Temporal Variation and Frequency Dependence of Seismic Ambient Noise on Mars From Polarization Analysis

We applied a polarization analysis of InSight seismic data to estimate the temporal variation and frequency dependence of the Martian ambient noise field. Low‐frequency (<1 Hz) P waves show a diurnal variation in their dominant back azimuths that are apparently related to wind and the direction of sunlight in a distant area. Low‐frequency Rayleigh waves (0.25–1 Hz) show diurnal variations and a dominant back azimuth related to the wind direction in a nearby area. Low‐frequency signals that are derived mainly from wind may be sensitive to subsurface structure deeper than the lithological boundary derived from an autocorrelation analysis. On the other hand, dominant back azimuths of high‐frequency (>1 Hz) waves point toward the InSight lander, especially in daytime, indicating that wind‐induced lander noise is dominant at high frequencies. These results point to the presence of several ambient noise sources as well as geologic structure at the landing site.


Introduction
When the National Aeronautics and Space Administration's (NASA's) Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) lander touched down in Elysium Planitia on 26 November 2018, it went on to deploy a geophysical observatory on Mars. One of its primary scientific investigations is the Seismic Experiment for Interior Structure (SEIS; InSight Mars SEIS Data Service, 2019; Lognonné et al., 2019). The lander also includes a set of environmental sensors, including temperature and wind sensors (Banfield et al., 2019;Spiga et al., 2018). The InSight seismometer has detected several hundred marsquakes, most of them much smaller than earthquakes typically felt on Earth, but some were nearly as large as magnitude 4 (Witze, 2019). The instrument is especially useful to identify small earthquakes at night, when the strong ambient noise generated during the day by wind is subdued (Witze, 2019). Martian ambient noise detected by the seismometer on the Viking 2 lander has been correlated with wind speed (Anderson et al., 1977;Nakamura & Anderson, 1979). However, that seismometer did not obtain seismic signals directly because it was deployed on the lander and not on the surface (Knapmeyer-Endrun et al., 2017).
Analysis of seismic ambient noise is a technique widely used on Earth to image and monitor the subsurface (e.g., Nimiya et al., 2017;Nishida et al., 2008), and several studies have made similar use of ambient noise on the Moon (e.g., Larose et al., 2005;Tanimoto et al., 2008). If ambient noise can be used to image and monitor the interior structures of Mars, this technique will be a powerful tool because it does not require any natural marsquakes or expensive artificial seismic sources.
In this paper, we characterize the ambient noise on Mars relying on the recent data from the InSight seismometer. We applied a polarization analysis to the InSight seismic records (InSight Mars SEIS Data Service, 2019) to extract the dominant back azimuth and directional intensity of ambient noise (Takagi et al., 2018). Furthermore, by comparing the characteristics of Rayleigh waves with autocorrelation functions (i.e., reflectivity), we achieved insight into the relationship between lithology and the sensitive frequency of Rayleigh waves included in ambient noise. By demonstrating the feasibility of ambient noise methods on Mars, this study shows that future seismic network projects on Mars will contribute to not only modeling and monitoring of Mars's interior structure but also exploration for Martian resources (e.g., ice deposits).

Data Preparation
The SEIS instrument includes a long-period, very broad band seismometer (SEIS-VBB) with a sampling rate of 20 Hz and a natural frequency of 0.5 Hz (InSight Mars SEIS Data Service, 2019; Lognonné et al., 2019). This seismometer was placed in Elysium Planitia in particular to satisfy the constraints on landing safety and the instrument deployment requirements . In this study, we used continuous seismic records from SEIS-VBB between February and June 2019. We corrected the data for the instrumental response using ObsPy (Beyreuther et al., 2010). The SEIS-VBB is a triaxial seismometer in which the three mutually perpendicular pendulums are mounted obliquely. Therefore, our first step was to numerically rotate the axes of the seismometer and construct seismic records with vertical and horizontal components (see Text S1 in the supporting information).
We then converted the seismic data from Earth time (UTC; Coordinated Universal Time) to the Mars time domain (LMST: Local Mean Solar Time) by using the procedures of Allison (1997) and Allison and McEwen (2000). The power spectral density on Mars calculated from ambient noise shows that the noise on Mars is lower at most frequencies than that of the Earth noise model (see Figure S1 in the supporting information). The power spectral densities of the horizontal and vertical components from Sols 194 to 197 ( Figure 1) are an example of the typical daily cycle, in which signal amplitudes are greater during the day than during the night. On Mars, high variability of wind in daytime is caused by convective mixing in the planetary boundary layer that results from near-surface gradients of atmospheric temperature (e.g., Smith et al., 2006;Spiga et al., 2018). At frequencies higher than~1 Hz, we observed large noise amplitudes in narrow frequency ranges. These local noise peaks correspond to the elastic resonances of the lander excited by the wind (Lognonné et al., 2020;Murdoch et al., 2017). These results demonstrate that the amplitude of ambient noise is strongly associated with the wind strength.
We divided continuous seismic data into 1-min segments because short time windows are suitable to remove glitches and other high-amplitude signals (Takagi et al., 2018). We excluded time segments whose rootmean-square (RMS) amplitudes exceeded 10 times the median RMS amplitude, treating daytime hours (from 6:00 to 18:00 LMST) and nighttime hours (from 18:00 to 6:00 LMST) separately because the surface wind velocity was high during the daytime at the InSight landing site (Figure 1) as anticipated by Spiga et al. (2018).

Polarization Analysis
We conducted a polarization analysis of the ambient seismic wave field recorded by the InSight station using the method developed by Takagi et al. (2018). This analysis uses a simple relationship between the vertical-horizontal cross spectra and the azimuthal energy distributions of incident waves in ambient noise. The real part of the cross spectra is related to linearly polarized waves, and the imaginary part is related to elliptically polarized waves. We computed vertical-horizontal cross spectra from 1-min segments data using the equations where Φ is the vertical-horizontal cross spectrum, u is the seismic record in the frequency domain of each component, and the subscripts Z, N, and E indicate vertical, north-south and east-west component, respectively. The asterisk indicates the complex conjugate. The cross spectra are normalized by the power spectra of the vertical component so as to equally weight each data segment. In this study, the cross spectra were calculated at each frequency and the results were averaged within each of six single-octave frequency bands: 0.125-0.25, 0.25-0.5, 0.5-1, 1-2, 2-4, and 4-8 Hz.
Following Takagi et al. (2018), the dominant direction and directional intensity of a Rayleigh wave (elliptically polarized wave) are given by and for a P wave (linearly polarized wave) by where ⟨⟩ denotes the ensemble average and φ R1 and φ P1 represent the phase angles of first-order terms of the azimuthal power spectra added to π, which provide the dominant back azimuths of Rayleigh waves and P waves, respectively. A R1 and A P1 indicate the amplitudes of the first-order terms representing the intensity of the directionality of the Rayleigh wave and P wave, respectively.
In the determination of Rayleigh wave azimuth, there is a 180°ambiguity depending on the direction of motions (prograde or retrograde). To evaluate the motion of Rayleigh waves on Mars, we computed analytical solutions of Rayleigh waves for the layered model of Knapmeyer-Endrun et al. (2017) of the InSight landing site (see Text S2 and Figure S2 in the supporting information). The results indicate that the fundamental mode of Rayleigh waves with retrograde motions is mostly dominant in our analyzed frequency range, whereas the first higher mode with prograde motions is dominant at some frequencies higher than 4 Hz. We therefore defined the azimuth of Rayleigh waves assuming retrograde motions, although the first higher mode with prograde motions might influence our results at frequencies higher than 4 Hz. Note that the azimuth of prograde or retrograde Rayleigh waves depends on the sign of the exponent in the Fourier transform. We used Equation 3 to estimate the back azimuth of retrograde Rayleigh waves because our analysis used the Fourier transform with a negative exponent. Shear waves with displacement in the vertical-horizontal plane (SV waves) also contribute to vertical-horizontal cross spectra (Takagi et al., 2018). Vertically incident SV waves contribute to the real part of the vertical-horizontal cross spectra, whereas horizontally incident SV waves with postcritical incident angles contribute to the imaginary part. For simplicity, we assumed that the contribution of P waves is dominant in the real part of the cross spectra and the contribution of Rayleigh waves is dominant in the imaginary part. Under the assumption that Rayleigh and Love waves are random uncorrelated waves, Love waves make no contribution to vertical and horizontal cross spectra (Takagi et al., 2018).

Autocorrelation Analysis
To estimate the geological structure beneath the InSight landing site, we applied autocorrelation analysis to the vertical and horizontal motions of the seismometer record. Autocorrelation of ambient noise records yields the zero-offset shot gather (e.g., Minato et al., 2012;Wapenaar & Fokkema, 2006). The method assumes that the noise source is randomly distributed and mutually uncorrelated for different source positions (e.g., Roux et al., 2005;Wapenaar & Fokkema, 2006;Weaver & Lobkis, 2004). In this analysis, we applied a band-pass filter of 5-7 Hz to each component record of 1-min segments, because we found clear reflectors of autocorrelation function in that frequency band. Furthermore, we sought to find and integrate information independent of the polarization analysis for the investigation of the lander site. We applied 1-bit normalization (e.g., Bensen et al., 2007) to ensure the exclusion of energetic signals. We calculated autocorrelation functions of the vertical component and the horizontal components in each sol to extract P and S wave reflections, respectively. Even if the lander near the seismometer generates vibration and becomes a noise source, the autocorrelation analysis with 1-bit normalization reduces the influence of the source but enhances the contribution of reflected waves from the source. Thus, we expect that autocorrelation analysis is suitable for subsurface imaging. the day (Figure 3a). The back azimuths at the lowest frequencies pointed southeast in daytime, roughly consistent with the wind direction. At night, the back azimuths of 0.25-1 Hz P waves usually pointed east, except just after sunset; more precisely, they differed notably from the wind direction at night, pointing east several hours before sunrise and pointing west to north after sunset. For 0.25-1 Hz Rayleigh waves (Figure 3b), the back azimuth pointed southwest before sunrise, south or southeast during the day, and southwest at night, similar to the wind direction.

Results
At high frequencies (>1 Hz), the dominant back azimuths of P waves (Figure 3a) pointed northeast in daytime, as did the back azimuths of high frequency Rayleigh waves (>2 Hz). As we discuss later, the Insight lander is located northeast of the seismometer.   (Figure 4a) indicates the presence of reflectors at 0.6 and 1.1 s. Because these reflectors persisted throughout the observation period, they appear to be reliable and may represent a lithological boundary that imposes a contrast in acoustic impedance. The autocorrelation functions of the two horizontal components (Figures 4b and 4c) display dominant reflectors at 1.1 s. They show evidence of polarization anisotropy of S waves, in that the reflector at~1.1 s is more prominent in the EW component (Figure 4c) than in the NS component (Figure 4b).

Discussion
The temporal variation of the dominant back azimuth of <1 Hz P waves could be related to the direction of sunlight (or related thermal effects) in addition to the wind direction when noise derived from the lander is

10.1029/2020GL087123
Geophysical Research Letters absent. During the several hours before sunrise, the area east of the lander site is in daylight and the wind speed is high; thus, the dominant P wave back azimuth could point east before sunrise (Figure 3a). This interpretation would also explain the westward P wave back azimuth after sunset, although the back azimuths are scattered from west to north. These results demonstrate that low-frequency P waves observed at the InSight site may be derived from wind and insolation effects (e.g., thermal cracking) in distant areas. Indeed, P waves on Earth are strongly influenced by distant events (Takagi et al., 2018). Seismic sources induced by temperature variation are capable of generating low-frequency ambient noise.
Because the variation of the directionality of 0.25-to 1-Hz Rayleigh waves was closely related to the wind direction (Figure 3b), low-frequency Rayleigh waves were likely derived from winds relatively close to the seismometer. The back azimuth of Rayleigh waves could be influenced by the radiation pattern of Rayleigh waves. Assuming that horizontal single forces exerted in the wind directions on rough surface topography excited seismic waves including Rayleigh waves, a symmetric radiation pattern (i.e., with 180°ambiguity) could be expected in the back azimuths ( Figure 3b). Although stacking the cross spectra for each hour improves the stability of estimated dominant back azimuths (Figure 3b), using shorter time windows could make it possible to extract secondary dominant back azimuths. To investigate this possibility, we computed the back azimuth from every 1-min segment ( Figure S3 in supporting information). The results of this exercise show that directionalities of 0.125-to 1-Hz Rayleigh waves have two trends 180°apart during certain periods; thus, the radiation pattern of Rayleigh waves could influence the observed back azimuth. Rayleigh waves in the 0.25-to 1-Hz range would be sensitive to the depth range of 0.8-3.2 km, if we assume a Rayleigh wave velocity of 2,400 m/s (Knapmeyer-Endrun et al., 2017). Therefore, the wind may be responsible for 0.25-to 1-Hz Rayleigh waves that are sensitive to the crustal structure beneath the shallow regolith layer.
At high frequencies, the back azimuths of P waves >1 Hz and Rayleigh waves >2 Hz are northeast in daytime. The direction is consistent with the location of the InSight lander (Figure 3), which generates mechanical noise as wind acts on the lander (Lognonné et al., 2020;Murdoch et al., 2017). If wind-induced lander noise is dominant at high frequencies, it would be difficult to observe high-frequency Rayleigh waves with the seismometer because the distance between the lander and the seismometer is too short (several meters) for surface waves to emerge. Therefore, instead of referring to "P and Rayleigh waves" in high-frequency (>1 Hz) results, it is preferable to refer to "linearly and elliptically polarized components of observed waves" as we have in Figures 2 and 3. These frequency-dependent variations of ambient noise characteristics could be mainly related to ambient noise sources and lithology beneath the seismometer. Ambient noise on Earth is caused by wind (Lepore et al., 2016) as well as ocean gravity waves, volcanic activity, and anthropogenic sources (e.g., Longuet-Higgins, 1950;Nakata et al., 2019;Nimiya et al., 2017;Takagi et al., 2018). Before the InSight project, a main source of ambient noise on Mars was expected to be the direct interaction between the atmosphere and the solid surface of the planet (Knapmeyer-Endrun et al., 2017). On the Moon, high-frequency Rayleigh waves are induced by ambient noise resulting from thermal events (Larose et al., 2005;Tanimoto et al., 2008). On Mars, there are numerous small craters near the InSight landing site (Warner et al., 2016) that could be locations of thermally triggered soil slumping (Knapmeyer-Endrun et al., 2017) that could generate high-frequency surface waves. Thus, wind-induced noises, thermal effects, surface pressure, or other sources may induce the ambient noise around the InSight landing area.
To further consider the relationship between the frequency dependence of Rayleigh waves (Figure 3b) and the lithology of the site, we investigated the autocorrelation results (Figure 4), in which several reflectors beneath the InSight landing site are evident. The P wave reflectors at 0.6 and 1.1 s in the vertical component ( Figure 4a) are stable, suggesting the existence of a significant lithological boundary. Furthermore, an S wave reflector appeared at 1.1 s in the horizontal component results (Figures 4b and 4c). If the 1.1-s S wave reflector is the same as the 0.6-s P wave reflector, we can estimate the ratio of~1.83 between the P wave and S wave velocities. Because we cannot estimate the seismic velocity of the subsurface formation, we cannot accurately estimate the depth of the reflectors from the autocorrelation functions. However, we can estimate the frequency of Rayleigh waves that are sensitive to the depth of a reflector from the autocorrelation function. Under the assumption that the autocorrelation function of the horizontal component represents S wave reflectivity, the depth of a reflector at two-way travel time t can be estimated as Z = t V S /2, where V S is S wave velocity. The sensitive depth of Rayleigh waves is Z = 1/3 λ (or Z = V S /3f) (e.g., Foti et al., 2014;Hayashi, 2008), where λ is wavelength and f is frequency. Therefore, the sensitive frequency of a Rayleigh wave for a reflector at two-way travel time t can be estimated as f = 2/(3 t). From this relationship, the frequency of a Rayleigh wave that is sensitive to a 1.1-s reflector shown in Figures 4b and 4c can be estimated as 0.6 Hz. Below 0.6 Hz, the azimuths of Rayleigh waves are associated with wind direction. Therefore, Rayleigh waves that are sensitive to depths beneath the lithological boundary identified by reflectivity could be extracted from wind-induced ambient noise. However, it would be difficult to extract Rayleigh waves propagating above the lithological boundary close to the landing site, because they are contaminated by lander-induced noise.

Conclusions
We have conducted a polarization analysis of InSight seismic data to estimate temporal variations of the ambient noise field on Mars. Our findings are the following: 1. Low-frequency (<1 Hz) P waves show a diurnal variation, and the dominant back azimuth is related to the wind and the direction of sunlight in distant regions. 2. Low-frequency (0.25-1 Hz) Rayleigh waves show a diurnal variation, and the dominant back azimuth points toward the wind direction in nearby regions. 3. The dominant back azimuth at high-frequency (>1 Hz for linearly polarized components and >2 Hz for elliptically polarized components) points in the direction of the lander, indicating that the wind-induced lander noise is dominant.
These results suggest that the dominant sources of ambient noise on Mars differ with frequency and wave type, and there may be several different ambient noise sources despite the absence of oceans on Mars. The high repeatability of P waves and Rayleigh waves derived from ambient noise suggests the feasibility of utilizing ambient noise for subsurface imaging and monitoring on Mars. Further studies are necessary to clarify the contribution of SV waves in ambient noise on Mars, which influences the results of our polarization analysis.