Inferring the Speed of Sound and Wind in the Nighttime Martian Boundary Layer From Impact-Generated Infrasound

Abstract

The properties of the first kilometers of the Martian atmospheric Planetary Boundary Layer have until now been measured by only a few instruments and probes. InSight offers an opportunity to investigate this region through seismoacoustics. On six occasions, its seismometers recorded short low-frequency waveforms, with clear dispersion between 0.4 and 4 Hz. These signals are the air-to-ground coupling of impact-generated infrasound, which propagated in an low-altitude atmospheric waveguide. Their group velocity depends on the structure of effective sound speed in the boundary layer. Here, we conduct a Bayesian inversion of effective sound speed up to 2,000 m altitude using the group velocity measured for events S0981c, S0986c and S1034a. The inverted effective sound speed profiles are in good agreement with estimates provided by the Mars Climate Database. Differences between inverted and modeled profiles can be attributed to a local wind variation in the impact→station direction, of amplitude smaller than 2 m/s.

Key Points

• InSight recorded impact-generated infrasound on Mars. Their group velocity is sensitive to the structure of the atmospheric boundary layer

• We conduct a Bayesian inversion of effective sound speed profiles with altitude based on group velocities measured for three impact events

• The inverted profiles provide an indirect measurement of the Martian boundary layer, and validate models of the Mars Climate Database

Plain Language Summary

The Martian Planetary Boundary Layer corresponds to the first few kilometers of the atmosphere. The InSight lander offers the opportunity to investigate its properties via the coupling of seismic and acoustic waves. Impact-generated infrasound waves were recorded for the first time on Mars by the seismometers of the InSight mission. These infrasound waves propagated in an atmospheric waveguide in the first kilometers above the Martian surface, and thus present a frequency-dependent group velocity. This frequency-dependence, also known as a dispersion relation, is influenced by the structure of the speed of sound in the waveguide. Here, we use group velocity measured for events S0981c, S0986c and S1034a to invert the variations of effective sound speed between 0 and 2,000 m altitude. For the three events, the inverted profiles are in good agreement with estimates provided by the Mars Climate Database using global climate modeling. The differences between inverted and modeled profiles can be attributed to a local variation in wind in the impact→station direction, with magnitude smaller than 2 m/s.

1 Introduction

The Planetary Boundary Layer (PBL) defines the region where the atmosphere of a planet interacts with the surface, through exchanges of momentum, heat and molecular species. On Mars, it extends from the surface up to about 10 km altitude, and it is also a critical environment where landers, rovers and airborne spacecrafts operate (Petrosyan et al., 2011). In the Martian PBL, temperature undergoes significant daily variations, of about 50–80 K in amplitude at surface levels. The bottom of the PBL shows a superadiabatic lapse rate in the daytime, with a strong negative temperature gradient with altitude, leading to instabilities and convective turbulences. Conversely, the temperature gradient reverses at night and becomes strongly stable. Capturing these phenomena is key to designing accurate models of the Martian climate (MEPAG, 2020), in particular General Circulation Models (GCMs) (see e.g., Forget et al. (1999); Moudden and McConnell (2005); Segschneider et al. (2005); Takahashi et al. (2006)). At high altitudes ($$\gtrsim 1$$ km), GCMs validate their results using orbiter data, and results at the surface level are validated using measurements from landers and rovers (Forget et al., 2001, 2014). However, data remains sparse at intermediate altitude including in most of the PBL (Petrosyan et al., 2011). Its properties have been sampled or inferred during entry, descent and landing of the Viking, InSight and Perseverance spacecrafts (Banfield et al., 2020; Paton et al., 2024; Seiff & Kirk, 1977). Temperature profiles up to 2 km altitude have notably been obtained by the Miniature Thermal Emission Spectrometer (Mini-TES) onboard Spirit and Opportunity, but these measurements were mostly occurred from the late morning to the afternoon due to operational constraints (Mason & Smith, 2021; Smith et al., 2006).

The NASA InSight mission offers a new opportunity for atmospheric science on Mars. The lander operated a seismometer, the SEIS instrument, supported by a meteorological sensor suite (APSS) between 2018 and 2022 on Elysium Planitia (Banfield et al., 2018; Lognonné et al., 2019). Over the course of the mission, more than a thousand seismic events of tectonic, but also of atmospheric origin were captured by SEIS (Banerdt et al., 2020; Ceylan et al., 2022; InSight Marsquake Service, 2023). In the case of atmospheric events, the ground near InSight responds to a local pressure perturbations in the Martian atmosphere, or to pressure waves excited by distant acoustic sources.

A unique type of atmospheric events was observed on sols 533, 793, 981, 986, 1,034 and 1,160, which denote the number of Martian days after the landing of InSight. These events present a clear seismic arrival with the characteristics of typical Very-high Frequency (VF) marsquakes (Ceylan et al., 2022), followed by late arrivals indicating the acousto-seismic coupling of atmospheric infrasound. The latter have a low frequency content (0.4–4 Hz) and exhibit dispersion. Using a combination of seismic analysis and orbital imaging, Garcia et al. (2022) showed that these arrivals originated from meteorite impacts. Precisely, the first VF arrivals are seismic waves generated by impact cratering, while the dispersed, slower ones are due to the air-to-ground coupling of the impact blast wave having traveled through the Martian atmosphere. The location of the source of both the seismic and the acousto-seismic signals is known thanks to orbital imaging of the craters.

The dispersion of these signals can be well explained by the presence of an atmospheric waveguide at low altitudes. On Earth, dispersed infrasound waves were recorded following surface explosions in the presence of such waveguide (Herrin et al., 2006; Negraru & Herrin, 2009). Likewise on Mars, a waveguide may exist at night due to the rapid radiative cooling of the surface, and can be enhanced by favorable seasonal wind conditions (Daubar et al., 2018; Garcia et al., 2017). Waves trapped in waveguides are referred to as “guided waves” and may propagate over large distances (e.g., Martire et al., 2020). Low-altitude guided waves interact with the surface, and thus excite ground deformation via compliance effects (Ben-Menahem & Singh, 2012; Sorrells, 1971). Xu et al. (2022) propose an analytical representation of Martian seismo-acoustic signals. They develop a 1D model for infrasound wave propagation and dispersion in a layered atmospheric waveguide, including their coupling through ground compliance (Tanimoto & Wang, 2019; Xu & Lognonné, 2024), yielding synthetic dispersed seismic signals at InSight's location.

The speed of sound in the Martian PBL defines the waveguide structure and governs infrasound propagation. In this previous work, the waveguide properties are estimated using models of the atmosphere of Mars provided by the Mars Climate Database (MCD) (Forget et al., 1999; Millour et al., 2015, 2018) at the time and place of various InSight events. The MCD interpolates meteorological fields, such as atmospheric temperature, density, pressure and wind, in time and space, based on grided outputs from GCMs. With limited alteration to the MCD models, Garcia et al. (2022) and Xu et al. (2022) obtain a good fit between synthetic waveforms and the dispersed signals recorded by InSight during events S0981c and S0986c. This result shows that we can extract further information on the Martian PBL and test MCD models using impact infrasound data.

In this study, we propose to invert profiles of the speed of sound up to 2 km above the surface of Mars from InSight dispersed seismo-acoustic signals, based on Xu et al. (2022)'s model for infrasound group velocities. We first describe this model and the sensitivity of group velocity to atmospheric structure. Then, we present the inversion method and its application to three seismic events (S0981c, S0986c and S1034a). The resulting atmospheric models are compared to MCD predictions at InSight location at the time of each event to validate results of climate modeling in the PBL.

2 Analytical Model of Ground-Coupled Guided Infrasound

We provide a brief description of the analytical model of coupled guided infrasound. We refer the reader to Xu et al. (2022) for further details.

2.1 Waveform Model

The synthetic waveform is represented in the frequency domain, as a function of pulsation $$\omega $$. We adopt the formalism of Xu et al. (2022) and model acoustic waves propagating in a laterally homogeneous atmosphere, and generating ground motion through compliance. The ground velocity in the upward direction is written $${u}_{z}(\omega )$$. The source, that is, the impact crater, is located at distance $$r$$ from the receiver. $${u}_{z}(\omega )$$ is the product of a source term with the Green's function of propagation for cylindrical pressure waves, and a ground-coupling, or compliance term:

$$${u}_{z}(\omega )=S(\omega )\mathrm{exp}(-ikr-ar)\frac{\mathrm{exp}(-i\pi /4)}{\sqrt{kr\pi /2}}\frac{{P}^{2}(\omega ,0)}{\int {P}^{2}(\omega ,z)dz}{C}_{z}(\omega ).$$$ (1)

The source term, $$S(\omega )$$, is the spectrum of the impact blast source. Due to limited current knowledge on impact blast dynamics, Xu et al. (2022) assume a Dirac impulse in time, so that $$S(\omega )=1$$. The complex factor $${C}_{z}(\omega )$$ is the vertical compliance, detailed in Xu and Lognonné (2024). It describes the amplitude of the quasi-static response of the ground to the infrasound pressure perturbation, and comes with a phase lag of $$\pi /2$$ between ground velocity and pressure. The remaining factors form the analytical Green's function for the fundamental mode of cylindrical pressure waves in a 1D refractive atmosphere with attenuation $$a(\omega )$$: $${P}^{2}(\omega ,0)/\int {P}^{2}(\omega ,z)dz$$ is an eigenfunction term and $$\mathrm{exp}[-i(kr+\pi /4)]/\sqrt{kr\pi /2}$$ the far-field, asymptotic form of a Hankel function (see e.g., Waxler (2002) for an analytical derivation).

The dispersion is caused by a frequency-dependent wave number $$k$$ and group velocity $${v}_{g}(\omega )=d\omega /dk$$. In the above model, dispersion occurs due to the propagation of the infrasound wave in a refractive atmosphere, showing an increase in the medium propagation velocity, or acoustic impedance, with altitude. It is not affected by compliance, which only brings a constant phase lag. Therefore, the dispersion curve measured from ground motion is the same as would be recorded from a direct infrasound signal (Garcia et al., 2022).

The phase velocity for infrasound, written $$\alpha =\omega /k$$, depends on both the local temperature $$T$$ and wind speed vector $$\boldsymbol{w}$$: they have an effective sound speed $${\alpha }_{\text{eff}}={\alpha }_{\mathrm{T}}(T)+\boldsymbol{w}\cdot \frac{\boldsymbol{k}}{\Vert \boldsymbol{k}\Vert }$$, which is enhanced parallel to the wind direction. The group velocity of the guided infrasound thus depends on the vertical structure of $${\alpha }_{\text{eff}}(z)$$. Following Xu et al. (2022), the atmosphere only varies in the vertical direction and is represented by a succession of $$N$$ layers, with layer $$n$$ of thickness $${H}_{n}$$ having a constant effective sound speed $$\alpha (z)={\alpha }_{n}$$ for $$z\in \left[{z}_{n},{z}_{n}+{H}_{n}\right]$$, and a density $${\rho }_{n}$$. The group velocity can then be computed using a propagator matrix method and a root finding algorithm (Aki & Richards, 2002; Xu et al., 2022).

2.2 Model Sensitivity and Parametrization

We assess the possibility of inverting the Martian atmospheric structure from the group velocities of coupled impact seismic signals. Parametric studies are performed to determine the sensitivity of $${v}_{g}$$ to variations of effective sound speed and density. This parametric study is detailed in Text S2 of the Supporting Information S1 and shows that group velocity is considerably more sensitive to variations in effective sound speed than in density. Moreover, $${v}_{g}$$ is more sensitive to changes in $${\alpha }_{n}$$ at low altitude.

This parametric study confirms that an atmospheric sound speed profile formed by several layers and a half-space can be inverted from chirp group velocity. The structure of the waveguide depends on both the amplitude of $${\alpha }_{n}$$ and the height $${H}_{n}$$ of each layer. On the other hand, the density within each layer can be fixed to values matching MCD models.

3 Methods

3.1 Data Selection

Among the six impact events, only three present a high signal-to-noise ratio (SNR) and unambiguous group velocity recording: chirps of S0986c, S0981c and S1034a are chosen for this inversion. We point out that event S0986c present three distinct acoustic arrivals, labeled A1, A2 and A3 in Garcia et al. (2022) (Figure 1 in Supporting Information S1). Garcia et al. interpret the strongest signal, A3, as being produced by the impact with known source location, while earlier ones are related to the entry and disruption of the associated meteoroid.

The properties of the three selected events (S0981c, S0986c A3 and S1034a) are summarized in Table 1. Their group velocity curve and their uncertainties are measured using the method described in Gaudot et al. (2021) (see also Text S1 in Supporting Information S1), and are shown on Figure 1.

Table 1. Known Properties of the Three Events Selected for Inversion, Obtained From Seismic Analysis, From Satellite Imaging (See Garcia et al. (2022), Daubar et al. (2023)) and From the InSight Event Catalog (InSight Marsquake Service, 2023)

Event	S0981c	S0986c A3	S1034a
Properties from seismic signal
utc Date (at event start time)	31 August 2021	5 September 2021	23 October 2021
utc Time (at event start time)	04:04:01.00	05:23:58.00	18:26:43.00
Properties from orbital imaging
Crater diameter (type) (m)	7.24 (single)	6.1 (cluster)	9.2 (single)
Crater latitude ($${}^{\circ}$$N)	0.397	3.974	3.866
Crater longitude ($${}^{\circ}$$E)	135.688	136.963	135.107
Distance to InSight (km)	240.6	85.1	48.4
Back azimuth $$({}^{\circ})$$	179.2	111.6	219
Relevant time information
Estimated utc origin/impact time	4:03:13	5:23:44	18:26:30
Solar Longitude $${L}_{s}$$	92.6	94.8	116.8
Local True Solar Time (ltst, hours)	23.2	21.3	3.3

• Note. Note that the distance of S0981c was reevaluated in Daubar et al. (2023)

Figure 1

The events chosen for this study are S0981c, S0986c, and S1034a. The dispersed vertical velocity signals $${u}_{z}(t)$$ recorded by SEIS and bandpass-filtered between 0.5 and 2 Hz are shown in (d), (e) and (f). Respectively, (a), (b) and (c) show the group velocity curves measured from the corresponding signals in black, and their uncertainty in gray. Colored plain and dashed lines show theoretical group and phase velocity ($${v}_{g}$$, $${v}_{\varphi }$$) predicted with Xu et al. (2022)'s method using MCD profiles of $$\alpha (z)$$ and $$\rho (z)$$ at the time of each event.

3.2 Bayesian Inversion Design and Tests

We wish to invert for the layer heights $${H}_{n}$$ and effective sound speeds $${\alpha }_{n}$$ in an $$n$$-layered atmosphere model topped by a halfspace. To quantify the uncertainty of each atmospheric models, a Bayesian inversion method is favored. Its result will be a distribution of probability for parameters $${\alpha }_{n}$$ and $${H}_{n}$$, given the information contained in the observation and a prior distribution of parameters. In this study, the Markov chain Monte Carlo (McMC) numerical method is chosen (Geyer, 1991), in combination with a Parallel Tempering technique, to ensure that potential multimodal distributions of probability can be explored (Sambridge, 2014).

The number $$N$$ of layers below the halfspace is an important choice in the inversion. To avoid overfitting the group velocity curves, the influence of the number of layers on the model misfit was measured and is detailed in Text S3 of the Supporting Information S1. No significant improvement in misfit is obtained above $$N=4$$, which is consequently chosen for all the subsequent inversions.

A uniform prior distribution is chosen for all the inverted parameters. The analysis of Garcia et al. (2017) shows that speed of sound may increase up to 2 km altitude in the Martian nocturnal boundary layer for solar longitudes $${L}_{s}\approx 90-100$$ similar to our three events (i.e., summer in the northern hemisphere). Consequently, each layer thickness is picked within [5,400] m, for a total possible height of 1,600 m initiating the halfspace. Effective sound speed takes values within $${\alpha }_{0}\in [220,240]$$ m/s in the first layer. Starting from the third layer, variations of effective sound speed $${\Delta }\alpha ={\alpha }_{n}-{\alpha }_{n-1}$$ are allowed within $$[-5,15]$$ m/s, in order to ensure an overall continuity of the fluid medium. Negative variations in sound speeds are not allowed in the second layer above the surface, as this would result in a very poor waveguide.

An in-house implementation of the McMC and parallel tempering method is used. Tests of this method with synthetic atmospheric models and synthetic group velocity curves are presented in Text S3 of the Supporting Information S1. They show that the inversion provides a satisfactory fit to the provided group velocity curves and initial atmospheric model.

4 Atmospheric Inversion Results

4.1 Effective Sound Speed Profiles

The posterior distribution of group velocity curves inverted for S0981c is shown on Figure 2d. The inverted models provide a good fit to the data within the uncertainty of group velocity measurements. Similar figures for S0986c and S1034a are shown in Text S4 of the Supporting Information S1. Figures 2a and 2c show the posterior PDFs of effective sound speed profiles inverted from the group velocity curves of each event. These PDF are constructed from a distribution of 4-layer models characterized by sharp increase in velocity in the atmosphere. However, we note that a smoother model passing through the region of high probability density, here shown in blue, also provides a good fit to S0981c's group velocities. This confirms that the choice of a “staircase” model is not bringing unrealistic constraints to the inversion: instead, it captures the average effective sound speed between two levels of altitude. The width of the posterior PDF is driven by model sensitivity and data uncertainty. Close to the surface, $${\alpha }_{\text{eff}}$$ appears to be well constrained, within $$\pm 1$$ m/s. However, the distribution of models becomes more spread out at higher altitude, especially for S1034a for which $${\alpha }_{\text{eff}}$$ takes values between $${\sim} 230$$ and $${\sim} 245$$ m/s above 250 m altitude. This variation is of the same order as the prior distribution, displayed in Text S4 of the Supporting Information S1, which means that the group velocity data of this event does not provide sufficient information to constrain effective sound speed at higher altitudes. At 500 m altitude, the region of high probability has a width of about 4 m/s for S0981c and 6 m/s for S0986c.

Figure 2

PDFs of the posterior distribution of effective sound speed profiles $${\alpha }_{\text{eff}}(z)$$ inverted for events S0981c (a), S0986c (b) and S1034a (c). The MCD profile at InSight location and its spatial variability over the scale of a GCM grid cell is shown with plain and dashed black lines for comparison. The group velocity measurements for S0981c is shown in (d) with its uncertainty, together with the group velocities (red shaded area) estimated from 100 atm models randomly chosen among the posterior distribution.

Our current objective is to compare atmospheric profiles inverted from impact infrasound to current models of the atmosphere using outputs of the Mars Climate Database. However, the resolution of MCD outputs is limited by the resolution of the GCM grids over which its interpolation is performed.

To ensure a meaningful comparison between inversion results and the MCD, we estimate a range of possible variations for wind, thermodynamical and effective sound speed during each event. To this aim, we query the database at a range of locations covering the approximate area of a GCM grid cell around InSight. This is done at the time of the event, but also one Martian hour before and after to match the database temporal resolution. We thus establish the minimum and maximum values of parameters based on which spatial and temporal interpolation is performed (see Figure S10 in Supporting Information S1 for details).

For event S1034a (Figure 2c), we observe that the inverted PDF fits the range of effective sound speed of the MCD. For S0986c (Figure 2b), the maximum of the posterior distribution is generally lower than the MCD estimate at InSight location and at the time of the event, but remains within the range of possible variations up to about 1 km altitude, above which the distribution of $${\alpha }_{\text{eff}}$$ is less constrained. On the contrary, the PDF of S0981c is constrained within $$\pm 4$$ m/s from the bottom layer to 2,000 m altitude. Although values of $${\alpha }_{\text{eff}}$$ agree with the MCD at the surface level, they are lower than the variability range by about $$\pm 2$$ m/s at high altitudes.

4.2 Estimation of Wind

We have focused so far on the effective sound speed, which sums the contribution of local winds to the thermodynamical sound speed, $${\alpha }_{\mathrm{T}}$$, itself a function of temperature. The group velocity data does not contain sufficient information to decouple variables $$T$$ and $$\boldsymbol{w}$$. However, the available knowledge allows for further simplification. At nighttime on Mars, temperature is driven by thermal radiation of the surface and air, and the MCD yields smooth and predictable profiles for each event (see, Figure S11 in Supporting Information S1). On the other hand, winds can be influenced by topography (slope winds or jets) (Savijärvi & Siili, 1993), shear-driven turbulences as well as gravity waves at InSight location (Banfield et al., 2020; Onodera et al., 2024). We also note that there exists more measurements of temperature in the PBL (Hinson et al., 1999; Seiff & Kirk, 1977; Smith et al., 2006; Spiga et al., 2021) than winds (Paton et al., 2021, 2024). This complexity of wind mechanisms and lack of observations suggests that at a specific time of day, temperatures are likely better predicted by climate models than winds. This implies winds could be driving fluctuations in effective sound speed along the source$$\to $$receiver path.

We propose to estimate wind profiles along this path from posterior models of $${\alpha }_{\text{eff}}$$. To this aim, based on the above argument, we consider that the temperature profiles, and thus the thermodynamical sound speed profiles calculated by the MCD are exact. The PDF of wind in the back-azimuth (baz) of the event, $$\text{pdf}\left[{w}_{\text{baz,}\,\text{est.}}\right]$$ can then be expressed as:

$$$\text{pdf}\left[{w}_{\text{baz,}\,\text{est.}}\right]=\text{pdf}\left[{\alpha }_{\text{eff,}\,\text{McMC}}\right]-{\alpha }_{\text{T,}\,\text{MCD}}.$$$ (2)

$$\text{pdf}\left[{w}_{\text{baz,}\,\text{est.}}\right]$$ is obtained in the following way: for each individual model $${\alpha }_{\text{eff,}\,\text{McMC}}\left({z}_{n}\right)$$ of the initial posterior distribution, we calculate and subtract a corresponding MCD profile $${\alpha }_{\text{T,}\,\text{MCD}}\left({z}_{n}\right)$$, whose values are extracted at the bottom of each layer of altitude $${z}_{n}$$. The new PDFs are shown on Figure 3. The estimated wind reaches a near zero value at the surface for each event, as expected from surface friction. We find a good agreement between the estimated PDF and the MCD range of wind velocities for S0986c and S1034a up to 500 m altitude. For S0981c (Figure 3a), both solutions yield low absolute wind values ($${< } 5$$ m/s), but they have opposite directions above 250 m altitude. Again, the region of high probability in the estimated PDF is outside the range delimited by the dashed lines, that is, they do not match values permitted by the MCD interpolation grid.

Figure 3

PDFs of the posterior distribution of wind speed profiles estimated for S0981c (a), S0986c (b) and S1034a (c) in the azimuth of each impact. These distributions are not a direct result of the inversion, but are instead obtained by considering that the temperature and thermodynamic sound speed profiles given by MCD are exact. Consequently, the wind speed PDF is estimated from $$\text{pdf}\left[{w}_{\text{baz,}\,\text{est.}}(z)\right]=\text{pdf}\left[{\alpha }_{\text{eff,}\,\text{McMC}}(z)\right]-{\alpha }_{\text{T,}\,\text{MCD}}(z)$$. The MCD wind profile in the event$$\to $$receiver azimuth and its variability over a GCM grid cell is shown with plain and dashed black lines.

5 Discussion

The inversion of S0981c yields an ensemble of atmospheric model valid above 500 m, with $$\pm 4$$ m/s sound speed uncertainty. This is surprising as its source is the most distant (240.6 km from InSight) and it has a low signal-to-noise ratio in Figure 1. Despite the long propagation distance causing high-frequency signal attenuation, S0981c has more group velocity data points at low-frequency compared to S0986c and S1034a. These low-frequencies help constrain atmospheric structures with larger wavelengths, including higher altitudes.

The results also show differences between the inverted PDFs of effective sound speed and the MCD predictions for event S0981c, with lower values of $${\alpha }_{\text{eff}}$$ above 500 m altitude. These differences might be due to an atmospheric phenomenon that cannot be captured at the scale of GCM simulations. Assuming temperature is less variable than wind near InSight at night, estimated wind profiles (Figure 3a) indicate that a small $${\sim} 2$$ m/s wind difference above 500 m altitude can explain the discrepancy in $${\alpha }_{\text{eff}}$$. Notably, winds in the event$$\to $$receiver direction are lowest for S0981c. At 200 m altitude, the true wind blows from East to West at around 10 m/s (see, Figure S10 in Supporting Information S1), while the crater lies directly south of InSight. Thus, an atmospheric phenomenon causing a slight shift in South-North winds could result in a negative amplitude in the event$$\to $$receiver direction without altering the predicted dominant East$$\to $$West flow.

Gravity waves, among other phenomena, can cause wind perturbations. Banfield et al. (2020) report examples of gravity waves detected by the APSS pressure sensor, with horizontal wavelength of 30 km and associated wind perturbation of 1–2 m/s. Recently, Onodera et al. (2024) claimed the detection of multiple gravity wave signals with high correlation between the pressure sensor and seismometer of InSight. A significant portion of the reported events occur at sunset, between 20 and 0 hr LMST, a window matching the time of event S0981c. The authors also identify a family of gravity wave events originating from 0 to 30° of azimuth. If it were to occur on sol 981, such gravity wave could generate a wind perturbation comparable to the mismatch of the PDF and MCD models. This hypothesis remains unfortunately challenging to test, as the pressure sensors were off at this stage of the mission, and the low frequency seismic data is heavily contaminated by glitches on sol 981.

6 Conclusion

Impact-generated infrasound were recorded for the first time on Mars by the seismometers of the InSight lander. We use this unique dataset to probe the structure of effective sound speed and winds in the Martian Planetary Boundary Layer. We invert the effective sound speed in the first 2 km of the Martian atmosphere using the infrasound group velocity measured for events S0981c, S0986c and S1034a. The inversion constrains the atmosphere mostly below 500 m altitude and confirms the presence of a waveguide above the surface, where $${\alpha }_{\text{eff}}$$ is increasing with altitude.

The precise characterization of winds in the lower Martian atmosphere was identified as one of the priorities in support of future human exploration (MEPAG, 2020). To this aim, our inverted data points may be used to evaluate the description of the nighttime boundary layer by any climate models. In this work, inverted profile agree with and validate the outputs of the Mars Climate Database within 2 m/s. We show that remaining differences between modeled and inverted profiles can be explained by wind fluctuations not captured at the MCD resolution. Hence, our results call for further investigation of possible causes of nighttime wind perturbations, for example, through the use of mesoscale models. This could particularly help understand the role of gravity waves in nighttime turbulence, as has already been identified near InSight (Murdoch et al., 2023; Temel et al., 2022).

Acknowledgments

We are grateful to the two anonymous reviewers for their constructive comments. This article is InSight Contribution Number 265 and LA-UR-23-33646. The authors acknowledge NASA, CNES, their partner agencies and institutions (UKSA, SSO, DLR, JPL, IPGP-CNRS, ETHZ, IC, and MPS-MPG) and the flight operations team at JPL, SISMOC, MSDS, IRIS-DMC, and PDS for providing the SEED SEIS data. Authors received financial support from CNES, ANR MAGIS (ANR-19-CE31-0008-08), the Initiative d’Excellence (IdEx) Université Paris Cité (ANR-18-IDEX-0001), The Center for Earth of Space Science (CSES) of LANL, as well as the Research Council of Norway (AIR project, 335903).

Open Research

Data Availability Statement

Data from the SEIS instrument of the InSight mission is available from the SEIS data service (InSight Mars SEIS Data Service, 2019a; InSight Mars SEIS Data Service, 2019b). The Mars Climate Database version 5.3 and above can be downloaded from https://www-mars.lmd.jussieu.fr/.