Advancing attenuation estimation through integration of the Hessian in multiparameter viscoacoustic full-Waveform inversion

Accurate seismic attenuation models of subsurface structures not only enhance subsequent migration processes by improving fidelity, resolution, and facilitating amplitude-compliant angle gather generation, but also provide valuable constraints on subsurface physical properties. Leveraging full wavefield information, multiparameter viscoacoustic full-waveform inversion ( Q-FWI) simultaneously estimates seismic velocity and attenuation ( Q) models. However, a major challenge in Q-FWI is the contamination of crosstalk artifacts, where inaccuracies in the velocity model get mistakenly mapped to the inverted attenuation model. While incorporating the Hessian is expected to mitigate these artifacts, the explicit implementation is prohibitively expensive due to its formidable computational cost. In this study, we formulate and develop a Q-FWI algorithm via the Newton-CG framework, where the search direction at each iteration is determined through an internal conjugate gradient (CG) loop. In particular, the Hessian is integrated into each CG step in a matrix-free fashion using the second-order adjoint-state method. We find through synthetic experiments that the proposed Newton-CG Q-FWI significantly mitigates crosstalk artifacts compared to the L-BFGS method and the conjugate gradient (CG) method, albeit with a notable computational cost. In the discussion of several key implementation details, we also demonstrate the significance of the approximate Gauss-Newton Hessian, the second-order adjoint-state method, and the two-stage inversion strategy.