Statistical and energetic characteristic of High Frequency (HF) and Very High Frequency (VHF) Martian events

The InSight seismometer SEIS recorded tens of High-Frequency (1.5-5Hz) and Very-High Frequency (1.5-15Hz) Martian events. They are characterized by two temporally separated arrivals with a gradual beginning, a broad maximum and a very long decay. This observation suggests that they are generated by the long-range propagation of seismic P and S waves in a heterogeneous crust (Van Driel et al., submitted). We employ basic multiple-scattering concepts to examine this hypothesis. We find that both HF and VHF signals are depolarized and verify Gaussian statistics, at the exception of the ballistic primary and secondary arrivals. These properties agree with a multiple-scattering origin. The energy partitioning ratio V²/H² between horizontal and vertical components is frequency dependent for VHF events. V²/H² is maximum at the 2.4Hz resonance, it decreases rapidly at frequencies higher than 5Hz and remains low up to frequencies of 15Hz. HF events do not exhibit a decrease of V²/H² at high frequencies but we observe a strong correlation between V²/H² and signal-to-noise (S/N) ratio for HF events. This observation suggests that, besides the unequal spectral shapes between HF and VHF events, a part of the difference between them can be explained by noise contamination. The low V²/H² ratio of VHF events is reminiscent of the response of unconsolidated layers, as observed at Pinyon Flats Observatory on Earth. Unlike earthquakes and moonquakes observed in the same frequency band, the delay time measured from onset to peak of the secondary arrival of HF and VHF events is independent of frequency. This suggests that the spectrum of heterogeneity of the Martian crust is smooth. We observe that the delay time is weakly dependent on hypocentral distance for HF and VHF events. This cannot be reconciled with the predictions of multiple-scattering theories in a statistically homogeneous medium but it suggests a stratification of heterogeneity in the Martian lithosphere. The coda quality factor Q_c of VHF events is high and shows a linear increase with frequency. Q_c of HF events is higher but it may be overestimated due to the noise contamination. The linear frequency dependence of Q_c is strongly reminiscent of the leakage effect in a crustal scattering waveguide and suggests that part of the observed coda attenuation may be of structural origin.