Data preprocessing sufficiently attenuates multiples and other artifacts in the data (Figures 2 and 3).
This is required to ensure that the data satisfy sufficiently the primaries-only assumption in our inversion formulation.
By warping the images before stacking, we ensure that defocusing effects due to velocity and compaction effects are minimized.
Because the overburden geology along the studied section is fairly simple, the monitor image (Figure 4) is sufficiently aligned to the baseline using only vertical components of the prestack apparent displacement vectors (Figure 5).
In practice, even with good repeatability between surveys, it is difficult to interpret an unprocessed time-lapse image (Figure 8(a)).
However, after careful processing, it is possible to make meaningful interpretation of amplitude information in the time-lapse image (Figure8(b)).
Although in many cases, results from a conventional processing workflow may suffice, the quality of the time-lapse image can be improved by wave-equation inversion (Figure 8(c)).
In the second example, because the monitor data is incomplete, the effective geometries differ for the two surveys, thereby leading to illumination mismatch (i.e., illumination ratios not equal to unity) in parts of the target area (Figure 11).
However, the Hessian diagonal gives only a partial measure of the illumination mismatch between time-lapse surveys (Figure 11).
Large geometry differences (e.g., an obstruction in the monitor acquisition) can cause large differences in the off-diagonal terms of the Hessian (Figure 12).
Such geometry differences lead to differences in wavenumber illumination between surveys (Figure 13).
Therefore, a point-by-point amplitude compensation using only the Hessian diagonal is inadequate.
Where there is significant geometry difference between surveys, conventional time-lapse processing is insufficient (Figure 14(b)).
In this case, wave-equation inversion provides a significant improvement to the time-lapse image (Figure 14(c)).
Although the amplitude information derivable from the interpolated monitor data (not shown) are of poor quality the kinematics are similar to those of the complete baseline image.
Therefore these provide adequate estimates of the warping parameters (Figure 10) comparable to those from the complete data case (Figure 5).
Wave-equation inversion of time-lapse seismic data sets