Full waveform inversion with smoothing of dilated convolutions

Full waveform inversion (FWI) is a method for building subsurface models with high resolution by optimizing a data-fitting problem. However, it is still a challenge to apply the FWI method to complicated subsurface models, because FWI is a highly ill-fitting inversion problem. When the simulated data differ from the observed data by more than half a cycle, FWI tends to suffer from the cycle-skipping problems and get trapped in a local minimum. To help the inversion to converge to the accurate subsurface model, we typically build a reasonable initial model or use low-frequency data to start our inversion. Here, we developed a novel technique called smoothing of dilated convolutions inversion (SDCI) to generate low-frequency components from seismic data to recover low-wavenumber components of the subsurface. In the theory part, we first present the objective function of the SDCI method and then derive the gradient of the objective function relative to the velocity using the adjoint-state approach. We then apply the method to a set of simulated data from the Marmousi model. The SDCI method can reasonably estimate the subsurface model even if the simulated seismic record does not contain information below 5 Hz. The numerical examples prove the effectiveness and feasibility of the proposed method. From the SDCI results, the FWI method recovers the velocity with higher accuracy and resolution.