Model-based seismic data redatuming with time-domain data-assimilated wavefield reconstruction

SUMMARY We present a novel model-based seismic data redatuming method based upon time-domain data-assimilated wavefield (DAW) reconstruction. Seismic redatuming refers to the positioning of sources and/or receivers from the acquisition surface to a virtual datum level along with the computation of the data set that would have been recorded by the virtual acquisition. Physically, DAWs approximate the true wavefields by least-squares time-reversal extrapolation of the recorded data in a background subsurface model. To this end, DAWs are first formulated as the sum of the background wavefields and an approximation of the scattered wavefields by the unknown contrasts between the true model and the background model. We estimate the scattered fields via the estimation of their volume scattering sources by fitting in a least-squares sense the differences between the recorded data and the simulated data in the background model, namely the restriction at receivers of the scattered fields. These underdetermined linear source problems involve two main steps: a multidimensional deconvolution of the scattered data by the data-domain Hessian, followed by the propagation of the deconvolved scattered data backward in time. Once the source problems have been solved, DAWs follow by solving the wave equation in the background model using the sum of the experimental sources and the scattering sources as extended sources. Finally, the redatumed data sets, whose accuracy depends on the precision of the background medium between the acquisition surface and the datum, are readily obtained by sampling the DAWs at arbitrary datum levels. The primary challenge in computing accurate DAWs lies in the multidimensional deconvolution of the scattered data, which requires solving a data-domain normal equation with pre-conditioned Krylov-subspace iterative methods, where each iteration requires one forward and one backward simulation. We assess the accuracy of the method and discuss its computational cost with several benchmarks representing various experimental environments (onshore with weathered layers, shallow and deep offshore).