We present an overview of the SEISCOPE project on frequency-domain full waveform inversion (FWI). The two main objectives are the reconstruction of multiple classes of parameters and the 3D acoustic and elastic FWI. The optimization relies on a reconditioned L-BFGS algorithm which provided scaled gradients of the misfit function for each classes of parameter. For onshore applications where body waves and surface waves are jointly inverted, P- and S-wave velocities (VP and VS) must be reconstructed simultaneously using a hierarchical inversion algorithm with two nested levels of data preconditioning with respect to frequency and arrival time. Simultaneous inversion of multiple frequencies rather than successive inversions of single frequencies significantly increases the S/N ratio of the models. For offshore applications where VS can have a minor footprint in the data, a hierarchical approach which first reconstructs VP in the acoustic approximation from the hydrophone component followed by the joint<br>reconstruction of VP and VS from the geophone components can be the approach of choice. Among all the possible minimization criteria, we found that the L1 norm provides the most robust and easy-to-tune criterion as expected for this norm. In particular, it allowed us to successfully reconstruct VP and VS on a realistic synthetic offshore case study, when white noise with outliers has been added to the data. The feasibility of 3D FWI is highly dependent on the efficiency of the seismic modelling. Frequency-domain modelling based on direct solver allows one to tackle small-scale problems involving few millions of unknowns at low frequencies. If the seismic modelling engine embeds expensive source-dependent tasks, source encoding can be used to mitigate the computational burden of multiple-source modelling. However, we have shown the sensitivity of the source encoding to noise in the framework of efficient frequency-domain FWI where a limited number of frequencies is inverted sequentially. Simultaneous<br>inversion of multiple frequencies is required to achieve an acceptable S/N ratio with a reasonable number of FWI iterations. Therefore, time-domain modelling for the estimation of harmonic components of the solution can be the approach of choice for 3D frequency-domain FWI because it allows one to extract an arbitrary number of frequencies at a minimum extra cost.


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