The connection of velocity and impedance sensitivity kernels with scattering-angle filtering and its application in full waveform inversion

Multi-scale strategies such as starting from the low-frequency and early-arrival part of recorded data are commonly used in full waveform inversion (FWI) to maneuver complex nonlinearity. An alternative way is to apply appropriate filtering and conditioning to the misfit gradient in the model domain. In acoustic constant-density media, we prove that velocity and impedance sensitivity kernels are equivalent to applying a high-pass and a low-pass scattering-angle filter to a conventional single-parameter velocity (CSV) kernel. The high-pass scattering-angle filter allows the velocity kernel to include low-wavenumber updates (tomography component). In contrast, the low-pass scattering-angle filter helps the impedance kernel to yield high-wavenumber updates (migration component). The velocity model can be updated using a hybrid gradient of two components combined with appropriate weights. This FWI scheme is able to overcome the potential nonlinearity and partially mitigate the cycle-skipping problem. Numerical examples for the SEG/EAGE overthrust model and the Marmousi model demonstrate that the hybrid gradient facilitates FWI to converge faster to the true model even in cases when conventional CSV-based FWI fails.