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This study investigates how different parameter combinations affect the outcome of 2D elastic full-waveform inversion (FWI) of shallow Rayleigh waves, recorded at a gravel site intended for geothermal exploration. Rayleigh waves are particularly sensitive to shear wave velocity (Vs), with decreasing sensitivity to density (ρ) and P-wave velocity (Vp). We tested several inversion setups using Vs alone and in combination with ρ and Vp to understand how each impacts model resolution and data fit. The FWI method uses a multiscale, adjoint-based approach to reduce errors, with added corrections for source wavelets and attenuation. The results confirm Vs as the most important parameter, with density models offering similar resolution. Vp models, however, remain unreliable due to weak sensitivity and poor signal quality, though no parameter crosstalk was observed. Overall, the study supports using Vs and ρ together for robust near-surface imaging with Rayleigh waves.