Full waveform inversion based on hybrid gradient

The low-wavenumber components in the gradient of full waveform inversion (FWI) play a vital role in the stability of the inversion. However, when FWI is implemented in some high frequencies and current models are not far away from the real velocity model, an excessive number of low-wavenumber components in the gradient will also reduce the convergence rate and inversion accuracy. To solve this problem, this paper firstly derives a formula of scattering angle weighted gradient in FWI, then proposes a hybrid gradient. The hybrid gradient combines the conventional gradient of FWI with the scattering angle weighted gradient in each inversion frequency band based on an empirical formula derived herein. Using weighted hybrid mode, we can retain some low-wavenumber components in the initial low-frequency inversion to ensure the stability of the inversion, and use more high-wavenumber components in the high-frequency inversion to improve the convergence rate. The results of synthetic data experiment demonstrate that compared to the conventional FWI, the FWI based on the proposed hybrid gradient can effectively reduce the low-wavenumber components in the gradient under the premise of ensuring inversion stability. It also greatly enhances the convergence rate and inversion accuracy, especially in the deep part of the model. And the field marine seismic data experiment also illustrates that the FWI based on hybrid gradient (HGFWI) has good stability and adaptability.