Convolution-based multi-scale envelope inversion

Envelope inversion (EI) is an efficient tool to mitigate the nonlinearity of conventional full waveform inversion (FWI) by utilizing the ultralow-frequency component in the seismic data. However, the performance of envelope inversion depends on the frequency component and initial model to some extent. To improve the convergence ability and avoid the local minima issue, we propose a convolution-based envelope inversion method to update the low-wavenumber component of the velocity model. Besides, the multi-scale inversion strategy (MCEI) is also incorporated to improve the inversion accuracy while guaranteeing the global convergence. The success of this method relies on modifying the original envelope data to expand the overlap region between observed and modeled envelope data, which in turn expands the global minimum basin of misfit function. The accurate low-wavenumber component of the velocity model provided by MCEI can be used as the migration model or an initial model for conventional FWI. The numerical tests on simple layer model and complex BP 2004 model verify that the proposed method is more robust than EI even when the initial model is coarse and the frequency component of data is high.