A sequential inversion with outer iterations for the velocity and the intrinsic attenuation using an efficient wavefield inversion

Full-waveform inversion (FWI) has become a popular method to retrieve high-resolution subsurface model parameters. It is a highly non-linear optimization problem based on minimizing the misfit between the observed and predicted data. For intrinsically attenuating media, wave propagation experiences significant loss of energy. Thus, for better data fitting, it is crucial sometimes to consider attenuation in FWI. Viscoacoustic FWI aims at achieving a joint inversion of the velocity and attenuation models. However, multiparameter FWI imposes additional challenges including expanding the null space and facing trade-off issues. Theoretically, an ideal way to mitigate the trade-off issue in multiparameter FWI is to apply the inverse Hessian operator to the parameter gradients. However, it is often not practical to calculate the full Hessian and its matrix inverse, as this will be extremely expensive. To improve the computational efficiency and mitigate the trade-off issue, we use an efficient wavefield inversion (EWI) method to invert for the velocity and the intrinsic attenuation. This approach is implemented in the frequency domain, and the velocity, in this case, is complex valued in the viscoacoustic EWI. We propose a sequential update strategy for the velocity and the intrinsic attenuation, and we repeat the separate optimizations, we refer to as outer iterations, until the convergence is achieved. As viscoacoustic EWI is able to recover a good velocity model, the velocity update leakage to the $Q$ model is largely reduced. We show the effectiveness of this approach using synthetic data generated for the viscoacoustic Marmousi and Overthrust models. To further prove the validity of the proposed approach, we generate data in the time domain using a viscoelastic wave equation solver, and obtain reasonable inversion results in the frequency domain using the viscoacoustic approximation.