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1. nature
2. nature communications
3. articles
4. article

The shallow structure of Mars at the InSight landing site from inversion of
ambient vibrations
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* Open Access
* Published: 23 November 2021

THE SHALLOW STRUCTURE OF MARS AT THE INSIGHT LANDING SITE FROM INVERSION OF
AMBIENT VIBRATIONS

* M. Hobiger1 na1 nAff6,
* M. Hallo ORCID: orcid.org/0000-0001-5865-77671 na1,
* C. Schmelzbach ORCID: orcid.org/0000-0003-1380-87142 na1,
* S. C. Stähler ORCID: orcid.org/0000-0002-0783-24892,
* D. Fäh1,
* D. Giardini ORCID: orcid.org/0000-0002-5573-76382,
* M. Golombek3,
* J. Clinton ORCID: orcid.org/0000-0001-8626-27031,
* N. Dahmen ORCID: orcid.org/0000-0002-9114-67472,
* G. Zenhäusern ORCID: orcid.org/0000-0001-9401-49102,
* B. Knapmeyer-Endrun4,
* S. Carrasco ORCID: orcid.org/0000-0002-6207-87574,
* C. Charalambous ORCID: orcid.org/0000-0002-9139-38955,
* K. Hurst ORCID: orcid.org/0000-0002-3822-46893,
* […]
* S. Kedar ORCID: orcid.org/0000-0001-6315-54463 &
* W. B. Banerdt3
* -Show fewer authors

Nature Communications volume 12, Article number: 6756 (2021) Cite this article

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ABSTRACT

Orbital and surface observations can shed light on the internal structure of
Mars. NASA’s InSight mission allows mapping the shallow subsurface of Elysium
Planitia using seismic data. In this work, we apply a classical seismological
technique of inverting Rayleigh wave ellipticity curves extracted from ambient
seismic vibrations to resolve, for the first time on Mars, the shallow
subsurface to around 200 m depth. While our seismic velocity model is largely
consistent with the expected layered subsurface consisting of a thin regolith
layer above stacks of lava flows, we find a seismic low-velocity zone at about
30 to 75 m depth that we interpret as a sedimentary layer sandwiched somewhere
within the underlying Hesperian and Amazonian aged basalt layers. A prominent
amplitude peak observed in the seismic data at 2.4 Hz is interpreted as an Airy
phase related to surface wave energy trapped in this local low-velocity channel.

Download PDF

INTRODUCTION

Mars has been the target of a large number of planetary science missions
involving flybys, orbiters, landers, and rovers that have focused on surface and
atmospheric remote sensing as well as surface geochemistry and mineralogy.
NASA’s InSight (Interior Exploration using Seismic Investigations, Geodesy and
Heat Transport) mission is the first to specifically target the subsurface using
seismic methods1 (see Supplementary Fig. 1 for a map of the landing region in
Elysium Planitia), deploying a very broad-band seismometer2 (SEIS). SEIS
operates continuously with the primary goal to detect marsquakes in order to
quantify Martian seismicity3,4 and to infer the interior structure of Mars at
all scales5. First results from the analysis of the SEIS data provide new
information on the large-scale internal structure, physical properties, and
tectonic activity of Mars3,6. Seismic studies of the shallow subsurface around
the InSight landing site so far5 have been limited to the uppermost 10−20 m
using seismic-traveltime measurements7 and ground compliance estimates8,9,
leaving structures at few tens to several hundreds of meters depth uncharted.

Detailed near-surface models can provide direct constraints for understanding
the processes that formed Elysium Planitia. Such models are required to
understand the stratigraphy and the role of volcanism as well as sedimentation
in the transition zone of the dichotomy between ancient southern heavily
cratered highlands and low-standing younger, smoother northern plains. The
surface plains near the dichotomy boundary on which InSight landed is mapped as
an Early Hesperian Transition (3.7−3.4 Ga) unit that could be volcanic or
sedimentary deposits10 from the 2 km high dichotomy to the south11. Geologic
mapping in high-resolution images, rocky ejecta craters, mafic minerals in
visible and infrared spectra and the presence of wrinkle ridges all argue that
the plains around InSight are underlain by about 200−300 m of layered basalts12.
Furthermore, small craters without rocky ejecta, images of nearby escarpments
and thermophysical properties argue for about 3 m of overlying dominantly sandy,
impact-generated regolith13. With its geophysical instrument suite, InSight is
the first mission capable of investigating the near-surface beyond a few
centimeters of depth. Such information will provide valuable ground truth to
orbital-data based surface and subsurface models.

The ground at the InSight landing site is in continuous motion, even during
periods without marsquake-related shaking. The composition of the Martian
ambient seismic wavefield is different from the terrestrial case, as two of the
main sources of seismic ambient vibrations on Earth, oceans and anthropogenic
activity, are absent. The oceans on Earth act as a very efficient way to
transfer atmospheric energy into seismic energy. On Mars, wind−surface
interaction is the main source of seismic ambient vibrations14. InSight
observations show that the level of ambient seismic vibrations on Mars is low
due to the absence of oceans, the hundred-fold thinner atmosphere and the around
50% reduction in the solar irradiation compared to Earth. The minimum seismic
noise level is found between 0.05 and 5 Hz5, with amplitudes significantly below
the Earth low noise model15.

SEIS records ambient vibrations, including those generated by lander motions,
that create a broad-band background signal. The amplitude of the low-frequency
(0.03−1 Hz) ambient seismic vibrations recorded by SEIS has been observed to be
frequency-dependent and strongly related to environmental effects such as wind
during the day16. In contrast, in the evening, the observed winds often drop
significantly and during this period and for the studied low-frequency window
between 0.3 and 1 Hz, it was concluded16 that the recorded polarized seismic
signals may indeed correspond to the wavefield of the Martian ambient seismic
background vibrations.

Across the first Martian year of InSight operation, highly repeatable wind
patterns were observed with steady winds during the morning and gusty winds
every afternoon resulting in periods of increased high-frequency noise
(Fig. 1a). Example spectrograms of single sols displayed in Fig. 2a show that
these noisy time periods are characterized by a number of discrete spectral
peaks (most prominently at 3.3, 4.1 and 6.8 Hz17; sol is a solar day on Mars).
These peaks are interpreted as eigenmodes of mechanical lander parts and the
lander’s solar arrays17,18 and cannot be produced by the underground structure
below the station.

Fig. 1: 2.4 Hz mode observation across the InSight mission.

a Vertical-component energy between 2.3 and 2.5 Hz for sols 80−650. Each row
corresponds to the data from one sol plotted against local mean solar time
(LMST). Vertical white dashed lines indicate sunrise and sunset. b Power
spectral density (PSD) plots averaged over 20 sols extracted for the time
windows marked in the spectrogram in (a). Note specifically the stable shape of
the peak around 2.4 Hz across the entire mission duration. Evenings are
generally quieter and more stable than any other time of day. The peak power
level of the 2.4 Hz mode marked by the dashed line weakly depends on the wind
speed17. In comparison, the lander-related mode at 3.3 Hz (black arrows) changes
its peak frequency and amplitude level considerably depending on wind and
temperature.

Full size image
Fig. 2: Frequency-domain characteristics of sols 422 and 423 SEIS data.

a Vertical-component spectrogram of sols 422 and 423. Typically, mornings and
afternoons show high levels of wind-induced noise, while evenings and nights are
characterized by significantly lower ambient noise levels due to largely absent
local winds. Note the lander-related modes (e.g., at 1.6, 3.3, 4.1, 6.8 Hz) that
show a time-dependent change of their resonance frequencies. The lander-related
modes correlate with the wind activity, suggesting that winds shaking the lander
are the cause of these resonances. b H/V ratio for the same data as in (a).
During quiet time intervals such as in the evening hours, the ambient vibration
power spectrum is relatively flat with the prominent exception of a distinct H/V
trough at around 2.4 Hz. (right) Three H/V curves extracted for two windy and
one quiet period of sols 422/423. The orange curve corresponds to the steady
morning wind time window, the green curve to the turbulent afternoon time window
and the red curve to the quiet evening time window (see colored bars marking the
time windows).

Full size image

During summer months at the landing site (sols 180−450), extended periods with
very low winds occur each evening beginning around dusk (Fig. 1a). In absence of
local wind-induced noise, the ambient seismic spectrum is relatively flat
between 1.5 and 8 Hz, with the prominent exception of a distinct spectral peak
at 2.4 Hz in the vertical-component data (Figs. 1 and 2). This peak at 2.4 Hz is
clearly distinct from the lander-related eigenmodes as its shape is much
broader, it is predominantly vertically polarized in contrast to the primarily
horizontally polarized lander-related modes, and, most importantly, is not
temperature-modulated in frequency in contrast to the lander-related modes17
(Fig. 1b). Furthermore, the peak at 2.4 Hz is the only resonance phenomenon
excited by marsquakes3,4,17. A weak proportionality is observed between the
amplitude of the 2.4 Hz peak and the measured wind between 4 and 6 m/s;
furthermore, the 2.4 Hz peak is unaffected by short wind bursts and strong
winds17. The wind-induced amplitude increase of the 2.4 Hz peak is about 200−500
times weaker than the increases observed for the resonances that are recognized
to originate on the lander17. Nevertheless, a mechanical resonator such as the
solar panels, assuming a different temperature- and wind-dependent behavior than
the lander-related modes, has been discussed within the SEIS team as an
alternative mechanism for the 2.4 Hz peak. Still, the 2.4 Hz peak is the only
observed ambient seismic vibration that could be produced as the natural seismic
response expected by the heterogeneous local subsurface at the landing site in
Elysium Planitia.

The Martian ambient seismic vibrations are expected to be generated mainly by
the wind interacting with topography14, and, similar to Earth, to be composed of
all types of seismic waves19,20,21. Because the source is at the surface, the
ambient vibration seismic wavefield will predominantly consist of surface waves,
namely Rayleigh and Love waves, modulated by the local subsurface structure on a
scale of a few wavelengths around an observation point. Rayleigh waves have an
elliptical motion in the vertical plane and their frequency-dependent elliptical
polarization depends on the local subsurface properties22,23,24,25.

On Earth, the horizontal-to-vertical spectral ratio (H/V) of ambient seismic
vibrations has been used for decades in engineering seismology for site
characterization20,26. Numerical and field studies have shown that the H/V ratio
is closely related to Rayleigh wave ellipticity, which is determined by the
local subsurface layering27. Several techniques have been developed to extract
the Rayleigh wave ellipticity from an ambient wavefield of unknown composition,
suppressing, for example, Love wave contaminations of the horizontal components
(e.g., Single-station determination of Rayleigh wave ellipticity by using the
random decrement technique, RayDec28). Furthermore, the inversion of the
ellipticity values for the subsurface structure has been a topic of intense
research29,30,31,32,33. Nevertheless, Rayleigh wave ellipticity curves alone are
not sufficient to retrieve the subsurface structure without additional
constraints30,34 because ellipticity is a unitless property and, hence, does not
carry information on absolute velocities of the underground, but only on the
relative shape of the velocity profile. Given the success of H/V and Rayleigh
wave ellipticity analyses on Earth, the potential to constrain the Martian
subsurface structure using the ellipticity obtained by analyzing ambient
vibrations was proposed before the mission24,25.

In this work, we perform a Rayleigh wave ellipticity analysis focusing on data
recorded during a representative quiet-period time window. For the first time,
using this classic seismological technique, we resolve the shallow subsurface
stratigraphy at the InSight landing site in Elysium Planitia on Mars to around
200 m depth, and are able to infer aspects of the local geologic history in
detail. While our seismic velocity model is largely consistent with the expected
layered subsurface structure consisting of a thin regolith layer above stacks of
lava flows, we find a seismic low-velocity zone at about 30−75 m depth that we
interpret as a sedimentary layer somewhere within the Hesperian and Amazonian
aged basalt layers. The prominent amplitude peak observed in the seismic data at
2.4 Hz is interpreted as an Airy phase related to surface wave energy trapped in
this local low-velocity channel.

RESULTS

DATA SELECTION

We carry out a Rayleigh wave ellipticity analysis focusing on data recorded
during a representative quiet-period time window of 7 h length in the night from
sol 422 to 423 (Sol 422 18:08:21 to Sol 423 00:57:07 local mean solar time
(LMST), corresponding to 3 February 2020, 14:15:00 to 21:15:00 UTC). Whereas H/V
curves computed from the windy periods show a large variability and are
dominated by the lander-related modes, the H/V ratio for the quiet evening is
stable over the whole mission. In these time periods, the local wind at the
landing site is relatively low and too weak to generate lander-related
disturbances by wind-induced shaking. Nevertheless, surface waves that compose
the ambient vibration field at the sensor can still be generated by distant
sources.

The H/V curves are largely constant for the frequency band between around 1.5
and 8 Hz except for the prominent trough at 2.4 Hz (Fig. 2b). Although a direct
interpretation and inversion of H/V curves is possible35, this requires an
isotropic wavefield and equipartitioning of the seismic energy among the
different wave modes36. Previous InSight studies suggest an isotropic wavefield
for the 0.3−1 Hz band in the quiet evening hours16. For the evening data window
used in this study, we find at 2.4 Hz predominately elliptical motion patterns
in the vertical plane with no preferred propagation direction using a
polarization analysis technique based on37,38 (Fig. 3). These observed
polarization patterns indicate that Rayleigh waves generated by randomly
distributed sources are likely the dominant component of the analyzed ambient
vibrations wavefield at 2.4 Hz. The extracted polarization attributes are a
further evidence of the subsurface-related nature of the 2.4 Hz peak, as the
lander-related resonances exhibit highly repeatable polarization azimuths.
Nevertheless, estimating polarization attributes depends on the chosen approach
and user-defined parameters such as the analysis window, and hence comes with
some uncertainty. To extract the ellipticity of Rayleigh waves from the recorded
data, we use the RayDec method28. RayDec is a powerful tool to retrieve the
Rayleigh wave ellipticity by statistical means, even in cases when isolated
Rayleigh waves are difficult to identify in the measured wavefield and the
overall observed polarization pattern is complicated.

Fig. 3: Polarization analysis of the entire data window from sol 422 to 423 at a
frequency of 2.4 Hz.

a Propagation azimuth between 0° and 180°, with a 180° ambiguity. b Tilt angle
of the major semiaxis of the ellipse from the vertical in propagation (radial)
direction. c Tilt angle of the major semiaxis of the ellipse from the vertical
in transverse direction.

Full size image

The frequency-dependent Rayleigh wave ellipticity functions obtained by the
RayDec method for the quiet time period are shown in Fig. 4. The shape of the
curves is relatively similar to the H/V curves displayed in Fig. 2b, but the
absolute ellipticity values are smaller than the H/V values. These smaller
values are expected because wavefield components other than Rayleigh waves such
as Love waves are mainly present on the horizontal components and are suppressed
by the RayDec processing. Between 1.5 and 2.0 Hz, the curve is relatively flat
with an ellipticity of about 0.7. At 2 Hz, we expect a strong influence of the
first harmonics of the so-called 1-Hz tick noise, which is an electronic
cross-coupling noise observed on all data acquired by SEIS39. Between 3 and
8 Hz, a plateau at a value of about 0.7 without significant peaks is observed.

Fig. 4: Extracted Rayleigh wave ellipticity curve compared with modeling results
for pre-mission near-surface seismic models.

The thick black line shows the Rayleigh wave ellipticity curve extracted for a
7-h duration time window in the evening of sol 422/423 (see Fig. 2). The
vertical bars show the estimated data errors. Note that the errors were manually
increased for the frequency range around 2 Hz that is known to be affected by
monochromatic electronic cross-coupling noise39. Ellipticity curves for the
fundamental and first higher Rayleigh wave modes computed for the two velocity
models are shown in red and blue, respectively (models 1 and 2; Tables 1 and 2).
Note that neither of the modeled Rayleigh wave ellipticity curves is able to
explain the observed trough at 2.4 Hz.

Full size image

The prominent trough at 2.4 Hz dominates the ellipticity curve between 2 and
3 Hz (Fig. 4). For comparison, on Earth, low H/V values across a wide frequency
range have been reported to be related to low-velocity layers at depth40. For a
seismic station in southern Italy, ellipticities below 1 between about 1.5 and
9.0 Hz were found41. The station was located on rigid conglomerates of about
15 m thickness over clays with lower velocity and a thickness of about 300 m. At
another site close to Mount Etna on the island of Sicily, low H/V values were
found for locations where high-velocity lava flow deposits overlay low-velocity
sedimentary layers42.

FORWARD MODELING

In a first attempt to interpret the observed Rayleigh wave ellipticity curve, we
tested its compatibility with layered subsurface structures derived in
pre-landing studies and based on first InSight results5,12,13,24,43,44,45,46. In
summary, the subsurface at the landing site is expected to consist of a thin
(< 5 m) regolith layer on top of stacks of fractured basaltic lava flows. Below
the basaltic unit, a weak sedimentary layer has been suggested at a depth of
around 150−200 m based on the analysis of flooded impact craters near the
lander. Loosely based on refs. 24,45, we established two conceptual S-wave (vS)
and P-wave (vP) velocity models of the shallow subsurface (< 200 m) summarized
in Tables 1 and 2 reflecting a stepwise increase in seismic velocities with
depth down to the low-velocity sedimentary layer at depth (see also “Methods”
section). Conceptual model 2 primarily differs from model 1 in that the seismic
velocities are overall lower based on the expectation that impact cratering can
be effective at cracking rock to significant depths, and that the weak and even
fissile sedimentary rocks on Mars likely have low seismic velocities.

Table 1 Simplified near-surface reference model (referred to as model 1; loosely
based on Knapmeyer-Endrun et al.24,25,45).
Full size table

We computed the theoretical Rayleigh wave ellipticity curves for the two models
and found that neither of these subsurface models leads to Rayleigh wave
ellipticity curves that even closely resemble the observed curve with a trough
at 2.4 Hz (Fig. 4). Also, the observed ellipticity curve cannot be explained by
the ellipticity of the first higher Rayleigh wave mode either. These findings
motivated us to perform a series of inversions of the observed Rayleigh wave
ellipticity curve for the Sol 422/423 data to resolve the vS- and vP-structure
of the topmost 200 m at the InSight landing site, using the reliable part of the
ellipticity curve between 1.5 and 8.0 Hz. For these inversions, we assume that
the extracted Rayleigh wave ellipticity curve reflects the fundamental mode
only. In general, the fundamental mode of Rayleigh waves exists at all
frequencies and higher modes are only present above certain frequencies, where
they may be even more energetic than the fundamental mode. In that case, a
mixture of different modes would be visible in the ellipticity curve as well.
The flat shape of the measured ellipticity curve between 3 and 8 Hz strongly
suggests that higher Rayleigh wave modes do not carry a significant amount of
energy within the 3−8 Hz frequency band.

BAYESIAN INVERSION

The inversion of the Rayleigh wave ellipticity curve to retrieve the underground
1D seismic velocity structure is a non-linear inverse problem characterized by
significant inherent non-uniqueness. This inversion is particularly challenging
due to ambiguous solutions, and in particular, if only very limited near-surface
information is available to constrain the inversion. We perform multiple
inversions of the ellipticity data in a Bayesian framework utilizing both flat
and depth-dependent constrained prior expectations of the underground structure.
The applied inversion technique32 relies on a trans-dimensional formulation of
the parameter space where the number of layers is an unknown parameter
itself47,48. The number of layers is treated as inversion parameter governed by
the law of parsimony49; we strive for the simplest possible layered models, but
not simpler than required by the data.

A first inversion with flat priors was used to infer the underground structure
without subjective influence on the solution (Fig. 5). Additional inversion runs
using parameter value constraints by depth-dependent bounds based on subsurface
model 2 (Table 2; depth-dependent bounds are prescribed to parameters vS, vP and
Poisson’s ratio) and additional inversion runs with fixed numbers of layers were
used to further explore the parameter space and support the inferred results
(Fig. 6 and Supplementary Figs. 3 and 4). These inversion tests and results are
described in detail in the “Methods” section.

Fig. 5: Result of the inversion of the Rayleigh wave ellipticity curve using a
flat prior probability density function (PDF).

a, b show the posterior marginal probability density functions of vS and vP,
respectively. c Histogram of the occurrence of layer interfaces. d Extracted
(black line) and modeled ellipticity curves for models drawn from the posterior
PDF (ML maximum likelihood, MAP maximum a posteriori). Vertical bars indicate
the expected data error (used as inverse data weight). e Posterior histogram of
the number of layers.

Full size image
Table 2 Modified near-surface reference model (referred to as model 2). The
numbers in brackets mark the full range explored in the inversion (i.e. bounds
of the depth-dependent multizonal prior PDF).
Full size table
Fig. 6: Result of the Rayleigh wave ellipticity inversion constrained by bounds
from model 2.

a, b show the posterior marginal probability density functions (PDF) of vS and
vP, respectively. c Histogram of the occurrence of layer interfaces. d Extracted
(black line) and modeled ellipticity curves (ML maximum likelihood, MAP maximum
a posteriori). Vertical bars indicate the expected data error. e Posterior
histogram of the number of layers.

Full size image

INFERRED SEISMIC VELOCITY MODELS

The Rayleigh wave ellipticity data depend mainly on the S-wave velocity
structure below the measurement site. Hence, the inference of the vS-profile is
of primary interest. The vP-profiles are constrained by plausible value ranges
for the Poisson’s ratio for the expected rock and soil (i.e., 0.2−0.4). The
ellipticity data reflect velocity contrasts in depth rather than absolute values
of velocities, and the inversion results may be affected by trade-offs between
absolute values of velocity and interface depth. Hence, a large family of
different models can explain the data equally well. Furthermore, our layer-based
Bayesian inversion favors simple models (i.e., with a minimum number of layers)
over models with a large number of layers (i.e., a staircase-like representation
of a gradual velocity change).

We focus our interpretation on common and robust features found in all inversion
results displayed in Figs. 5 and 6, rather than interpreting a single final
model. For illustration purposes, we display models with the least data misfit
(ML model) and the maximum a posteriori (MAP) model estimate. Our MAP model
estimate corresponds to the layered vS-model from the ensemble of solutions that
has the smallest L1-norm misfit with the most probable posterior vS-profile32.
The green and light blue curves (mean and median profiles, respectively)
displayed in Figs. 5 and 6 provide in addition an overall impression of the
probable velocity changes with depth.

Due to the limited frequency bandwidth of the ellipticity curve ranging from 1.5
to 8 Hz and lacking higher-frequency information, the shallowest part of the
model is only poorly resolved. According to the guidelines of the InterPACIFIC
project50, a surface wave inversion can constrain the velocity structure below
about half of the minimum used wavelength. According to Supplementary Fig. 5,
the Rayleigh wave phase velocity of the MAP model at 8 Hz is around 200 m/s,
corresponding to a wavelength of about 25 m. This rough estimation indicates
that we cannot constrain the shallowest 12.5 m and we are cautious not to
overinterpret our results for the uppermost 20 m.

A particular feature of the extracted ellipticity curve are unusually low values
below 1 (see Fig. 4), which have been found to be indicative of low-velocity
layer(s). Indeed, a low-velocity layer between around 30 and 75 m depth, not
present in the pre-landing models (see dashed line in Figs. 5a, b and 6a, b),
was found to be a robust feature of the inversion results displayed in Figs. 5
and 6 based on various tests with different input parameters and constraints.
Even though the primary feature of the Rayleigh wave ellipticity data is the
prominent trough at 2.4 Hz, the constant ellipticity values and absence of
additional peaks and/or troughs between 1.5 and 8 Hz additionally constrain the
models. To test the robustness of the results, we performed additional inversion
tests with ellipticity data from the limited frequency bands of 1.5–3 Hz and
1.5–4 Hz. These resulted in velocity profiles similar to those using the full
bandwidth, but with an increased overall uncertainty, especially in the
shallower part (< 20 m depth). However, a low-velocity zone was found in all
tests using limited frequency bands, highlighting that this feature is related
to the 2.4 Hz trough.

For the following geological interpretation, we revert to the ML and MAP models
extracted from the weakly constrained and model-2 constrained inversion runs
that are summarized in Fig. 6a, b.

REGOLITH AND COARSE BLOCKY EJECTA LAYER

While the Rayleigh wave ellipticity inversion for frequencies below 8 Hz has a
limited resolution for the topmost around 20 m depth, the comparison of
forward-modeled and measured data still allows us to rule out shallow subsurface
features that lead to ellipticity curves inconsistent with the actual
observations. Based on such forward-modeling tests, we found that the shallowest
layer with vS < 150 m/s (vP < 300 m/s) cannot be thicker than 1−1.5 m, and a
significant increase to S-wave velocities above 400 m/s (vP > 700 m/s) below
that depth is required, otherwise a high-value Rayleigh wave ellipticity peak
should be visible below 8 Hz. Both the velocity values and the relatively small
thickness of the top low-velocity layer are consistent with previous compliance
inversions5,9 and the seismic-traveltime measurements5, suggesting vS and vP
values of 84–152 and 136–304 m/s close to or at the surface, respectively.
Furthermore, the compliance inversions indicate a relatively thin uppermost
layer of less than about 2 m thickness and a structural discontinuity between
0.7 and 7 m depth5,9.

The low seismic velocities in the upper few meters of the surface are likely
produced by an impact-fragmented regolith built up by cratering of basalts and
eolian processes during the Amazonian after the formation of the Homestead
hollow crater, where InSight is located, about 400−500 Myr ago11,13,51 (regolith
layer in Fig. 7c). The regolith is dominated by sand-sized particles that are
mostly unconsolidated with low densities, based on interpretations of thermal
inertia and observations of soils (and few rocks), and thermal conductivity
measurements around the lander13,52,53. Estimates of the thickness of this
mostly sandy regolith layer are based on the source depth of observed ejecta.
Fresh 30−60-m-diameter craters with non-rocky ejecta in the vicinity of InSight
suggest a variable, but likely around 3-m-thick regolith layer near the
lander12,52.

Fig. 7: Interpretation of the seismic velocity models.

a, b show vS models for the weakly constrained (flat prior) and model-2
constrained inversion, respectively (see Figs. 5 and 6). The maximum likelihood
(ML) and maximum a posteriori (MAP) models that both explain the observed
ellipticity are displayed together with the two pre-landing subsurface models
(gray dashed lines; reference models 1 and 2). Note that the low-velocity zone
between around 30 and 75 m is a consistent feature found with both inversion
approaches. Furthermore, note that the uppermost 20 m are not well resolved in
both inversion runs. c Geological interpretation of the inferred models.

Full size image

High-resolution images of scarps in similar terrain nearby indicate that this
relatively sandy surface unit grades into coarse breccia and then jointed
bedrock51. The uppermost meter of regolith is most likely finer-grained material
than at deeper levels because small impacts generally break up the near-surface
material more readily than at deeper levels where fewer large impacts penetrate.
Within the topmost fine-grained sand layer, the seismic velocity increase is
governed primarily by compaction44. At some depth, basaltic blocky ejecta with a
higher seismic velocity (vS of around 1800 m/s44,54) mixed with the fine-grained
sand will lead to an increase of the bulk seismic velocity (blocky ejecta layer
in Fig. 7c). The significant velocity increase at 1–2 m depth required by the
compliance inversions9 reflect this change in regolith composition, or a
significantly shallower regolith thickness at the landing site than suggested by
orbital observations.

AMAZONIAN AND HESPERIAN BASALTIC LAVA FLOW UNITS

Beneath the lander, the top of the basaltic bedrock is estimated to be below 3 m
depth. Geological mapping reveals volcanic vents and flow fronts that partially
fill large craters13, mafic mineral spectra46, and the presence of wrinkle
ridges, which have been interpreted as fault-propagation folds in weakly bonded,
but strong layered materials such as basalt flows55. The thickness of the
Amazonian (1.7 Ga) and Hesperian (3.6 Ga) basalt flows51,56 has been estimated
from the lack of rocks in the ejecta of large (>2 km) fresh craters13 and from
depth- and rim height−diameter relations of partially filled older and larger
craters46. Near the lander, these estimates indicate that the Amazonian and
Hesperian basalts are 160−180 m thick. These basalts are consistent with the
high subsurface seismic velocities above about 175 m (likely vS > 1800 m/s)54
and the thickness estimates from partially filled craters (Amazonian and
Hesperian basalts in Fig. 7c). Beneath the basalts, phyllosilicate-bearing
layered sedimentary rocks have been documented in the central peaks of large
impact craters46. These physically weak sedimentary deposits are likely of
Noachian age (>3.7 Ga) and are probably responsible for the lower seismic
velocities below the Hesperian basalts at 175 m depth (sedimentary rock in
Fig. 7c).

LOW-VELOCITY SEDIMENTARY UNIT SANDWICHED BETWEEN LAVA FLOWS

The discussion above thus could readily explain the low seismic velocities in
the top few meters (sandy, impact-fragmented regolith), the higher seismic
velocities between 25 and 175 m (strong layered basalt flows), and the lower
seismic velocities below 175 m (sedimentary deposits). The existence of the
low-velocity zone spanning between around 30 and 75 m depth requires further
explanation. The top of this low-velocity zone is less well resolved and is
located at a depth somewhere between 25 and 40 m, whereas the bottom, located
somewhere between 75 and 90 m depth, is a robust feature generally present
through the whole ensemble of solutions and also different inversion settings.

The age of the basalt flows beneath the lander has been estimated from the
size-frequency distribution of craters and cratering production functions. For
craters with diameter above 2 km, the crater numbers indicate an Early Hesperian
age (~3.6 Ga)51. However, for craters with diameter 200−700 m, the crater
distribution suggests an Amazonian age (~1.7 Ga)51,56, indicating a younger
resurfacing. As a result, there are ~2 Ga between the deposition of the
Hesperian basalts and the younger resurfacing Amazonian basalts. To the south of
the InSight lander, there are Noachian through Hesperian transition units10 that
indicate active erosion and deposition of sedimentary materials near the
dichotomy boundary of the southern Noachian highlands and the northern plains.
To the east, Amazonian-Hesperian transition units include the Medusae Fossae
Formation10, which is older than the Amazonian basalts. To the south, some of
the Amazonian-Hesperian transition units10 are sedimentary deposits at least
10−30 m thick46 and alluvial activity has occurred further south in the Gale
crater during the interval between the deposition of Hesperian and Amazonian
basalts beneath InSight57,58. As a result, it is reasonable that the
low-velocity zone spanning between 30 and 75 m depth could be a layer of
sedimentary deposits sandwiched either between the Hesperian and Amazonian
basalts (sediments in Fig. 7c) or somewhere within the Amazonian basalts.

DISCUSSION

Surface waves generated by sources like the interaction of wind with topography
are ubiquitous on Earth, and are expected to be present on Mars. Regional-scale
aeolian activity modeling around the Mars 2020 landing sites showed that strong
winds are expected sol-around at topographic slopes59. Because the local
topography around the InSight lander is relatively flat, the surface-wave source
regions are likely located at regional distances around InSight, such as large
craters and/or the topographic step of the dichotomy, though currently we cannot
determine their exact locations.

As surface-wave trains propagate along the surface of a planet, the local
subsurface structure on the scale of a few wavelengths around an observation
point modifies their characteristics, leading to, for example, dispersion
phenomena60. Low-velocity zones result in channel waves (trapped waves) and the
build-up of amplitude for dispersed wave trains propagating as normal modes,
generally termed Airy phase60. Airy phases are stationary phases associated with
a minimum in the frequency-dependent group velocity that can propagate over
considerable distances. For example, for continental travel paths, Airy phases
at periods of 15−20 s are a prominent feature of terrestrial seismograms61. On
local scales, Airy phases related to (low-velocity) coal seams are a
well-studied phenomenon62.

We find that a low-velocity layer is required to explain the observed
ellipticity curve. We interpret the prominent peak at 2.4 Hz observed in the
vertical-component SEIS data as an Airy phase with associated amplitude
build-up. The modeling of group and phase velocities for representative 1D
velocity models displayed in Figs. 5 and 6 shows a clear group-velocity minimum
at 2.4 Hz (see Supplementary Fig. 5).

This paper focuses on ambient vibrations, though the amplification of the
vertical-component motion at 2.4 Hz has also been observed in broad-band and
high-frequency marsquake recordings3,4,63. These observations of a consistent
excitation of the 2.4 Hz peak during events can be readily explained by
body-to-surface wave conversions close to the receiver at, for example,
topographic features (e.g., craters) and/or shallow subsurface heterogeneities.
Such body-to-surface wave conversions are commonly observed on Earth64,65,66.

METHODS

DATA PREPARATION

The 2.4 Hz mode is a very stable feature in the SEIS dataset and is persistently
visible on the recordings of Insight’s SEIS VBB (very broad-band) seismometer
during quiet periods17. We investigated the variation of seismic background
vibrations around and including the 2.4 Hz mode for the entire mission (see
Fig. 1). Figure 2 illustrates the large variability of the noise recorded by
SEIS during one sol. Windy time periods are not only characterized by elevated
ambient noise levels but also prominent lander-related modes. In contrast,
evening hours are usually very quiet with winds largely absent.

For the analysis reported here, we focused on a quiet 7-h long window of 100
samples-per-second VBB data recorded on the evening of Sol 422 (03/02/2020,
14:15 to 21:15 UTC, Sol 422 18:08–Sol 423 00:57 LMST; Fig. 2). We performed
polarization analyses in the time-frequency domain37,38 of the entire data
window. The polarization attributes (azimuth and tilt angles of the dominant
motion38) displayed in Supplementary Fig. 2 reveal that the particle motion in
this window and at 2.4 Hz is predominately elliptically polarized, with no
preferred propagation azimuth, and a vertical to near-vertical orientation of
the semimajor axis of the ellipse. Hence, the observed polarization indicates
that elliptically polarized Rayleigh waves are the dominant component of the
ambient seismic vibration at 2.4 Hz within our analysis window.

In this window, the lander-related modes were not excited. The H/V curves shown
in Fig. 2b were calculated using the Geopsy software33. For each signal, the H/V
curves for time windows of 120 s length were obtained according to

$$\frac{H}{V}\left(f\right)=\frac{\sqrt{{\left|E\left(f\right)\right|}^{2}+{\left|N\left(f\right)\right|}^{2}}}{\left|Z\left(f\right)\right|},$$
(1)

where E(f), N(f) and Z(f) are the spectra of the eastern, northern and vertical
components, respectively. The final H/V curve for each of the three analysis
windows is obtained as the geometric mean of the 120 s time windows.

We assume that we can retrieve Rayleigh wave ellipticity from the ambient
vibration wavefield recorded by SEIS for the fundamental mode of Rayleigh waves
using the RayDec method28. This method is based on the random decrement
technique67,68 where the basic concept is as follows: (I) a narrow frequency
filter is applied; (II) the zero-crossings from negative to positive amplitude
values are searched for on the vertical-component signal; (III) time windows of
a given length (corresponding to ten cycles at the given frequency in our case)
are extracted on all three components, shifting the horizontal signals by a
quarter-period of the selected frequency to compensate for the typical 90° phase
shift of Rayleigh waves; (IV) the two horizontal components are projected in a
direction maximizing the correlation with the vertical signal. Steps (III) and
(IV) are repeated for each zero-crossing and the resulting vertical and
horizontal signals are summed; (V) by calculating the square root of the ratio
of the energies in the respective vertical and horizontal signals, the
ellipticity at the given frequency is estimated; (VI) the processing is repeated
for each frequency of interest. The RayDec processing suppresses other wave
types than Rayleigh waves. Love waves are not present on the vertical component
and are therefore supposed to be canceled out by the averaging process. Body
waves do not show a phase shift between vertical and horizontal signals and
should be suppressed as well. However, large contributions of other wave types
on the horizontal components may lead to overestimated ellipticity values. The
RayDec-derived ellipticity curve is shown in Fig. 4. The signal was cut in
10-min windows and each of them was analyzed independently. The resulting curve
is the geometrical mean of these curves and the standard deviation is calculated
accordingly.

In order to test the robustness of our Rayleigh wave ellipticity estimation, we
compared the RayDec-derived ellipticity curve with other established techniques.
Another method to estimate the Rayleigh wave ellipticity is the calculation of
H/V using a time-frequency analysis (H/V TFA69). This approach performs a
continuous wavelet transform of the three-component signals, finds the maxima on
the vertical component and calculates the ratio between the 90° phase-shifted
horizontal- and vertical-component signals at the identified times. In this way,
transient Rayleigh waves are identified and their ellipticity is estimated.
Supplementary Fig. 2 shows an overview of the analyzed Sol 422 signals using the
classical H/V, RayDec and H/V TFA. In the Sol 422 data, the H/V curve shows the
clear trough around 2.4 Hz and is relatively flat with values around 1 Hz at
other frequencies between 1 and 8 Hz. At the trough frequency itself, the RayDec
and H/V TFA approaches both yield very low ellipticity values of about 0.4. H/V
TFA estimates even lower ellipticity values than RayDec in the other parts of
the curve, but both are significantly lower than the classical H/V curve.

The extracted ellipticity values are low when compared with Earth sites. In
theory, for a homogeneous half-space with a Poisson ratio of 0.25, the
ellipticity of Rayleigh waves is about 0.68 at all frequencies60. As a boundary
condition, the ellipticity of Rayleigh waves should approximate this value
towards low frequencies. For realistic underground models where velocity
increases with depth, the ellipticity value is frequency-dependent and shows a
peak at the fundamental frequency of the site23. For sites with a strong
velocity contrast, the peak frequency corresponds to a singularity in
ellipticity, where the vertical-component signal vanishes and the ellipticity
goes towards infinity29, followed by a trough at a higher frequency where the
horizontal component vanishes and ellipticity goes towards zero. In the observed
InSight data, we observe neither a singularity nor ellipticity values going
towards zero at the trough. This provides a constraint on the velocity
contrasts. In any case, ellipticity values below 1 are rarely observed over a
wide frequency range on Earth and are indicative for low-velocity zone(s)40,41.
For the inversion of the InSight data, we interpret the ellipticity values
assuming that they reflect the characteristics of the Rayleigh wave fundamental
mode in the frequency range from 1.5 to 8.0 Hz. The data errors estimated by the
RayDec method were manually increased around 2.0 Hz and above 3.5 Hz (increase
of 10% of the uncertainty multiplication factor in the logarithmic domain), to
account for the higher harmonics of the 1-Hz electronic cross-talk noise39 and
potential contamination with lander-related modes. These data errors work as an
inverse weight in the inversion procedure, meaning a higher error results in a
lower weight.

PRIOR SUBSURFACE MODELS TO CONSTRAIN THE INVERSION

To constrain the generally ambiguous inversion of ellipticity curves, we took
the near-surface (depths < 200 m) velocity models established before the
landing12,24,44,45 and the ones based on first results5 as a starting point to
establish suitable parameter space bounds of the inversion. A modified version
of the near-surface model proposed by24,45 is summarized in Table 1 (model 1).
The original model was condensed into a new model with fewer layers and the
proposed low-velocity layer at 170 m depth was added. For this study, we updated
model 1 in the following way to obtain the new conceptual model given in Table 2
(model 2): We expect to find a 3−6-m-thick low-velocity regolith layer at the
surface that gradually transitions into a unit of coarse blocky ejecta. At a
depth of a few tens of meters, heavily fractured basaltic rocks are expected,
consisting of stacks of few to several tens of meters thick lava flows. Impact
cratering is expected to be effective at cracking and breaking rocks at
significant depth and we therefore assume relatively low seismic vP velocities
of around 1500 m/s for the basaltic units. Below the lava unit, at a depth of
150−200 m, a weak sedimentary unit has been suggested13,46. We expect rather low
vP velocities of around 750 m/s for these sedimentary rocks based on the
observation that sedimentary rocks visited by rovers were observed to be very
weak, even fissile. The vS velocities were assigned keeping in mind the range of
plausible values of Poisson’s ratio of such rock and soil materials. Still,
neither of these conceptual reference models can explain the ellipticity trough
at 2.4 Hz as shown by the forward modeling in Fig. 4.

BAYESIAN INVERSION OF THE RAYLEIGH WAVE ELLIPTICITY CURVE

The inversion of the Rayleigh wave ellipticity curve to retrieve the underground
1D structure is a non-linear inverse problem characterized by significant
inherent non-uniqueness as different models may fit the data equally well.
Therefore, we perform the inversion of the ellipticity data in the Bayesian
framework retrieving posterior probability on the presence of a particular wave
velocity at depth. The applied inversion technique32 relies on a
trans-dimensional formulation of the parameter space, where the number of layers
is an unknown parameter itself47,48. The layered subsurface model is
parameterized by a variable number of Voronoi cells with assigned values of vS,
vP, and $\rho$. These assigned values, the positions of the Voronoi nuclei at
depth, and the total number of layers are the sought parameters of the inverse
problem. The number of layers is treated as self-adapting model complexity49
that is governed by the law of parsimony. The parameter space is explored by the
Metropolis−Hastings algorithm70 with the implemented Parallel Tempering
technique71. Furthermore, the multizonal formulation of the prior32 allows us to
include depth-dependent prior expectations (i.e., minimal and maximal expected
values in Tables 1 and 2) that constrain the inversion and restrict the
ambiguous solution of this inverse problem. The result is an ensemble of
solutions drawn from the posterior probability density function (posterior PDF)
on the parameter space. Some representative velocity profiles may be selected
(e.g., the maximum likelihood (ML) model providing the lowest data misfit or the
maximum a posteriori (MAP) model estimate); nevertheless, they should be used
only for illustration of the underground velocity pattern, in this case, as the
ellipticity data do not carry information about absolute values of seismic
velocities and depths.

INVERSION WITH FLAT PRIOR

An inversion assuming strong prior expectations on the parameter space (prior
PDF) may be misleading if the prior is not correct. Hence, we first performed an
inversion of the ellipticity data in a parameter space with a flat prior PDF
without any preference on layer depths or velocities (by setting the priors to a
uniform distribution with relatively wide bounds). Such a weakly constrained
inversion may still produce ambiguous and unrealistic models; however, it
provides valuable information about the velocity profile pattern without an
influence of the prior PDF. Besides, the implemented Parallel Tempering
technique71 reduces the dependence on an initial (i.e., starting) model by using
a large amount of parallel Markov chains with random and independent initial
models. The result of such a weakly constrained inversion is shown in Fig. 5.
The ensemble of solutions consists of more than 1,250,000 models that fit the
ellipticity data well. The inversion result indicates that: (I) there are
underground structures explaining the ellipticity data; (II) seismic velocities
of the expected underground model in Table 2 (black dashed line) are reasonably
within the range of likely values of the inferred posterior PDF (this does not
apply to the model in Table 1); (III) a low-velocity zone at the depth of
roughly 30−75 m is likely underlain by a compact thick high-velocity zone; (IV)
the bottom of the compact high-velocity zone at a depth of around 170 m seems to
be in agreement with the expectations from Table 2; (V) there might be a thin
high-velocity zone located above the low-velocity zone; however, its properties
are uncertain (cannot be uniquely resolved from data); VI) the histogram in
Fig. 5e shows that at least five layers (four layers and half-space) are
necessary to fit the data. Less than five layers do not fit the data
sufficiently, while more layers do not provide significantly better data
fitting.

MULTIZONAL CONSTRAINED INVERSION

The inversion result displayed in Fig. 5 implies that the use of model 2
(Table 2) as the prior may not introduce a strong divergent effect in the
inversion results. Hence as a next step, we performed an inversion of
ellipticity data in a parameter space constrained by the bounds summarized in
Table 2 (using a multizonal prior and allowing for low-velocity zones). The
parameter space is constrained by means of the depth-dependent prior PDF having
four zones with thicknesses and velocity bounds as presented in Table 2. The
results of such a constrained inversion are shown in Fig. 6, where the ensemble
of solutions consists of more than 1,350,000 models. The main features remain as
observed for the weakly constrained inversion, which we interpret as a good sign
regarding a possible effect on the posterior PDF. Additionally, a thin
high-velocity layer is likely above the low-velocity zone even in this inversion
with constrained seismic velocities. However, its thickness and depth remain
very ambiguous and unclear. To conclude the inversion tests, the ellipticity
trough at 2.4 Hz can be explained by at least one low-velocity zone within the
expected thick volcanic layer (the basalt layer in Table 2). Such a low-velocity
zone divides the volcanic layer into the upper (ambiguous) high-velocity layer,
low-velocity zone, and bottom compact high-velocity zone (see inferred models in
Fig. 7). Nevertheless, the ellipticity data reflect rather the velocity
contrasts in depth than absolute values of velocities; hence, we can interpret
only the velocity pattern.

ADDITIONAL SUPPORTING INVERSION TESTS

We have performed several Bayesian inversion tests with various settings to
reveal the robustness of the inferred features. As examples, Supplementary
Figs. 3 and 4 show additional inversion tests with a fixed number of layers
(i.e., a standard non-trans-dimensional Bayesian inversion with a flat prior).
In these two tests, the seismic velocity structure is without an influence of
the prior, the initial models are random and independent, and the number of
layers is fixed to five and six layers, respectively. These tests support the
seismic velocity pattern as described above, and show that models with five
layers (four layers above a half-space) are most suited to explain the observed
ellipticity curve.

DATA AVAILABILITY

The seismic waveform data that support the findings of this study are available
from NASA PDS (National Aeronautics and Space Administration Planetary Data
System, https://pds.nasa.gov/; InSight Mars SEIS Data Service, 2019;
https://doi.org/10.18715/SEIS.INSIGHT.XB_2016). The Rayleigh wave ellipticity as
well as supporting H/V data displayed in Supplementary Fig. 2 that form the
basis for the presented study are available with the paper as supplementary
files (MS Excel sheets).

CODE AVAILABILITY

The RayDec code used for data preparation (extraction of Rayleigh wave
ellipticity values as a function of frequency) is available at
https://github.com/ManuelHobiger/RayDec
(https://doi.org/10.5281/zenodo.5534777). The Geopsy open-source software33
(http://www.geopsy.org/) was used for all forward computations. The Rayleigh
wave ellipticity curves were inverted using the software package MTI (ver.
Desert) utilizing the Multizonal Trans-dimensional Bayesian Inversion developed
at SED, ETH Zurich, available upon request. MTI uses some routines from the
Parametric Slip Inversion49 available under the GNU General Public License, and
the computer package Parallel Tempering (Inversion Laboratory, ilab), made
available with support from the Inversion Laboratory (ilab,
http://www.iearth.edu.au/), which is a program for construction and distribution
of data inference software in the geosciences supported by AuScope Ltd, a
nonprofit organization for Earth Science infrastructure funded by the Australian
Federal Government. Data processing was done using ObsPy72, NumPy73 and SciPy74,
figures were created using matplotlib75 and MATLAB76.

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ACKNOWLEDGEMENTS

We acknowledge NASA, CNES, their partner agencies and institutions (UKSA, SSO,
DLR, JPL, IPGP-CNRS, ETHZ, IC, MPS-MPG) and the flight operations team at JPL,
SISMOC, MSDS, IRIS-DMC and PDS for providing SEED SEIS data. We thank N. Warner
and J. Grant for discussions. We acknowledge funding from (1) Swiss State
Secretariat for Education, Research and Innovation (SEFRI project “MarsQuake
Service-Preparatory Phase”), (2) ETH Research grant ETH-06 17-02, and (3) ETH+02
19-1: Planet MARS. The Swiss contribution in implementation of the SEIS
electronics was made possible through funding from the Swiss Space Office (SSO),
the contractual and technical support of the ESA-PRODEX office. A portion of the
work was supported by the InSight Project at the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration. This is InSight contribution number 207.

AUTHOR INFORMATION

Author notes

1. M. Hobiger

Present address: Federal Institute for Geosciences and Natural Resources
(BGR), Hanover, Germany

2. These authors contributed equally: M. Hobiger, M. Hallo, C. Schmelzbach.

AFFILIATIONS

1. Swiss Seismological Service (SED), ETH Zurich, Zurich, Switzerland

M. Hobiger, M. Hallo, D. Fäh & J. Clinton

2. Institute of Geophysics, ETH Zurich, Zurich, Switzerland

C. Schmelzbach, S. C. Stähler, D. Giardini, N. Dahmen & G. Zenhäusern

3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA,
91109, USA

M. Golombek, K. Hurst, S. Kedar & W. B. Banerdt

4. Bensberg Observatory, University of Cologne, Bergisch Gladbach, Germany

B. Knapmeyer-Endrun & S. Carrasco

5. Department of Electrical and Electronic Engineering, Imperial College
London, London, UK

C. Charalambous

Authors
1. M. Hobiger
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