Multi-parameter waveform inversion in complex terrains Rene-Edouard Plessix Shell Over the past years, full waveform inversion became a standard tool to determine the shallow velocities from long offset seismic data. In order to fully incorporate this technique in an imaging workflow, multi-parameter inversion is often required. Most of the implementations rely then on an acoustic but anisotropic wave equation to model the compressional waves. This approach follows the standard paradigm of exploration geophysics with active seismic data that focuses on the interpretation of the recorded compressional waves only and assumes that the propagation is acoustic but the reflectivity is elastic. However, this paradigm more or less assumes that one can distinguish the different seismic events and split the seismic events between traveltimes, that can be treated acoustically, and the amplitudes, that often should be treated elastically. This more or less implies to work with the full frequency spectrum to have a good resolution in time (or to neglect the elastic effects). In full waveform inversion, to mitigate the oscillatory nature of the data misfit function, one relies on a frequency continuation approach. At low frequencies, the seismic events are tuned. This means that the phase of the seismic events may also depend on elastic effects in presence of large elastic parameter contrasts. This raises the limit of the acoustic assumption and challenges the inversion procedure. During this presentation, I shall discuss some of the aspects of the multi-parameter inversion, especially in presence of large elastic contrasts or viscous effects. Taking into account more parameters and more physics poses the question of the wave equation modelling efficiency and the inversion approach. I shall present some intermediate approaches and illustrate them with inversion results.