Based on an updated model of the regolith’s elastic properties, we simulate the ambient vibrations background wavefield recorded by InSight’s Seismic Experiment for Interior Structure (SEIS) on Mars to characterise the influence of the regolith and invert SEIS data for shallow subsurface structure. By approximately scaling the synthetics based on seismic signals of a terrestrial dust devil, we find that the high-frequency atmospheric background wavefield should be above the self-noise of SEIS’s SP sensors, even if the signals are not produced within 100–200 m of the station. We compare horizontal-to-vertical spectral ratios and Rayleigh wave ellipticity curves for a surface-wave based simulation on the one hand with synthetics explicitly considering body waves on the other hand and do not find any striking differences. Inverting the data, we find that the results are insensitive to assumptions on density. By contrast, assumptions on the velocity range in the upper-most layer have a strong influence on the results also at larger depth. Wrong assumptions can lead to results far from the true model in this case. Additional information on the general shape of the curve, i.e. single or dual peak, could help to mitigate this effect, even if it cannot directly be included into the inversion. We find that the ellipticity curves can provide stronger constraints on the minimum thickness and velocity of the second layer of the model than on the maximum values. We also consider the effect of instrumentation resonances caused by the lander flexible modes, solar panels, and the SEIS levelling system. Both the levelling system resonances and the lander flexible modes occur at significantly higher frequencies than the expected structural response, i.e. above 35 Hz and 20 Hz, respectively. While the lander and solar panel resonances might be too weak in amplitude to be recorded by SEIS, the levelling system resonances will show up clearly in horizontal spectra, the H/V and ellipticity curves. They are not removed by trying to extract only Rayleigh-wave dominated parts of the data. However, they can be distinguished from any subsurface response by their exceptionally low damping ratios of 1% or less as determined by random decrement analysis. The same applies to lander-generated signals observed in actual data from a Moon analogue experiment, so we expect this analysis will be useful in identifying instrumentation resonances in SEIS data.