A guided tour of multi-parameter full waveform inversion with multi-component data: from theory to practice
Résumé
Building high-resolution models of several physical properties of the subsurface by multi-parameter full waveform inversion (FWI) of multi-component data is one of the challenge of seismic imaging for the next decade. The physical properties, which govern propagation of seismic waves in visco-elastic media, are the P and S wavespeeds, density, attenuation and anisotropic parameters. Updating each of these properties is challenging because several parameters of 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 cross-talk between parameters. Moreover, different parameter classes can have different order 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 multi-parameter 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 over-parameterization of the optimization problem. The purpose of this tutorial is to provide a comprehensive overview of the promise, pitfalls and open questions underlying multi-parameter FWI. We first review the main FWI ingredient that controls the trade-off 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 multi-parameter 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 multi-component marine data, which has been inspired by a real data case study from Valhall.