Wavefield decomposition in arbitrary direction and an imaging condition based on stratigraphic dip

Abstract

In reverse-time migration (RTM), wavefield decomposition can play an important role in addressing the issue of migration noise, especially the low-frequency noise. The complete wavefield decomposition based on Hilbert transform is a commonly used method in RTM, but it is accompanied by extra wavefield simulation and wavefield storage. We present three distinct methods. First, we present a convenient method for wavefield decomposition, which is based on Poynting vectors. Only the unit vector in one direction is needed to realize the wavefield decomposition in an arbitrary direction by this method. It breaks through the limitation that the Hilbert transform based method is only applicable to the up- and down-going wave or left- and right-going wave decomposition and the calculation cost is negligible compared with RTM. Second, we present a method based on the instantaneous wavenumber, which is presented for calculating the wave propagation direction. On the basis of wavefield decomposition, the imaging angle gather from the new method performs better than that of Poynting vector method. Meanwhile, it is also used for generating incident angle gather and dip angle gather. The latter expresses the dip angle of underground strata. More importantly, the above methods allow to control the wavefield decomposition direction and three angles at any position underground. Finally, we propose stratigraphic imaging condition and briefly analyze the relationship between the new method and the inverse-scattering imaging condition. The stratigraphic imaging condition maps the results to the dip angle of the stratum through spatial gradient wavefield, which can enhance the effective imaging information. The above three kinds of angle gathers can also be constructed by the stratigraphic imaging condition. Numerical experiments show that the imaging results and the angle gathers obtained by the proposed method have higher accuracy and resolution.

Attenuation compensation for wavefield‐separation‐based least‐squares reverse time migration in viscoelastic media

“…2015; Guo et al . 2020, 2021). Instead of separating the up‐ and down‐going waves, we intend to smooth the velocity models to mitigate such artefacts.…”