In this study, an innovative layer stripping approach for FWI specifically adapted to the physics of surface waves is investigated, to mitigate the cycle skipping problem. A combined high-to-low frequency filtering with gradually increasing offset ranges, are applied to observed and calculated data to update gradually deeper layers of the shear velocity model. Successful results for a synthetic data example are presented.

The aim of this study is to determine the advantages and limitations of different misfit functions for an application of Full Waveform Inversion (FWI) to surface waves. The difference-based L2 norm, classically used in FWI and sensitive to both amplitude and phase information, suffers from cycle-skipping and local minima. For slow surface waves propagating in the low velocity near surface, the problem of cycleskipping is even greater due to their small wavelengths. In the absence of low frequencies, convergence may not be possible when starting from a smooth initial mode. Alternative misfit functions applied in various data domains are therefore investigated with the aim of overcoming this issue. Taking the difference-based L2 norm as a basis for comparison, simple synthetic tests are conducted to evaluate a weighted cross-correlation and a singular value decomposition approach as alternative misfit functions, as well as investigating the effect of calculating the residual in different data domains such as the (omega-k), (tau-p) and (omega-p) domains.

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A key feature of FWI is the misfit function that considers the point-to-point difference between the observed data and the calculated data, to provide high-resolution imaging using a local optimization approach. However, in the case of slow surface waves propagating in the low velocity medium of the near surface, cycle-skipping can occur, and the optimization may be locked in a local minimum. More robust misfit functions have recently been proposed with the aim of mitigating this problem for surface waves, integrating recipes used for 1D surface wave analysis in FWI and moving to misfit functions in alternative domains. The aim of this study is to define the gradient expression of such misfit functions through a generic adjoint formalism and to present a simple synthetic example showing the more robust behavior of these approaches compared to the classical FWI approach.

We investigate the capacity of extracting near-surface shear-wave velocity by considering dispersive surface waves and non-dispersive reflected waves. We show that indeed the full waveform fitting of these waves requires a dedicated approach by using lateral spatial and frequential coherence for surface waves and by explicitely introduces the fitting of reflected waves in the inversion formulation. On a simple example as a two-layers model, lateral variations of the velocity are reconstructed while the lowwavenumber content of the velocity could be improved through reflection waves. Combining these two sources of information on the shear-wave velocity could improve our shear-wave velocity imaging in the near-surface context.