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.

International audienceThe validity of isotropic approximation to perform acoustic full waveform inversion (FWI) of real wide-aperture anisotropic data can be questioned due to the intrinsic kinematic inconsistency between short- and large-aperture components of the data. This inconsistency is mainly related to the differences between the vertical and horizontal velocities in vertical-transverse isotropic (VTI) media. The footprint of VTI anisotropy on 2-D acoustic isotropic FWI is illustrated on a hydrophone data set of an ocean-bottom cable that was collected over the Valhall field in the North Sea. Multiscale FWI is implemented in the frequency domain by hierarchical inversions of increasing frequencies and decreasing aperture angles. The FWI models are appraised by local comparison with well information, seismic modelling, reverse-time migration (RTM) and source-wavelet estimation. A smooth initial VTI model parameterized by the vertical velocity V0 and the Thomsen parameters δ and ε were previously developed by anisotropic reflection traveltime tomography. The normal moveout (inline image) and horizontal (inline image) velocity models were inferred from the anisotropic models to perform isotropic FWI. The VNMO models allows for an accurate match of short-spread reflection traveltimes, whereas the Vh model, after updating by first-arrival traveltime tomography (FATT), allows for an accurate match of first-arrival traveltimes. Ray tracing in the velocity models shows that the first 1.5 km of the medium are sampled by both diving waves and reflections, whereas the deeper structure at the reservoir level is mainly controlled by short-spread reflections. Starting from the initial anisotropic model and keeping fixed δ and ε models, anisotropic FWI allows us to build a vertical velocity model that matches reasonably well the well-log velocities. Isotropic FWI is performed using either the NMO model or the FATT model as initial model. In both cases, horizontal velocities are mainly reconstructed in the first 1.5 km of the medium. This suggests that the wide-aperture components of the data have a dominant control on the velocity estimation at these depths. These high velocities in the upper structure lead to low values of velocity in the underlying gas layers (either equal or lower than vertical velocities of the well log), and/or a vertical stretching of the structure at the reservoir level below the gas. This bias in the gas velocities and the mispositioning in depth of the deep reflectors, also shown in the RTM images, are required to match the deep reflections in the isotropic approximation and highlight the footprint of anisotropy in the isotropic FWI of long-offset data. Despite the significant differences between the anisotropic and isotropic FWI models, each of these models produce a nearly-equivalent match of the data, which highlights the ill-posedness of acoustic anisotropic FWI. Hence, we conclude with the importance of considering anisotropy in FWI of wide-aperture data to avoid bias in the velocity recon...

Multiparameter full waveform inversion (FWI) is a challenging quantitative seismic imaging method for lithological characterization and reservoir monitoring. The difficulties in multiparameter FWI arise from the variable influence of the different parameter classes on the phase and amplitude of the data, and the trade-off between these. In this framework, choosing a suitable parametrization of the subsurface and designing the suitable FWI workflow are two key methodological issues in non-linear waveform inversion. We assess frequencydomain visco-acoustic FWI to reconstruct the compressive velocity (V P ), the density (ρ) or the impedance (I P ) and the quality factor (Q P ), from the hydrophone component, using a synthetic data set that is representative of the Valhall oil field in the North Sea. We first assess which of the (V P , ρ) and (V P , I P ) parametrizations provides the most reliable FWI results when dealing with wide-aperture data. Contrary to widely accepted ideas, we show that the (V P , ρ) parametrization allows a better reconstruction of both the V P , ρ and I P parameters, first because it favours the broad-band reconstruction of the dominant V P parameter, and secondly because the trade-off effects between velocity and density at short-to-intermediate scattering angles can be removed by multiplication, to build an impedance model. This allows for the matching of the reflection amplitudes, while the broad-band velocity model accurately describes the kinematic attributes of both the diving waves and reflections. Then, we assess different inversion strategies to recover the quality factor Q P , in addition to parameters V P and ρ. A difficulty related to attenuation estimation arises because, on the one hand the values of Q P are on average one order of magnitude smaller than those of V P and ρ, and on the other hands model perturbations relative to the starting models can be much higher for Q P than for V P and ρ during FWI. In this framework, we show that an empirical tuning of the FWI regularization, which is adapted to each parameter class, is a key issue to correctly account for the attenuation in the inversion. We promote a hierarchical approach where the dominant parameter V P is reconstructed first from the full data set (i.e. without any data preconditioning) to build a velocity model as kinematically accurate as possible before performing the joint update of the three parameter classes during a second step. This hierarchical imaging of compressive wave speed, density and attenuation is applied to a real wide-aperture ocean-bottom-cable data set from the Valhall oil field. Several geological features, such as accumulation of gas below barriers of claystone and soft quaternary sediment are interpreted in the FWI models of density and attenuation. The models of V P , ρ and Q P that have been developed by visco-acoustic FWI of the hydrophone data can be used as initial models to perform viscoelastic FWI of the geophone data for the joint update of the compressive and shear wave speeds.