Hybrid gradient full waveform inversion based on Hilbert transform

Abstract Full waveform inversion (FWI) delivers high-resolution imaging of subsurface structures. However, its performance is highly dependent on the accuracy of initial velocity model. Cycle-skipping, caused by model inaccuracy, often traps conventional FWI in local minima dominated by short-wavelength components, impeding the recovery of essential long-wavelength structures. To overcome this, we propose a hybrid gradient FWI (HFWI) method that incorporates the Hilbert transform and Gaussian filtering. The key innovation lies in decomposing the FWI gradient into tomographic and migration components via the Hilbert transform, followed by the suppression of residual high-wavenumber components in the tomographic gradient using a Gaussian filter. Comparative analyses demonstrate that HFWI offers two principal advantages: (i) the filtered tomographic gradient effectively constructs background velocity models, providing an excellent starting point for subsequent conventional FWI, and (ii) the integrated migration gradient enhances final inversion accuracy. Sensitivity kernel tests confirm the successful separation of gradient components. Numerical experiments on a layered model with a high-velocity anomaly and the Marmousi model show that HFWI can recover missing low-wavenumber components even from poor starting models.