Migration results of the SEG-EAGE Salt data set

In the previous two sections I have analyzed the theoretical differences between common-azimuth migration and offset plane wave migration. In this section, I compare the migration results.

The theoretical analysis identified two approximations that are made in offset plane wave migration: first, the setting of the cross-line offset ray parameter to zero, and second, downward continuing the offset plane waves separately, when in lateral varying media they should be allowed to mix. To enable the independent analysis of the effects of both approximations, I run three migration programs:

(A)

Common-azimuth migration

(B)

Hybrid offset plane wave migration (with plane-wave mixing)

(C)

Offset plane wave migration (without plane-wave mixing).

All three programs implement the downward-continuation operators in the frequency-wavenumber domain and adapt to lateral velocity variations by an extended split-step method Stoffa et al. (1990). When required, the offset-plane wave decomposition was performed inside the migration by Fourier transforms, relying on the well-known relations between ray parameters and wavenumbers ($p_{x_h}=k_{x_h}/\omega$ and $p_{y_h}=k_{y_h}/\omega$). Both the offset plane wave migration (C) and the hybrid offset plane wave migration (B) apply the dispersion relation in equation (8). The only difference between the two is that in (C) the offset-wavenumber axis is not transformed into the space domain when applying the split-step correction; that is, each offset-wavenumber (plane-wave) component is downward continued independently for all depths. On the other hand, the only difference between migration (A) and migration (B) is that in migration (B) the cross-line offset wavenumber was set to zero, while in migration (A) it was evaluated using equation (3).

The input data set was the same for all three programs, and the same as I used for my previous comparison of common-azimuth migration and Kirchhoff migration Biondi (1999a). The Salt Model C3-NA data set Clapp et al. (1999); SEG-EAGE (1997) was transformed to effective common-azimuth data by applying Azimuth Moveout Biondi et al. (1998). The regularized common-azimuth data set was binned with a 20 meter CMP spacing in both the in-line and cross-line directions, and with 100 meter sampling along the in-line offset direction. The data were muted with a ``deep'' mute because the early arrivals are contaminated by all sorts of modeling noise. This mute affected the imaging of the shallow events. A more careful mute could accomplish both noise removal and shallow event preservation.

With respect to the previous tests, I increased the number of reference velocities from four to six. I wanted to verify the hypothesis that the poor imaging of a fault by common-azimuth migration was caused by having used too few reference velocities (Figure 5 in the previous report). Indeed, the fault is much better imaged when six reference velocities are used (Figure 10 in this report).