The SEIS seismometer of the InSight mission was deployed on the ground of Elysium Planitia, on 19 December 2018. Interferometry techniques can be used to extract information on the internal structure from the autocorrelation of seismic ambient noise and coda of seismic events. In a single-station configuration, the zero-offset global reflection of the ground vertically below the seismometer can be approximated by the stacked ZZ autocorrelation function (ACF) for P-waves and the stacked EE and NN ACFs for S-waves, assuming a horizontally layered medium and homogeneously distributed and mutually uncorrelated noise sources. We analyze continuous records from the very broadband seismometer (SEIS-VBB), and correct for potential environmental disturbances through systematic preprocessing. For each Sol (martian day), we computed the correlations functions in 24 windows of one martian hour in order to obtain a total correlation tensor for various Mars local times. In addition, a similar algorithm is applied to the Marsquake waveforms in different frequency bands. Both stability analysis and inter-comparison between background noise and seismic event results suggest that the background seismic noise at the landing site is reliably observed only around 2.4 Hz, where an unknown mechanism is amplifying the ground shaking, and only during early night hours, when the noise induced by atmospheric disturbances is minimum. Seismic energy arrivals are consistently observed across the various data-sets. Some of these arrivals present multiples. These observations are discussed in terms of Mars’ crustal structure.