Observation 20-s periodic signals on Mars from InSight, Sols 800−1,000

1.   Introduction

The InSight mission has been working for more than three years since the probe’s successful landing at the Elysium Planitia of Mars in November 2018 (Banfield et al., 2019; Banerdt et al., 2020; Lognonné et al., 2019, 2020). Its seismic package, SEIS, has recorded seismic signals continuously since February 2019. SEIS is equipped with both very broad band (VBB) instruments and short period (SP) instruments to measure ground motion. The former are sensitive to frequencies from 0.01 to 10 Hz; the latter are more reliable at the higher frequency range of 5–50 Hz (Lognonné et al., 2019, 2020). By November 2022, more than one thousand marsquakes had been recorded (Ceylan et al., 2022; InSight Marsquake Service, 2022), classified by frequency range as “low”, “high”, and “other” (super high frequency events). High quality marsquakes as well as seismic noise have been used to study the interior structure of Mars with different seismic techniques (Khan et al., 2016; Compair et al., 2021; Deng SZ and Levander, 2020; Lognonné et al., 2020; Joshi et al., 2021; Knapmeyer-Endrun et al., 2021; Stähler et al., 2021; Schimmel et al., 2021; Huang QC et al., 2022; Deng SZ and Levander, 2022; Garcia et al., 2022; Li C et al., 2022; Panning et al., 2023). However, the low signal-to-noise ratios of the data restrain further usage of the seismic data collected by InSight.

Among different type of noise detected by the InSight lander, periodic noises are generated by wind and pressure fluctuations (“natural” modes) and their coupling to the InSight lander (“lander modes”) (Ceylan et al., 2021; Lognonné et al., 2020). Several main distinct high frequency modes at 1 Hz and above have been identified (Ceylan et al., 2021). First, “donks”, displayed as short-duration pulses, are typically observed on all three components simultaneously at frequencies higher than ~12 Hz; these are regarded as transient energy correlated with stress released from temperature cycling on the lander. Second, modes at 4 Hz and above, whose strengths are positively related to the intensity of winds at the lander site, are thought to be natural frequencies of the lander or its tether system. The third mode is at 2.4 Hz, which is an important natural ambient resonance. This vertically polarized signal appears to originate from the subsurface beneath the lander (Hobiger et al., 2021). Fourth, the 1 Hz mode, also named the tick-noise, is an electrical disturbance (cross-talk) produced by the synchronized acquisitions of the temperature and seismic channels at a sample rate of 1 sp/s inside SEIS (Compaire et al., 2021). The tick noise peaks in the frequency domain at 1 Hz but also exhibits a nonnegligible amplitude at each harmonic (2 Hz, 3 Hz, etc.).

In addition to these noise modes at high frequencies, “glitch”, with spectrum covering a broadband range from the lowest frequencies up to above 1 Hz, is frequently observed on both VBB and SP channels. It has been shown that glitch is a particular type of transient instrumental self-noise with a duration of ~25–30 s (Scholz et al., 2020; Ceylan, 2021). Strong noise contamination at lower frequencies has made it challenging to detect reliable signals of marsquakes and periodic noises at periods longer than 10 s. Nevertheless, if such longer-period seismic signals, generated by either environment changes or marsquakes, can be identified, such data can help us understand better both the background noise on Mars and the Martian deep interior.

In this paper, we report the first observation of a low frequency periodic signal with a dominant period at ~20 s. This signal occurs at the local quiet time from Martian solar days (Sol; 1 Sol = 88,775 s) 800 to Sol 1,000. By analyzing the time-varying characteristics of this signal, we provide hypotheses on the origin of this long-period signal.

2.   Observation of the 20-s Signal

Figure 1 shows an example of the raw VBB UVW components. records from 20:00 Local Mean Solar Time at the InSight landing site (LMST) of Sol 888 to 06:00 LMST of Sol 889 and their spectrograms from 200 s to 10 Hz. To minimize the strong effects of the “glitch” on the spectrogram, we apply the deglitch algorithm MPS (Scholz et al., 2020) to detect and remove from the raw seismic data the obvious large-amplitude glitches. In Figure 1, besides the high frequency modes, we can clearly see a strong energy peak at a period of ~20 s (referred to as “20-s signal” hereafter) on all three components, lasting for about three hours. On the low-pass (<1Hz) seismograms, we can easily identify this periodic signal, which emerges quite abruptly on Sol 888 at 22:38 LMST. The energy of this signal gets weaker gradually until it disappears around 02:45 LMST on Sol 889. Two other energy peaks, at around 7 s and 10 s, most noticeable on the BHV component, are synchronized with the 20-s signal. Ceylan et al. (2022) also identify this long period signal but no details are discussed. It is also interesting to note in Figure 1 that the high-frequency modes get stronger during this period and last much later.

Figure  1.  Three components of VBB acceleration data from 20:00 LMST of Sol 888 to 06:00 LMST of Sol 889 and their spectrogram and power spectral density (PSD). The continuous data have a sample rate of 20 sp/s. The raw data are preprocessed using the MPS algorithm (Scholz et al., 2020) to detect and remove most glitches. (a) BHU channel. The blue and red solid lines in the upper plane present the low- and high-frequency filtered seismic waveform at 1 Hz. In the right panel, the indigo line is the 50th percentile of the PSD, the gray dashed lines show the 95th percentile and 5th percentile of the PSD, and the indigo dotted lines are the 99th percentile or the 1st percentile of the PSD. The energy spikes in the low-frequency PSD are the residual glitches. For the time label, UTC is Universal Coordinated Time, and LMST is the Local Mean Solar Time at the InSight landing site. (b) and (c) are the same as (a) but for BHV and BHW channels, respectively.

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To better analyze these long period signals, we rotate the UVW seismograms into North-East-Vertical (N-E-Z) components as shown in Figure 2. In the inset of Figure 2b, we further select the time window with the strong periodic signals and plot the corresponding power spectral density (PSD). The 20-s signal is strong on the two horizontal components, of which the N component has the stronger energy. In contrast, the vertical component of the 20-s signal can barely be detected (Figure 2c). We also notice that the dominant frequency of this 20-s signal is not constant but varies with time by approximately 0.05 Hz. The other two periodic signals at ~6.5 s (0.15 Hz) and 10 s (0.10 Hz) are apparent only on the N component; their amplitudes are comparatively much smaller. These two periodic signals synchronize with the 20-s signal in both time and amplitude (Figure 1), which indicates that these long-period overtones may be induced by the same source. Thus, in the later analysis, we focus mainly on the 20-s signal.

Figure  2.  Spectrogram and Power Spectral Density (PSD) for components of (a) BHE, (b) BHN, and (c) BHZ. The inset in (b) shows the PSD of data from 22:30 LMST of Sol 888 to 00:30 LMST of Sol 889, outlined by the yellow box.

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To capture the temporal variation of the dominant frequency of the 20-s signal, we divide the continuous seismic data into 30-minutes segments and calculate their PSD. Figure 3 displays examples of the PSD of NEZ components for each 30-minutes segments from 22:00 LMST to 04:00 LMST on Sol 888, Sol 889, and Sol 935, respectively. The dominant frequency of the strong periodic signal on the two horizontal components varies, but concentrates in a range of 0.04–0.06 Hz. In addition, this signal is visible only at certain nighttime periods and its vertical component is usually so weak as to be undetectible. In Figure 4, we plot the ten-day normalized amplitude spectrum on the BHN component for the time periods 22:00 LMST to 04:00 LMST of two continuous periods of 10 Sol days: Sols 880−890, and Sols 930−940. The dominant frequency of the periodic signal fluctuates around 0.05 Hz; the occurrence time of this signal also varies from day to day — most of the strong 20-s signals appear around midnight during the Sol 880 to Sol 890 period, but extend into the early morning hours from Sol 930 to Sol 940. By examining all the VBB seismic data available up to Sol 1200, we find that for 200 Sols, from Sol 800 to Sol 1,000, this 20-s signal occurred primarily during the local quiet time from 22:00 LMST to 04:00 LMST.

Figure  3.  Representative PSDs for NEZ components for every 30 minutes from 22:00 LMST to 04:00 LMST of three continuous Sols. (a) PSDs from 22:00 LMST of Sol 888 to 04:00 LMST of Sol 889. Each color line represents the PSD computed from the half-hour data with the start time indicated in the legend. The gray band shows our focusing frequency band of 0.04–0.06 Hz. (b) is from 22:00 LMST of Sol 889 to 04:00 LMST of Sol 890; (c) is from 22:00 LMST of Sol 935 to 04:00 LMST of Sol 936.

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Figure  4.  Diurnal variations of the normalized amplitude spectrum of the BHN component for the time period of 22:00 LMST–04:00 LMST in ten Sols. The spectrum is calculated for every 30-minutes data segment. (a) and (b) show the results for Sols 880−890 and for Sols 930−940, respectively. The colorbars show the normalized amplitude spectrum.

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2.1   Polarization of the 20-s Signal

Determining the polarization of the periodic signal helps us to better understand its origin. We filter the deglitched waveforms to a frequency band of 0.02–0.1 Hz, cut the data showing the 20-s signal into 300 s segments, and then plot corresponding particle motions on N-E and N-Z components. Figure 5 shows that the particle motion is mainly in the horizontal plane and is mostly rectilinear along the Northeast–Southwest (NE–SW) direction (Figure 5). By linear fitting the particle motion data of each time window of 300 s, we obtain the polarization angle (azimuth from the north) in the horizontal plane.

Figure  5.  Three-component velocity seismograms and their particle motions. In (a), (d), and (g), the data are filtered in the frequency range of 0.02–0.10 Hz and their particle motions are plotted in blue lines for the horizontal plane (b, e, h) and the north-vertical plane (c, f, i). The red dashed line in the horizontal particle motion hodogram is the fitted line (via the Least Squares Linear Regression method); the corresponding parameters are annotated at the lower right corner, including the polarization angle defined as azimuth from the north, ${R}^{2}$ value (R-value), and standard deviation value (std).

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Figure 5 presents three typical results of fitting the particle motion. Figures 5a–c show an example with the periodic signal clearly observed on both N and E components; the result is an excellent fit of the particle motion with an R-value of 0.82 and a polarization angle of ~27.5°. Figures 5d–f show another typical result, in which the 20-s signal is less obvious on the E component; in this case the R-value is low, the derived polarization angle is ~32°. Figures 5g–i show a third example with R-value high — close to 1. For this case, the data are dominated by the large amplitude signal of a residual “glitch”, although the deglitching process has been applied. Figure 4, too, illustrates the influence of glitches — strong energy appears across the whole frequency range and greatly affects our ability to detect the targeted periodic signal. To reduce the influence of a too large window length on polarization angle fitting and error estimation (e.g., Figure S1), we calculate the fitting angle and error by using a 40 s moving time window within the large time window of 300 s, and taking the weighted average of these shorter windows as the final polarization angle, as shown in Figure S2. As expected, the polarization angles are almost the same but the errors get larger.

2.2   Temporal Variation of the 20-s Signal

In order to minimize the influence of residual “glitches” on the measurement of the polarization angle, and obtain a precise occurring time of the periodic signal, we adopt a simple matched-filter method to detect the 20-s signal (Sun WJ et al., 2019; 2022). Since the strongest energy of the 20-s signal is observed in the N-component, we perform its detection only on this component. Considering the fluctuation of the main frequency of the periodic signal (Figure 3), we select three good quality waveforms with a length of 300 s and representative periods at 18, 20, and 22 s, respectively, as the templates (Figure 6). Then we cross-correlate the three templates separately through the continuous waveform data in a moving window of 300 s. Here, both templates and continuous data are bandpass-filtered to 10–50 s. Figure 6a shows the three templates; Figure 6b shows three detection examples with different templates, all of which have normalized Cross-correlation Coefficients (CC) larger than 0.7.

Figure  6.  Examples of detecting the 20-s signal. (a) N-component velocity seismogram of three selected templates filtered in the frequency range 0.02–0.1 Hz. From top to bottom, the dominant periods of the selected templates are 20, 18, and 22 s, respectively. (b) Three examples of the periodic signals newly detected through the matched-filter method with the templates in (a). The normalized cross-correlation values between the templates and detected waveforms are annotated in the upper right.

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Here, we set the threshold of the CC to 0.55 for a valid detection of the 20-s signal. If this value is too high, many target signals will be missed; if the value is too low, aperiodic signals will be detected (Figure S3). As shown in Figures 7a–c, the 20-s template gives the most detections, suggesting that 20 s is the dominant period. Then we merge the detections using different templates (Figure S4 gives a merge example), and confirm that most of the 20-s periodic signals occur at quiet night — from 22:00 LMST to 04:00 LMST (Figure 7d). Furthermore, before Sol 900, most signals occur between 22:00 LMST and 01:00 LMST, while after Sol 900, most signals occur between 01:00 LMST and 04:00 LMST.

Figure  7.  Detected periodic signals during Sol 800 to Sol 1,000. Different color denotes the different CC. (a), (b), and (c) show the detections with different templates (Figure 6a) having dominant periods of 20, 18, and 22 s, respectively. (d) shows the merged detections in (a)–(c).

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Figure  8.  Temporal variation of the 20-s signal. (a) the polarization angle in the horizontal plane and (b) amplitude of the detected periodic signals in Figure 7d. The color of the dot denotes the R-value of the linear fitting of the particle motion as displayed in Figure 5. The gray band outlines the 20-s signals with high R-value (red color). The 20-s signal located in the yellow band has a relatively low R-value. The yellow line shows the mean SCIT-A (scientific temperature A) inside the Remote Warm Enclosure Box (RWEB) but outside the Evacuated Container of VBB, from 20:00 LMST to 22:00 LMST; the green line shows the mean SCIT-A at a later time, 22:00 LMST to 04:00 LMST. The symbols in (b) – “circle”, “x”, “plus” – are for Z, N, and E components, respectively.

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We then calculate polarization angles of the merged periodic signals (Figure 7d) and plot the results with R-values larger than 0.5 in Figure 8a, which shows that horizontal polarization angles vary between 24° and 46°. Those with higher R-values concentrate around 30°. It appears that the polarization angles decrease before Sol 900 but slightly increase after Sol 910. Such a variation seems to be related to the change of atmospheric temperature, which may indicate that the polarization angle change of the 20-s signal is temperature-dependent. We also use Principal Component Analysis and a moving short time window (same as Figure S1) to compute the horizontal polarization angles of the detected periodic signals, both of which show similar variation trend of the angles (Figures S5–S6). Besides, we examine the amplitudes of the detected 20-s signals (Figure 8b), defined as the root mean squares (RMS) of their velocity seismograms. We note that the periodic signals have much larger amplitudes on the N-component and that the amplitudes increase before Sol 900 but decrease after Sol 915. To examine the effects of different band-pass filtering widths on the matched-filtering result, we filter the data into a different frequency band, 0.025–0.2 Hz (Figures S7–S8), and repeat the above process, which produces results similar to those with the frequency of 0.02–0.1 Hz.

3.   Possible Origins of the 20-s Signal

3.1   Activities of the Instrument

Many high-frequency noise modes in the SEIS data are related to the operational activities performed by the lander’s robotic arm, or to artifacts caused by responses of the sensors to the severe Martian environment (Ceylan et al., 2021). Some of these non-seismic events are visible on the VBB and SP channels simultaneously (Ceylan et al., 2021). To investigate the possibility that the VBB instrument itself might produce this periodic signal, we check whether it appears also in data recorded by the SP instrument; we do this by calculating the amplitude spectral densities (ASD) of both the VBB and the SP data. As displayed in Figure 9a, the SP data also show a strong periodic signal at ~0.05 Hz, especially on the N-component. The very high coherence value of the N-components of the 20-s signal between VBB and SP (Figure 9b) suggests that both instruments respond to it simultaneously. Moreover, considering that the dominant frequency of this signal is quite low and varies with time, this 20-s signal is different from known lander modes, such as tick-noise, and is thus unlikely to be caused by the instrument itself. In addition, the inconsistency between the sensitivity directions of three-component seismometers (Lognonné et al., 2019; Scholz et al., 2020) and the horizontal polarization angle of the 20-s signal (~30°) also indicates that the long period periodic signals observed here are not related to the internal activities of the instrument.

Figure  9.  Computed amplitude spectrum density (ASD) and coherence among different data on the InSight. The start- and end- time of all data types are from 22:00 LMST to 24:00 LMST of Sol 888. (a) ASD on three components of VBB and SP data. Red, blue, and gray lines are for the N, E, and Z components, respectively. Solid lines are VBB data and dashed lines are SP data. (b) Coherence between the VBB and SP data. (c) Raw pressure (red line) and detrended pressure data (blue line). The detrended pressure is obtained by subtracting the 100 s-window-averaged pressure from the 0.5 s-window-averaged pressure to obtain local turbulence (Chatain et al., 2021). (d) Coherence between the VBB data and the detrended pressure data. (e) Horizontal wind speed (blue dot) and wind direction (red dot) recorded by TWINS (Temperature and Wind for InSight) pointing in the −Y lander axis direction (BMY). The gray line is the N-component velocity seismogram filtered in the frequency range 0.02–0.1 Hz. (f) Coherence between the VBB data and the horizontal wind speed (hws) data. (g) Raw temperature data recorded by TWINS. Blue and orange lines are for sensor pointing in the −Y lander axis direction (BMY) and pointing in the +Y lander axis direction (BPY). Green line is SCIT-A, same as Figure 8a. (h) Coherence between the VBB data and temperature recorded as BMY.

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3.2   Atmospheric Effect

The primary sources of noise in data collected on the Martian surface are wind and pressure (Mimoun et al., 2017; Lognonné et al., 2020; Scholz et al., 2020; Clinton et al., 2021; Stutzmann et al., 2021; Ceylan et al., 2021). Atmospheric pressure and temperature variations can induce ground tilting and displacements through elastic deformations. A small tilt angle $\theta$ produces a first-order effect for the horizontal components (~$\mathrm{s}\mathrm{i}\mathrm{n}\left(\theta \right)\approx \theta$) but only a second-order effect for the vertical component (~$[1- \mathrm{c}\mathrm{o}\mathrm{s}\left(\theta \right)]\approx {\theta }^{2}/2$), which provides a candidate explanation for our observation of the 20-s signal mainly on the horizontal components. Thus, we investigate such a possibility — that of air pressure-induced deformation — by measuring the tilt angle $\theta$, which is defined as

where ${\mathrm{A}\mathrm{C}\mathrm{C}}_{N}$ and ${\mathrm{A}\mathrm{C}\mathrm{C}}_{E}$ are amplitudes of the recorded ground acceleration of N and E components, respectively. ${g}_{\mathrm{M}\mathrm{a}\mathrm{r}\mathrm{s}}$ (≈3.71 $\mathrm{m}/{\mathrm{s}}^{2}$) is the gravitational acceleration on the surface of Mars. For the identified 20-s signals in Figure 7, the calculated tilt angle $\theta$ varies between $\left(1 - 5\right)\times {10}^{-8}$ degree and the corresponding vertical acceleration increment due to tilting is ~${10}^{-18}\;\mathrm{m}/{\mathrm{s}}^{2}$, which is much smaller than the recorded noise level of ${10}^{-9}\;\mathrm{m}/{\mathrm{s}}^{2}$. Thus, the signal on the vertical component can be very weak and difficult to separate from the noise.

We further examine the relationship between the seismic records and the corresponding atmospheric data, including measurements of pressure (Figure 9c), wind (Figure 9e), and temperature (Figure 9g). The lack of strong correlations between pressure and temperature data and the seismic records near the frequency of ~0.05 Hz suggests that the 20-s signal is unlikely to be associated with those atmospheric variations (Figures 9d, f, g). However, the emergent times of the 20-s signal and wind bursts are sufficiently consistent to suggest a possible link between the 20-s signal and wind (Figure 9e). Indeed, the wind can exert forces of drag and lift on the InSight lander and these stresses will be propagated through the ground to the SEIS as an acceleration noise (Murdoch et al., 2017a, 2017b; Kenda et al., 2017; 2020), which may generate the 20-s signal that we have observed.

To verify this possibility, we plot the wind and temperature variations in the same period time of Sol 194, which is about one Martian year before Sol 888 (Figure 10a–b). The wind speed and direction of the two Sols vary similarly due to seasonal changes in the Martian atmosphere (Spiga et al., 2018; Chatain et al., 2021). However, we cannot identify the 20-s signal in data of Sol 194. Furthermore, we notice that some 20-s signals appear before (Figure S9) or long after the starting of the wind burst causing high-frequency noise modes (Figure S10), which indicates that wind is less likely to generate the 20-s signal. If the 20-s signal is indeed related to the wind, the “20-s wind” may occur at a location far away from InSight, and its characteristics can not be fully captured by the onboard atmospheric data. It is worth noting that we have analyzed only nighttime data. The daytime on Mars is much noisier due to strong wind effects (Ceylan et al., 2021), which restrains us to further explore whether the 20-s signal occurs also at daytime. Also worth noting is that the long-period signals observed at the other two frequencies — of 0.10 and 0.15 Hz (Figure 2b) — may suggest the presence of resonance effects, possibly caused by topography or tunneling.

Figure  10.  Atmospheric data during 22:00 LMST to 24:00 LMST of Sol 194. The atmospheric data are recorded by TWINS. The N-component velocity seismogram (gray line) is filtered in the frequency range 0.02–0.1 Hz. (a) is for wind speed (blue) and direction (red) and (b) is for air temperature data. Blue and orange lines are BMP and BPY data, respectively.

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Another possibility is that the dusty Martian environment may generate the long-period signals. In the autumn/winter “dusty” season (~Sol 550, northern autumn; ~Sol 700, northern winter), most meteorological parameters experience characteristic abrupt fluctuations during the passage of convective vortices, such as surface pressure drop, temperature increase, and rapid changes in wind direction (Kenda et al., 2017; Banfield et al., 2020). Under such conditions, the Martian surface is more easiy deformed; such deformations can act as strong seismic sources (Murdoch et al., 2017a,　2017b; Kenda et al., 2017). Moreover, Chatain et al. (2021) concluded that shear-driven local turbulence at the InSight landing site in the nighttime at the dusty season is almost as powerful as in the convective daytime, resulting from the strong ambient wind (low-level jet) and the weak stability in these dustier conditions. However, based on the wind data at the InSight location (Figure 9e), “dusty” nights in Sols 800−1,000 are not likely the case. Thus, the appearance of the 20-s signal only in Sols 800−1,000 suggests that its source may not be associated with seasonal variations on Mars.

Due to insufficient power from solar panels, we lack many wind data during Sols 800–1,000 and cannot give a precise correlation of wind and the 20-s signal, but we think that the wind might yet prove to be the dominant factor producing the 20-s signal.

4.   Discussion

4.1   Possible Tremor Source?

We notice that the observed spectral characteristics, with mode peaks at frequencies of 0.05, 0.10, and 0.15 Hz (Figure 2b), appear to be similar to “harmonic tremor”, which is a subclass of volcanic tremor. The harmonic tremor, which has frequenlty been observed on Earth, has a fundamental peak in spectral energy, and harmonics with frequencies of integer multiples of the fundamental frequency (Schlindwein et al., 1995; Benoit and McNutt, 1997; Lyons et al., 2013; Yamamoto et al., 2002; Chen YY et al., 2022). Long period tremors (LPTs) with a dominant period of about 15 s are observed at the Aso volcano and have been related to the resonance of shallow cracks (Kawakatsu et al., 2000; Niu et al., 2021). In addition, at stations near the crater, the LPT has exhibited linear particle motion in the horizontal plane (Kawakatsu et al., 2000; Legrand et al., 2005), which is similar to the periodic signal observed in this study.

The landing site of the InSight is at the Elysium Volcanic Province (hereinafter referred to as Elysium), which is the second largest volcanic region on Mars and is composed of shield volcanoes, tholi, and flood lava flows (Mouginis-Mark et al., 1984, 2021; Greeley and Guest, 1987; Hodges and Moore, 1994; Zimbelman et al., 2015). Such a volcanic setup may provide the source for generating LPT. The polarization of LPT particle motions points to the source direction (Legrand et al., 2000; Kawakatsu et al., 2000). Here, the Elysium Mons, one of the three main volcanoes in the Elysium region, exhibits some of the youngest flows on Mars — as young as a few million years old (Plescia, 1990; 2003; Vaucher et al., 2009; Horvath et al., 2021); this volcano lies to the northeast of the InSight location (Figure 11), within the range of the calculated polarization angle of the 20-s signal.

Figure  11.  Topographic map of Mars (MOLA; Smith et al., 2001). The InSight landing site is indicated by the black triangle. The Elysium Mons is located northeast of the InSight, with an azimuth of ~27°. The area I shows a region with azimuths of 24°–37° (a 180° ambiguity) from the InSight, corresponding to the gray band in Figure 8a, having a good fit to the particle motions. The area II with azimuths of 37°–46° (a 180° ambiguity) corresponds to the yellow band in Figure 8a, representing a poor fit to the particle motions.

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However, it is challenging to generate a horizontal dominant motion caused by a remote tremor source; and equally challenging to explain away the possible link between the 20-s signal and the wind. Yukutake et al. (2017) found that the vertical component recorded at a local station OWD from the 2015 phreatic eruption of the Hakone volcano had a much smaller amplitude than those of the horizontal components, at the frequency range of 1 to 6 Hz.

We must admit that we have not yet found a proper source mechanism that can convincingly satisfy our observations. Alternatively, if the source is very close to InSight, a periodic change in subsurface pressure might induce ground tilting and displacements through elastic deformations. Nonetheless, if our observed periodic signals are indeed associated with the volcano, the InSight data will provide important information about current volcanic activity on Mars.

4.2   Influence on the Noise Correlation

The rapid development of seismic interferometry has allowed seismologists to extract important information from passive records of random vibrations generated by natural processes such as winds, waves, etc. (Berg et al., 2018; Miao WP et al., 2022; Qiu HR et al., 2020, 2021; Schimmel et al., 2018; Wang et al., 2020; Yao HJ et al., 2006). The base of the method is that the cross-correlation of a diffuse wavefield, recorded at two sensors, can provide a Green's function (GF) at one of the sensors for a virtual source placed at the other sensor (Weaver and Lobkis, 2002; Derode et al., 2003; Snieder, 2004; Wapenaar, 2004, etc). A zero-offset GF can be obtained by an autocorrelation (AC), which has been routinely applied for the single-station data of the InSight. For instance, Suemoto et al. (2020) extracted propagating signals from AC and then inferred the presence of a very shallow interface underneath InSight. Subsequently, (Compaire et al., 2021; Deng SZ and Levander, 2020; Schimmel et al., 2021), a prominent reflection phase, that may correspond to the crust-mantle boundary (Moho) or a mid-crust discontinuity at ~35 km, was observed in the stacked ambient noise autocorrelations. The core-reflected phase (PcP) has also been observed from ambient noise autocorrelations (Deng SZ and Levander, 2020) and coda correlations (Wang S and Tkalčić, 2022), although the observation of the PcP phase might possibly be due to repeated glitches in the SEIS-data (Barkaoui et al., 2021; Kim et al., 2021). The Mars orbiting surface waves, R2, are also observed in the stacked autocorrelation series filtered between 0.005 and 0.01 Hz (Deng SZ and Levander, 2022).

Whether the observed periodic signals are caused by the air pressure or the tremor, such signals, as a possible stable source, may affect the results of the noise correlation. To examine the effects of the long periodic signals on the AC, we compute and compare the hourly autocorrelations in three cases. One case is before Sol 800 with no periodic signals, such as 03:00 LMST to 04:00 LMST during Sol 700 to Sol 750. The second case is for the interval from Sol 800 to Sol 1,000 during which strong periodic signals are detected. To illustrate this second case, we pick one-hour records with strong periodic signals, from 22:00 LMST to 04:00 LMST during Sol 800 to Sol 1,000, according to PSD. The third case is for the hour after the ends of occurrences of the periodic signals, such as 03:00 LMST to 04:00 LMST during Sols 860−910 (Figure 7).

We use the program NoiseCorr_SAC_v4 developed by Yao HJ et al. (2006) to compute the autocorrelation for each hourly deglitched data. The processes include time-domain and frequency-domain normalizations with the goal of removing the effects of nonstationary phases such as instrumental problems, marsquakes, and whitening of the amplitude spectrum. To exclude the effect of residual glitches (Barkaoui et al., 2021; Kim et al., 2021), after the first deglitching process with MPS (Scholz et al., 2020), we apply another round of deglitching with the UCLA algorithm (Scholz et al., 2020). Figure S11 shows the difference between stacked autocorrelations with and without this extra deglitching. Both phase-weighted stacking (Schimmel and Paulssen, 1997) and linear stacking are used to stack the hourly autocorrelation functions to obtain autocorrelograms of all three components. As shown in Figure 12, there are differences among autocorrelograms generated with data in different time periods. For the first case, we do not observe strong phases near the theoretical arrival times of several typical core phases. In the second case, two phases at ~550 s and ~700 s, which may correspond to the PcS/ScP and ScS, are noticeable on the N-component autocorrelograms at the frequency of 0.02–0.1 Hz for both stacking methods (Figure 12b), which may also correspond to the strong energy of the observed 20-s signals on the N component. For the third case, a phase at ~360 s correlating to PcP is clear on both Z and N autocorrelograms at the frequency of 0.02–0.1 Hz (Figure 12b). However, the energy of the 20-s signal is very weak on the vertical component. Whether the 20-s signals can efficiently generate prominent core-reflected phases, such as PcP with vertical ray paths, is still an open question. Thus, further detailed studies are required to verify that these phases in the autocorrelograms are indeed robust features. Nonetheless, the observed long-period periodic signals have strong effects on the autocorrelograms, which may be crucial for extracting information on the internal structure of Mars.

Figure  12.  Stacked autocorrelograms for three different time periods. Both stacks, with the PWS (heavy line) and linear (light line) stacking, are displayed. The autocorrelograms are filtered into (a) 0.01–0.05 Hz and (b) 0.02–0.1Hz). Hourly autocorrelations are calculated and stacked for three cases at different time periods. Case I (black): one-hour data each Sol, from 3:00 LMST to 4:00 LMST during Sol 700 to Sol 750. Case II (red): one-hour data with strong energy of the 20-s signal, from 22:00 LMST to 4:00 LMST during Sol 800 to Sol 1,000. Case III (blue): one-hour data each Sol, from 3:00 LMST to 4:00 LMST during Sol 860 to Sol 910 (refer to Figure 8d). The four gray areas represent the theoretical travel times calculated by 100 Mars velocity models (Stähler et al., 2021) for four core reflected phases, i.e., PcP, PcS/ScP, ScS, and ScSScS as purple text noted. The black arrows in (b) outline the prominent phases in the stacked autocorrelograms.

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5.   Conclusion

We observe a low frequency periodic signal in the VBB data of the InSight from Sol 800 to Sol 1,000. This signal has a dominant period of ~20 s, which occurs at local nighttime and lasts even up to five hours. This periodic signal has strong horizontal component amplitudes but almost undetectible vertical amplitude; it indicates linear particle motion in the horizontal plane, with a polarization angle between 24° and 46°. Although we cannot determine the exact origin of this long period signal, we think that atmospheric effects such as wind and temperature may be candidates for generating such a signal. Furthermore, the difference between the autocorrelograms, calculated by InSight data with or without the 20-s signal, suggest that this long-period periodic signal may be able to play an important role in the study of noise interferometry.

Acknowledgments

We acknowledge NASA, CNES, partner agencies and institutions (UKSA, SSO, DLR, JPL, IPGP-CNRS, ETHZ, IC, MPS-MPG), and the operators of JPL, SISMOC, MSDS, IRIS-DMC, and PDS for providing SEED SEIS data. SEIS raw data are available at https://doi.org/10.18715/SEIS.IN,SIGHT.XB_2016. The raw-to-calibrated datasets of InSight are available via the Planetary Data System (PDS). The direct link to the InSight data archive at the PDS Atmospheres node is: https://atmos.nmsu.edu/data_and_services/atmospheres_data/INSIGHT/insight.html. We also thank Editor Yong Wei and two anonymous reviewers. Their suggestions and comments led to significant improvements to the manuscript. This study is supported by B-type Strategic Priority Program of the Chinese Academy of Sciences, Grant XDB41000000, National Natural Science Foundation of China 42241117.

Supplementary Materials for "Observation 20-s periodic signals on Mars from InSight, Sols 800−1,000"

S1. Moving Weighted Average

The weighted average is computed by

where the ${\sigma_i}$ is the standard deviation of ith linear fit.

  S1.  An example of moving a short time window of 40 s (purple band) with overlap 5 s (orange band) in a long time window (300 s) (a) and computing fitted polarization angle and error with Least Square Method (b). The NE-components velocity seismograms filtered in the frequency range of 0.02–0.10 Hz in (a) are same as Figure 5d in main text. The gray band in (b) displays the good fit with small error.

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  S2.  Three-components velocity seismograms and their particle motions. The data used here is same as Figure 5 in main text. The polarization angle and error are weighted average values computed by moving a short time window in a time window of 300 s as Figure S1 shown.

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S2. Matched-filter Method

We compute the normalized cross-correlation coefficients (CC) that evaluate the similarities between the template and continuous waveform data by

where $v(t_v)$ and $w(t_w)$ are the discrete time-series of template and cut continuous data, < > denotes the inner product, N and $\Delta t$ are the sampling number and interval.

In this study, we cut continuous VBB data into one-hour segments each Sol and do cross-correlation with templates (the time length is 300 s). For each segment, the time length of a valid CC is one hour minus 300 s. Here, we abandon the traditional concept of lag time in cross-correlation but focus on the CC of each point.

Figure S3 shows the effect of threshold of CC to detection.

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  S3.  Three detection examples of different threshold of CC. (a) 0.35; (b) 0.55; (c) 0.75. The others are same as Figure S1.

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Figure S4 gives an example that how we merge the detected results by three different templates and pick the detected periodic signals from raw continuous data. We first locate the peak time as occurrence time of periodic signal within each triggered window, in which the CC are larger than the threshold (set to be 0.55, here). Then we sort the occurrence times detected by three different templates. If the adjacent time difference is less than the template length (300 s), it is considered to be a continuous period of periodic signal; otherwise, the moment when the time difference is greater than 300 s is considered to be the start of the next periodic signal. The final length of this periodic signal cut from raw continuous data will be the continuous period added a template length.

  S4.  An example of merging the detected results by three different templates. From up to bottom: the first picture shows the VBB BHN component velocity seismogram of a given trace filtered in the frequency range 0.02–0.10 Hz; the next three pictures show the computed normalized cross-correlation coefficients (CC) used three different templates (22 s, 18 s, 22 s), respectively. In each picture, the red dashed line represents the threshold of CC (0.55) and the plotted symbols represent the peak CC within each triggered window; the last picture shows the sorted peak times detected by three templates.

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S3. Principal Component Analysis (PCA)

  S5.  Temporal variation of the polarization angle of the 20-s signal in the horizontal plane computed by PCA. The yellow band outlines the concentrating range of the angles. The yellow line shows the mean SCIT-A (scientific temperature A) inside the Remote Warm Enclosure Box (RWEB) but outside the Evacuated Container of VBB during 20:00 LMST to 22:00 LMST and the green line shows the mean SCIT-A at a later time of 22:00 LMST to 04:00 LMST.

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  S6.  Temporal variation of the polarization angle of the 20-s signal in the horizontal plane computed by moving a short time window in a time window of 300 s as Figure S1 shown. The others are same as Figure 8a in main text.

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S4. Different Filtering Widths in Matched-filtering

In addition to the 0.02–0.1 Hz frequency band used in the main text, we also use the 0.025–0.2 Hz frequency band to band-pass filter the template and the waveform to be detected to detect the impact of different filter frequency bands on the matched-filtering results.

  S7.  Same as Figure 7 in the main text but for 0.025–0.2 Hz frequency band.

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  S8.  Same as Figure 8 in the main text but for 0.025–0.2 Hz frequency band.

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S5. Some Examples of 20-s Signal Not Related to Wind

  S9.  N-component VBB acceleration data from 21:00 LMST of Sol 884 to 06:00 LMST of Sol 885 and its spectrogram and power spectral density (PSD) same as Figure 1 in main text.

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  S10.  N-component VBB acceleration data from 20:00 LMST of Sol 957 to 06:00 LMST of Sol 958 and its spectrogram and power spectral density (PSD).

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S6. Comparison of Stacked Autocorrelograms Between Deglitching Once and Twice

  S11.  Comparison of stacked autocorrelograms with deglitching once (only MPS (Scholz et al., 2020)) and twice (first MPS; second UCLA (Scholz et al., 2020)). The used data for three cases are same as Figure 12 in main article. The two phases (~550 s and ~700 s), may corresponding to PcS/ScP and ScS, can be noticed on N autocorrelograms at frequency band 0.02–0.1 Hz either deglitching once (b) or twice (d), but their amplitudes get larger with deglitching twice (d) in the second case. The phase (~360 s) on Z autocorrelograms at frequency band 0.02–0.1 Hz in the third case also shows the same characteristic.

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