Up: Sava et al.: 4-D
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 is derived
from the reference survey and that it perfectly focuses the
reference data to create the reference image .
Figure 2 Synthetic model: reflectivity
(left) and slowness (right).
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
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:
- Although the changes in the reservoirs occur at only two
levels, the changes in the images occur at all levels underneath.
This situation is common for 4-D seismic surveys. Typically
only the top reservoir can be properly analyzed since
the 4-D effects created by the deeper reservoirs are either
masked or seriously shadowed by the top reservoir.
- Completely different changes in the reservoirs yield fairly
similar perturbations of the images. Even for such a simple
model, as the one we use in this analysis, it is really hard to
visually analyze the image perturbation and distinguish among the
two cases (Figure 3).
In practice, this distinction is virtually impossible,
and the only place where we can extract reliable information
is at the top-most producing reservoir.
Figure 3 Image perturbation: scenario 1
on the left and scenario 2 on the right.
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
in Equation (1) applied to the image perturbation in Figure 3.
The two cases can be better distinguished now,
although the information is not yet localized at the
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.
Up: Sava et al.: 4-D
Stanford Exploration Project