Full waveform inversion (FWI) is a nonlinear waveform matching procedure, which suffers from cycle skipping when the initial model is not kinematically-accurate enough. To mitigate cycle skipping, wavefield reconstruction inversion (WRI) extends the inversion search space with a penalty method to relax the wave-equation constraint. Moreover, an alternating-direction strategy decomposes WRI into two linear sub-problems capitalizing on the wave-equation bilinearity. The first one reconstructs wavefields by fitting data with wave-equation relaxation, while the second updates subsurface parameters by minimizing the source residuals the relaxation generated. Iteratively-refined WRI (IR-WRI) improves WRI by replacing the penalty method with an augmented Lagrangian method equipped with operator splitting (ADMM). Compared to penalty methods, augmented Lagrangian methods refine the solution more efficiently and accurately when a fixed penalty parameter is used. Moreover, ADMM provides a suitable framework to implement bound constraints and edge-preserving regularizations in IR-WRI.

So far, IR-WRI has been assessed for mono-parameter velocity estimation from the isotropic Helmholtz equation. Here, IR-WRI is extended to acoustic VTI multiparameter reconstruction. We first show that the VTI acoustic wave equation is bilinear and formulate IR-WRI in this framework. Then, we validate our method against a simple inclusion test and a more realistic North Sea synthetic example.


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