They demonstrate how the concept of Point Spread Functions (PSF) and a joint reflectivity inversion process can be successfully applied to time-lapse seismic when the respective acquisition geometries are very different. The aim of the study is to highlight the benefit of the joint inversion in the image domain and to define a 4D formulation which is not dependent on geological and/or reservoir production constraints.

Optimizing the 4D signal

Successful time-lapse (or 4D seismic) studies require special care when it comes to the removal of undesirable artifacts 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 so that subtle seismic signal variation induced by reservoir production can be detected. It is commonly accepted that the required repeatability accuracy is directly linked to the desired sensitivity and resolution of the 4D signal.

However, in some cases it is not possible to repeat the survey geometries between vintages. When the geometry differences are small, corrections can be made during data processing by including steps such as 4D binning, which aim to preserve those seismic traces that are associated with the smallest variation in source and receiver positions. 

Nevertheless, 4D binning does not perform well when both acquisition vintages comprise significant differences in their respective source and receiver positions. This is for example the case when different streamer acquisition azimuths are involved or when large cable feathering differences at long offsets are observed or indeed when a towed streamer survey is to be compared with an OBS acquisition.

Wave Equation Reflectivity Inversion using PSF

The First Break article presents an image domain approach for correcting for illumination differences between 4D datasets and the process is built on previously published work concerning wave equation reflectivity inversion using Point Spread Functions. In this two-step least-squares imaging method, the reflectivity of depth migrated images is recovered by explicitly computing multi-dimensional PSFs using wave-equation modeling and deconvolving these PSFs with the final migrated image.

They reveal that image domain 4D reflectivity inversion using multi-dimensional PSFs can compensate for significant illumination differences when substantially different survey geometries are used for 4D imaging. The proposed methodology is particularly advantageous in 4D studies where the geometry of the different acquisitions cannot be replicated. This is likely be the case when towed streamer surveys with different acquisition directions are used in a 4D experiment or when streamer and OBN (Ocean Bottom Node) surveys are combined.

Resulting 4D reflectivity difference at OWC for the case of the separate application of PSFs to each time-lapse survey (left) and the joint application of cross-survey PSFs (right). Separate inversion approach shows more 4D noise above the OWC location than the joint reflectivity inversion.

Synthetic data examples illustrate that the joint reflectivity inversion process delivers improved results when compared to the use of separate inversions as it ensures a more robust recovery of the 4D effects and results in lower 4D noise. The presented new methodology using cross-survey Point Spread Functions (XPSFs) ensures consistency in the wavefields of the different time-lapse surveys and does not require additional constraints.

Combining this new 4D imaging inversion technique with an optimum 4D repeated acquisition design will provide the best results when subtle 4D effects are to be detected.