An intrinsic problem during migration and imaging of seismic wavefields using the two-way wave equation is the crosstalk interference between the up/down propagation of the corresponding source and receiver wavefields. To mitigate this crosstalk, the downgoing source and upgoing receiver wavefield imaging condition (IC) is adopted at an early stage of the inversion process, improving convergence and obtaining cleaner reflection images. A wavefield decomposition methodology can also be incorporated into a least-squares reverse time migration (LSRTM) algorithm. The separation of wavefields based on the propagation direction in the early iterations of LSRTM is to reduce interference noise during the inversion process given that the IC considers only primary reflections. Wavefields decomposed with respect to the vertical direction can be easily obtained by Fourier transforms on the time and vertical axes; however, they usually require significantly higher computational effort especially for 3D applications. Vertical wavefield decomposition by a complex-valued analytic signal is an alternative method implemented by the Hilbert transform, which can be conducted by 1D Fourier transform only on the vertical axis. An LSRTM algorithm adopting this decomposition method has a disadvantage in that it requires two additional wave modelings at each iteration. However, by adapting the deprimary IC into LSRTM, only one more modeling is additionally required in the backward wavefield propagation as compared with conventional LSRTM. Our LSRTM using wavefield decomposition has the ability to produce broader band reflectivity images than conventional LSRTM. This is demonstrated with numerical examples using synthetic and real data resulting artifact-free migration results and broadband reflectivity images.

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