offsets is 64.
The maximum half-offset *h* is 1575 meters.
The modeling was done by calculating the travel-time from
source to diffractor and back to receiver, and assigning to each
midpoint an amplitude equal to the product

The second model represents a dipping reflector through a medium with 2000 m/s velocity. Figure shows the first and last panel in the prestack data cube corresponding to the zero-offset and the maximum-offset common-midpoint (CMP) sections. The model was produced by considering the dipping reflector comprised of diffractors, each modeled separately. Figure a shows the output of the stacked FT-MZO, while Figure b shows the output of the Ps-MZO algorithm. Figure shows the amplitudes along the dipping reflector. This is the case where Zhang's amplitude curve is superimposed on the FT-MZO curve as I expected from theory. Figure b shows results obtained when applying the spherical divergence correction. The values at the sides of the figure should be discarded as the picking algorithm I used to collect the amplitudes along the reflector, chose the amplitudes along the artifacts generated by spatial wraparound. Figure compares the wavelets obtained after MZO. For each method I selected the trace passing through the middle of the section. Again Figure b has spherical divergence applied. Observe that in both cases the FT-DMO follows the zero-offset original curve, while the phase of the Ps-MZO wavelet is very different.

The third model represent a horizontal reflector through a medium with 2000 m/s velocity. Figure shows the first and last panel in the prestack data cube corresponding to the zero-offset and the maximum-offset common-midpoint (CMP) sections. Figure a shows the output of the stacked FT-MZO, while Figure b shows the output of the Ps-MZO algorithm. Figure shows the amplitudes along the horizontal reflector. Figure b shows results obtained when applying the spherical divergence correction. Again the maximum amplitude corresponds to the Ps-MZO, followed by Zhang's DMO, original zero-offset model and FT-MZO. When spherical divergence is applied all three methods show amplitudes higher than the original model. Figure compares the wavelets obtained after MZO. For each method I selected the trace passing through the middle of the section. Again Figure b has spherical divergence applied. While the two FT-MZO wavelets follow closely the zero-offset original model, the phase of the Ps-MZO wavelet is less similar.

I don't have a good explanation yet for the difference in amplitudes between Zhang's DMO and FT-MZO in the case of the single diffractor and in the case of the horizontal reflector. A loss in amplitude in the FT-MZO methods, occurs due to stacking, as the amplitude of the zero-offset sections after DMO tend to decrease slightly with the offset. This could be due to my modeling or to the fact that the DMO Jacobian doesn't completely account for the loss in amplitude with offset. In think the spherical divergence correction should be part of the DMO process and not an independent process, as it should be dip dependent.

Figure 3

a. First panel in the input cube: zero-offset.

b. Last panel in the input cube: maximum-offset.

Figure 4

a. DMO+NMO.

b. MZO from Prestack Migration.

Figure 5

b. Amplitudes with spherical divergence applied.

Figure 6

b. Zero-offset wavelets with spherical divergence applied.

Figure 7

a. First panel in the input cube: zero-offset.

b. Last panel in the input cube: maximum-offset.

Figure 8

a. DMO+NMO.

b. MZO from Prestack Migration.

Figure 9

a. Amplitudes along a dipping reflector.

b. Amplitudes with spherical divergence applied.

Figure 10

a. Zero-offset wavelets.

b. Zero-offset wavelets with spherical divergence applied.

Figure 11

a. First panel in the input cube: zero-offset.

b. Last panel in the input cube: maximum-offset.

Figure 12

a. DMO+NMO.

b. MZO from Prestack Migration.

Figure 13

a. Amplitudes along a horizontal reflector.

b. Amplitudes with spherical divergence applied.

Figure 14

a. Zero-offset wavelets.

b. Zero-offset wavelets with spherical divergence applied.

11/17/1997