Multiscale viscoacoustic waveform inversion with the second generation wavelet transform and adaptive time-space domain finite-difference method

Full waveform inversion (FWI) has the potential to provide preferable subsurface model parameters. The main barrier of its applications to real seismic data is heavy computational amount. Numerical modelling methods are involved in both forward modelling and backpropagation of wavefield residuals, which spend most of computational time in FWI. We develop a time-space domain finite-difference (FD) method and adaptive variable-length spatial operator scheme in numerical simulation of viscoacoustic equation and extend them into the viscoacoustic FWI. Compared with conventional FD methods, different operator lengths are adopted for different velocities and quality factors, which can reduce the amount of computation without reducing accuracy. Inversion algorithms also play a significant role in FWI. In conventional single-scale methods, it is likely to converge to local minimums especially when the initial model is far from the real model. To tackle the problem, we introduce the second generation wavelet transform to implement the multiscale FWI. Compared to other multiscale methods, our method has advantages of ease of implementation and better time-frequency local analysis ability. The L2 norm is widely used in FWI and gives invalid model estimates when the data is contaminated with strong non-uniform noises. We apply the L1-norm and the Huber-norm criteria in the time-domain FWI to improve its antinoise ability. Our strategies have been successfully applied in synthetic experiments to both onshore and offshore reflection seismic data. The results of the viscoacoustic Marmousi example indicate that our new FWI scheme consumes smaller computer resources. In addition, the viscoacoustic Overthrust example shows its better convergence and more reasonable velocity and quality factor structures. All these results demonstrate that our method can improve inversion accuracy and computational efficiency of FWI.