A Time-Domain Preconditioned Truncated Newton Approach to Visco-acoustic Multiparameter Full Waveform Inversion
Résumé
A truncated Newton (TRN) method for time-domain full waveform inversion (FWI) in a visco-acoustic medium has been developed based on the 2nd-order adjoint state formulation. Time-domain gradient estimation and Hessian-vector product are managed by recomputing, without numerical instabilities, the incident wavefield at the same time as the adjoint wavefield for mitigating memory issues. Generic algorithm workflow has been proposed to switch between parameterizations, thanks to the chain rule. An efficient preconditioner adapted to the multiparameter configuration is developed to enhance the convergence rate of the inner conjugate gradient iterations. An additional user-defined scaling is introduced in the preconditioner to mitigate the weak sensitivity of specific parameters to waveform variations. The importance of the inverse Hessian for mitigating interparameter trade-off is validated on a toy example. Through a realistic 2D synthetic case based on a North Sea real data application, encouraging numerical results under $(V_p,\rho, Q^{-1})$ parametrization demonstrate that considering the Hessian influence significantly improves the multiparameter reconstruction, mitigating the coupling between parameters, for a reasonable increase of the computational cost compared to standard quasi-Newton optimization strategies.