Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversion (FWI) of wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challenging because of the increased nonlinearity introduced by free-surface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting model if low frequencies are unavailable in the data. We evaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm thatoutperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin (DG) method on triangular mesh, which allows accurate modeling of free-surface effects. Sequential inversions of increasing frequencies define the most natural level of hierarchy in multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complex-valued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Among the possible strategies for sampling frequencies in the inversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when considering complex wave phenomena.

B uilding high-resolution models of several physical properties of the subsurface by multiparameter full waveform inversion (FWI) of multicomponent data will be a challenge for seismic imaging for the next decade. The physical properties, which govern propagation of seismic waves in visco-elastic media, are the velocities of the P-and S-waves, density, attenuation, and anisotropic parameters. Updating each property is challenging because several parameters of a different nature can have a coupled effect on the seismic response for a particular propagation regime (from transmission to reflection). This is generally referred to as trade-off or crosstalk between parameters. Moreover, different parameter classes can have different orders of magnitude or physical units and footprints of different strength in the wavefield, which can make the inversion poorly conditioned if it is not properly scaled. These difficulties raise the issue of a suitable parameterization for multiparameter FWI, where the term parameterization must be understood as a set of independent parameter classes that fully describe the subsurface properties. Many combinations of parameters can be viewed and this choice is not neutral as the parameterization controls the trade-off between parameters and the local resolution with which they can be reconstructed. Once this parameterization is selected, the subset of parameter classes in the parameterization, that can be reliably updated during the inversion, must be identified to avoid overparameterization of the optimization problem. The purpose of this tutorial is to provide a comprehensive overview of the promise, pitfalls, and open questions underlying multiparameter FWI. We first review the main FWI ingredient that controls the tradeoff between parameters, namely the radiation pattern of the so-called virtual sources, and some tools for analyzing these trade-offs. Then, we present some illustrative examples of multiparameter FWI, which should provide some guidelines to choose a suitable parameterization for FWI in visco-acoustic anisotropic media. We conclude by proposing a data-driven and model-driven workflow for visco-elastic anisotropic FWI of multicomponent marine data, which has been inspired by a real data case study from Valhall.

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