A common problem in many time-lapse seismic monitoring studies is the presence of obstructions that create gaps in the monitor data.
Such obstructions, usually caused by production and drilling facilities, generate artifacts that contaminate production-related seismic amplitudes changes, thereby limiting our ability to accurately interpret observed time-lapse amplitudes.
The Valhall LoFS project provides data with high repeatability of both source and receiver locations (Figure 1).
Therefore, in this case study, the major source of time-lapse amplitude contamination is the synthesized gap in the monitor data.
Because CMP fold provides only limited information about the geometry difference (Figure 2), it is insufficient to compensate for subsurface illumination differences.
As shown in Figure 4, the Hessian diagonal provides a robust measure of the subsurface illumination for any given geometry.
A measure of the subsurface illumination differences can be obtained from the ratio of the Hessian diagonal for the different survey geometries (Figure 5).
Although the Hessian diagonal provides information about subsurface illumination and differences, the band-limited wave-propagation effects are provided by the Hessian off-diagonals (not shown).
Because the least-squares problem is in the image space, we are able to solve it for a small target around the reservoir (Figure 6).
This enables us to try different combinations of inversion parameters efficiently and to focus on improving the results in the region around the reservoir, where the most important production/injection-related changes are expected.
Because the Hessian serves as a geometry- and propagation-dependent deconvolution operator, it provides images with improved resolution compared to migration (Figure 8).
Because of the gap in the monitor data, there is a large disparity in the distribution of time-lapse amplitudes in the migrated images (Figures 9(a) and 9(b)).
Inversion corrects for this disparity, thereby leading to comparable time-lapse amplitude distributions in both the complete and incomplete data examples (Figures 9(c) and 9(d)).
Least-squares wave-equation inversion of time-lapse seismic data sets - A Valhall case study