Implicit versus explicit 3-D poststack depth migration

**Seismic Data Analysis**
Series	Investigations in Geophysics
Author	Öz Yilmaz
DOI	http://dx.doi.org/10.1190/1.9781560801580
ISBN	ISBN 978-1-56080-094-1
Store	SEG Online Store

Finally, we compare the performance of the implicit and explicit schemes using the circularly symmetric salt-dome model data set of Figure 8.4-2. The implicit scheme uses the 45-degree extrapolator in a split mode, and the explicit scheme uses a one-dimensional (1-D) explicit filter combined with the 5 × 5 McClellan filter template (Section G.2). Selected inline sections are shown in Figure 8.4-13, and depth slices are shown in Figure 8.4-14. The top-salt boundary is imaged more accurately by the explicit scheme because of the near-circular symmetry of its impulse response (Figure 7.3-14). Positioning errors by the implicit scheme implied by its impulse response (Figure 7.3-3) are better observed on the depth slices. Note in Figure 8.4-14 that the top-salt boundary image by the implicit scheme is not circularly symmetric; instead, significant undermigration especially along the two diagonals has resulted. In contrast, the explicit scheme has preserved the circular character of the salt dome.

Figure 8.4-2 Velocity-depth model (left column) and cross-sections of the zero-offset 3-D synthetic wavefield (right column) for a circularly symmetric salt dome. The base map is shown in Figure 8.4-1.
Figure 8.4-13 A comparison of implicit and explicit 3-D migrations. Velocity-depth model and cross-sections of the zero-offset 3-D synthetic wavefield are shown in Figure 8.4-2. The base map is shown in Figure 8.4-1. Time slices are shown in Figure 8.4-14.
Figure 8.4-14 A comparison of implicit and explicit 3-D migrations. Velocity-depth model and cross-sections of the zero-offset 3-D synthetic wavefield are shown in Figure 8.4-2. The base map is shown in Figure 8.4-1. Vertical sections are shown in Figure 8.4-13.
Figure 7.3-14 Impulse response of a 3-D migration operator based on a 39-point explicit 1-D operator transformed into a 2-D operator using the 5 × 5 McClellan filter template in Table G-2. Compare with Figures 7.3-11, 7.3-12, and 7.3-13.
Figure 7.3-3 A 45-degree split 3-D migration operator impulse response. See Figure 4.2-1 for the 2-D equivalent response. Except for the amplitudes, the vertical cross-section at center line (51) is the same as the 2-D impulse response.