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Full waveform inversion (FWI) is a nonlinear waveform matching procedure,which suffers from cycle skipping when the initial model is notkinematically-accurate enough. To mitigate cycle skipping, wavefieldreconstruction inversion (WRI) extends the inversion search space by computingwavefields with a relaxation of the wave equation in order to fit the data fromthe first iteration. Then, the subsurface parameters are updated by minimizingthe source residuals the relaxation generated. Capitalizing on thewave-equation bilinearity, performing wavefield reconstruction and parameterestimation in alternating mode decomposes WRI into two linear subproblems,which can solved efficiently with the alternating-direction method ofmultiplier (ADMM), leading to the so-called IR-WRI. Moreover, ADMM provides asuitable framework to implement bound constraints and different types ofregularizations and their mixture in IR-WRI. Here, IR-WRI is extended tomultiparameter reconstruction for VTI acoustic media. To achieve this goal, wefirst propose different forms of bilinear VTI acoustic wave equation. Wedevelop more specifically IR-WRI for the one that relies on a parametrisationinvolving vertical wavespeed and Thomsen's parameters delta and epsilon. With atoy numerical example, we first show that the radiation patterns of the virtualsources generate similar wavenumber filtering and parameter cross-talks inclassical FWI and IR-WRI. Bound constraints and TV regularization in IR-WRIfully remove these undesired effects for an idealized piecewise constanttarget. We show with a more realistic long-offset case study representative ofthe North Sea that anisotropic IR-WRI successfully reconstruct the verticalwavespeed starting from a laterally homogeneous model and update thelong-wavelengths of the starting epsilon model, while a smooth delta model isused as a passive background model.

ADMM-based multi-parameter wavefield reconstruction inversion in VTI acoustic media with TV regularization