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Next: Discussion Up: Sava et al.: 4-D Previous: Methodology

Example

We illustrate this technique with a synthetic model that resembles a typical producing reservoir in the North Sea. The model is depicted in Figure 2: the reflectivity on the left, and the reference slowness on the right. The model consists of several fractured horizontal reservoirs which are in production. The reference slowness is smooth and not conformant with the stratigraphy. We assume that the reference slowness ${\bf S}$ is derived from the reference survey and that it perfectly focuses the reference data $\d_0$ to create the reference image $\r_0$.

 
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model
Figure 2
Synthetic model: reflectivity (left) and slowness (right).
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Figure 4 shows the slowness perturbations we introduce in the slowness model. For each of the two scenarios, we generate data using the same reflectivity (Figure 2) but different slowness models generated by adding the respective slowness perturbations to the reference slowness. We then image using the reference slowness to create repeat survey images. Finally, we subtract the reference image from each of these two images and obtain the image perturbations (a.k.a. the 4-D seismic data) depicted in Figure 3.

Figure 3 enables us to make two observations:

 
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dimag
Figure 3
Image perturbation: scenario 1 on the left and scenario 2 on the right.
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We address the ambiguity of the 4-D interpretation using WEMVA. Figure 5 shows the slowness perturbations obtained by the adjoint of the WEMVA operator ${\bf L}$ in Equation (1) applied to the image perturbation $\Delta \r$in Figure 3. The two cases can be better distinguished now, although the information is not yet localized at the producing reservoirs.

The least-squares inversion result, shown in Figure 6, is much better focused at the reservoirs. Despite the inherent vertical smearing mainly caused by the limited data aperture, we can precisely indicate the location of the producing reservoirs, the sign of the slowness change, and even the relative magnitude of the change from one reservoir to the other.


next up previous print clean
Next: Discussion Up: Sava et al.: 4-D Previous: Methodology
Stanford Exploration Project
11/11/2002