Successful time-lapse studies require special care when it comes to the removal of undesirable artefacts caused by the differences in acquisition geometries. By attempting to repeat the source and receiver geometries between surveys as precisely as possible, any subsequent 4D noise is minimized. However, in some cases it is not possible to repeat the survey geometries between vintages. This is the case when a towed streamer survey is compared with an OBS acquisition. The image domain approach for correcting illumination differences between 4D datasets builds on wave equation reflectivity inversion using Point Spread Functions (PSFs). In this two-step least-squares imaging method, the reflectivity is recovered by explicitly computing multi-dimensional PSFs using wave-equation modeling and de-convolving these PSFs with the final migrated image.

We define a 4D formulation which is not dependent on geological and/or reservoir production constraints by introducing the concept of cross-survey PSFs (XPSFs). As shown using synthetic data examples, the joint reflectivity inversion process delivers superior results when compared to separate inversions as it ensures a more robust recovery of the 4D effects. The presented new methodology using cross-survey Point Spread Functions (XPSFs) ensures consistency of the wavefields for recovering the 4D signal.


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