Wave-equation migration velocity analysis for anisotropic models on 2-D ExxonMobil field data

Field data tests

We extract a 2-D line from ExxonMobil dataset where the salt body is far away. Source spacing is 100 m, and receiver spacing is 50 m. The maximum offset in this 2-D line is about 4 km. This surface seismic dataset was acquired more than a decade ago; therefore the limited offsets of this dataset are insufficient from enough to constrain the anisotropic parameters. Fortunately, this area has been studied extensively by various types of other acquisitions: vertical check shots, offset check shots, and sonic logs. Therefore, a very well-defined anisotropic model is obtained from previous studies. We migrated the 2-D line using the anisotropic model provided (Figure 4(a) and Figure 4(b)). The initial stack image is shown on the top panel in Figure 6. Although the apparent dip is high due to the large vertical stretch (3 km in depth vs. 16 km on the horizontal axis), the reflectors in this 2-D line are pretty flat. We then estimate the dip field (Figure 3) from the initial image and use it to regularize the gradient for both velocity and $\eta$ .

We can see many small-scale faults in this area on the top panel in Figure 6. Migration artifacts at $x =13$ km and $z = 2500$ m are caused by a big vertical fault running from $x = 14$ km on the top to the bottom of the section. The initial angle gathers are shown in the bottom row in Figure 6. Since this is a streamer geometry, the subsurface reflectors are only illuminated from positive angles. Although the gathers are almost flat, we can still see upward residual moveouts in the angle domain. Therefore, we have a chance to improve the model and the image by flattening the gathers.

Updates between the initial and the inverted velocity and $\eta$ models are shown in Figure 5(a) and Figure 5(b), respectively. First, notice the spatial correlation between velocity updates and $\eta$ updates, although no such constraints are applied during the inversion. However collocated, the update directions in velocity and $\eta$ are not necessarily the same. We are able to resolve a localized shallow anomaly between $13$ km and $15$ km at around 800 m below surface. Comparing the initial stack image on the top panel in Figure 6 with the final stack image on the top panel of Figure 7, we can see improved continuity and signal strength in the area highlighted by the oval. The fault in this area is also better defined in the final image. Notice that the updates in velocity are less than 10%, whereas the updates in $\eta$ are around 25%. These positive updates in both velocity and $\eta$ agree well with the negative travel time misfits in the previous OCS modeling results (Figure 1).

We can also verify the updates in velocity and $\eta$ on the angle gathers at different CMP locations. The initial angle domain common image gathers (ADCIGs) are shown in the bottom row in Figure 6, and the final ADCIGs produced using the inverted models are shown in the bottom row in Figure 7. To better illustrate the effects of the model updates, the ADCIGs are sampled more densely between CMP = $13$ and $16$ and sparsely outside of this range. In general, we can see improved flatness for all the reflectors. Specifically, for the shallower events above $1$ km, most improvements happen at large angles over $35^\circ$ . Therefore, we interpret the improvements for the shallow events primarily as the contribution of the improved $\eta$ model.

For the deeper events at the same CMP location, both the depth and the flatness of the angle gather have been changed by inversion. The upward-curving events in the angle domain from the initial migration has been flattened by the improved velocity and $\eta$ model. This result would be more convincing if we had the corresponding well logs at the same location to verify the depth shifts.

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Figure 3. Estimated dip field from the initial image on the top panel of Figure 6.

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Figure 4. Initial velocity model (a) and initial $\eta$ model (b).

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Figure 5. Updates in velocity model (a) and updates in $\eta$ model (b) after inversion.

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Figure 6. The initial stack image (Top panel) and initial angle domain common image gathers at CMP $= 7, 10, 13, 14, 14.5, 15$ km (Bottom row).

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Figure 7. The final stack image (Top panel) and final angle domain common image gathers at CMP $= 7, 10, 13, 14, 14.5, 15$ km (Bottom row). Compared with Figure 6, improvements in continuity and enhancements in amplitude strength are highlighted by the oval.

Wave-equation migration velocity analysis for anisotropic models on 2-D ExxonMobil field data