<figure><img src="image_1.png" /></figure>

HAL
open science

# The Effect of Mars Impact Crater Topography on Seismic Signals

J. Charoensawan, L. Adam, K. van Wijk, Ludovic Margerin, K. Miljkovic, C.

Nunn

► To cite this version:

J. Charoensawan, L. Adam, K. van Wijk, Ludovic Margerin, K. Miljkovic, et al. The Effect of Mars Impact Crater Topography on Seismic Signals. Journal of Geophysical Research. Planets, 2025, 130 (8), pp.e2024JE008440. 10.1029/2024je008440. hal-05390599

HAL Id: hal-05390599

https://hal.science/hal-05390599v1

Submitted on 1 Dec 2025

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
JGR Planets

RESEARCH ARTICLE

10.1029/2024JE008440

**Key Points:**

* Impact craters scatter more surface wave energy than body wave energy, possibly explaining observations of weak surface waves on Mars

* Topographically scattered surface waves increase coda wave energy and reduce its decay rate

* Surface wave scattering could be amplified for Martian seismic events by topographical features not incorporated into our models

**Correspondence to:**

J. Charoensawan,
jcha673@aucklanduni.ac.nz

**Citation:**

Charoensawan, J., Adam, L., van Wijk, K., Margerin, L., Miljkovic, K., & Nunn, C. (2025). The effect of Mars impact crater topography on seismic signals. *Journal of Geophysical Research: Planets*, 130, e2024JE008440. https://doi.org/10.1029/2024JE008440

Received 12 APR 2024

Accepted 18 JUL 2025

© 2025. The Author(s).
This is an open access article under the
terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

<figure><img src="image_3.png" /></figure>

# The Effect of Mars Impact Crater Topography on Seismic Signals

J. Charoensawan¹ ID, L. Adam¹ ID, K. van Wijk², L. Margerin³, K. Miljkovic⁴ ID, and C. Nunn⁵

¹School of Environment and Dodd Walls Centre, University of Auckland, Auckland, New Zealand, ²Department of Physics and Dodd Walls Centre, University of Auckland, Auckland, New Zealand, ³CNRS, CNES, Institut de Recherche en Astrophysique et Planétologie, Université Toulouse III Paul Sabatier, Toulouse, France, ⁴School of Earth and Planetary Sciences, Space Science and Technology Center, Curtin University, Perth, WA, Australia, ⁵Jet Propulsion Laboratory—California Institute of Technology Pasadena, Pasadena, CA, USA

**Abstract** Meteorite impacts on Mars result in seismic recordings with relatively small surface wave amplitudes compared to body wave amplitudes, unlike what is generally observed in earthquakes. Here, we test with numerical modeling whether Mars' topography could be responsible for the preferential attenuation of surface waves. We use a spectral element method to simulate 3D seismic wave propagation from impact events. The model topography is based on Mars' digital elevation model, and the crustal structure is based on published works. Our results show that surface waves encountering a crater lose energy proportionally to the crater depth via scattering because the surface waves are partially converted to body waves and scatter out of the original direction of propagation. The energy loss from scattering can be recovered through multiple scattering, but the result is a net loss. The multiply scattered surface waves from distant craters arrive late, adding energy to the recorded coda waves. Body waves excited by impacts, after reflection in the subsurface, arrive at steep incidence angles on the seismometer and therefore, are almost unaffected by topography. The difference between topographic scattering of body and surface waves could explain the weak or total lack of surface waves recorded by InSight's seismometer.

**Plain Language Summary** Earthquakes commonly consist of two types of seismic waves: surface waves, typically stronger, traveling along the Earth's surface, and body waves traveling inside the Earth. Marsquakes—seismic events similar to earthquakes but occurring on Mars—sourced from meteoroid impacts have been reported to have weak surface waves compared to their body waves, unlike earthquakes where the surface waves are stronger than the body waves. We suspect that abundant impact craters on Mars are responsible for this observation. We use a series of computer models to simulate how seismic waves behave when interacting with Mars' craters. Furthermore, we modify the craters' depth to investigate how the depth affects the seismic waves. We found that surface waves are partially scattered when they encounter a crater. More scattering occurs for deeper craters. The body waves, however, are mostly unaffected by the craters. The different interactions between body and surface waves with craters could explain the weak or lack of surface waves recorded by NASA's seismometer on Mars.

## 1. Introduction

From 2018 to 2022, NASA's InSight (Seismic Investigations, Geodesy and Heat Transport) mission (Lognonné et al., 2019; Giardini et al., 2020) recorded over 1,300 seismic events on Mars, including marsquakes and meteorite impacts (Lognonné et al., 2023). In the waveforms recorded for these events, surface waves have been reported for impact events S0986c, S1000a, S1034a and S1094b (Kim et al., 2022; Drilleau et al., 2023), and the highest magnitude recorded marsquake S1222a (Kawamura et al., 2022). The Rayleigh (R-) waves from S1094b and S1222a (>2,000 km distance) have observable surface waves between 8–15 s and 10–35 s periods, respectively. For impacts within 100 km of InSight, surface waves are observed for S1034 (~48 km) and S0986c (~85 km) between 0.9 and 1.1 Hz frequency (Drilleau et al., 2023). Surprisingly, the surface waves from the distant events (e.g., S1094b) have a low amplitude compared to the body waves generated by the impacts because geometrical spreading would have reduced body wave amplitudes more than surface wave amplitudes. Surface waves in near (Daubar et al., 2023; Xu et al., 2022) and distant (Kim et al., 2022) impact events are indistinguishable from the S-wave coda (Figure 1) unless a bandpass filter is applied (Drilleau et al., 2023; Kim et al., 2022). Similarly, the surface waves from the S1222a marsquake can only be observed after applying a 10–100 s period bandpass filter.
<figure><img src="image_4.png" /><figcaption>**Figure 1.** (a) Seismogram from the S1094b impact event bandpass filtered between 1 and 10 s (Kim et al., 2022). Onsets for P- and S-waves are annotated. R-waves are hidden within the S-wave coda. (b) Three-component seismograms of the same event bandpass filtered between 1 and 5 s (light gray) and 8–15 s (blue, orange, dark gray). The arrival of the minor-arc Rayleigh wave (R1) is annotated.</figcaption></figure>

Even then, the surface wave amplitude is still a magnitude lower than the S-wave amplitude (Kawamura et al., 2022).

A lack of surface-wave energy in Martian seismic records can have several reasons. For example, deep marsquakes may not excite significant surface waves (Durán et al., 2022) and Jacob et al. (2022) proposed source mechanisms where the excited surface waves are weaker than the noise level of the seismometers on Mars. Alternatively, surface waves could get attenuated, rendering them undetectable (Stutzmann et al., 2021). Seismic energy attenuation refers to the energy loss from either intrinsic attenuation, for example, due to pore fluids (Adam et al., 2009), or from scattering attenuation and is represented by an inverse of quality factor (i.e., $1/Q$). $Q$ estimated from direct arrivals carries the contribution of both intrinsic $Q_i$ and scattering $Q_s$ attenuation. The late arrivals on a seismogram (i.e., coda) are due to wave scattering (Aki & Chouet, 1975; Maeda et al., 2008).

Mars' crust is believed to have low intrinsic attenuation (Lognonné et al., 2020; Menina et al., 2021), but scattering due to crustal heterogeneity could contribute to surface-wave amplitude attenuation. On Mars, this heterogeneity is in the form of fracturing and layering (Bean et al., 2008; Driel et al., 2021; O'Brien & Bean, 2009), and surface topography (Jousset et al., 2004; Ripperger et al., 2003; Schmerr et al., 2011) dominated by impact craters. Previously, body (Menina et al., 2023) and surface (Onodera et al., 2023) wave scattering due to crustal heterogeneity have been studied. Similarly, the effects of large-scale topographic variations such as the Martian crustal dichotomy have been included in global simulations (Bozdağ et al., 2017). Smaller topographic variations, particularly the effect of individual craters, have received little attention. On Mars, numerous impact craters of different sizes and depths (Robbins & Hynek, 2012) can act as scatterers of surface waves. It is highly possible that these craters will affect Mars' seismic signal, although how much is unknown. Scattering is a three-dimensional phenomenon that affects body and surface waves. Surface wave energy can be redirected (or scattered) along the surface or converted into body waves traveling below the surface (Maeda et al., 2008). As a result, the surface wave energy recorded at a seismometer is reduced.

Seismic scattering has also been widely studied on the Moon. The Apollo missions to the Moon, which took place in the late 1960s and early 1970s, included seismic experiments. Lunar seismic signals were described as long-
duration, emergent oscillations which lack the discrete phases and coherence of earthquake signals (Latham et al., 1970). Seismic signals on the Moon commonly last over an hour. Latham et al. (1970) noted that the signals likely implied transmission within a low attenuation environment but with intense wave scattering. The Moon has been bombarded by meteoroids throughout its history and in addition to the surface topography of the craters, the subsurface is highly fractured. Latham et al. (1972) suggested that the fractured layer must be at least a few kilometers thick (Soderblom et al., 2015) and more recent work suggests it may be as much as 100 km thick (Gillet et al., 2017). The very low intrinsic attenuation of seismic signals is thought to be related to the low levels of volatiles within the Moon's fractured crust (Latham et al., 1973). Martian seismic signals exhibit less scattering than the Moon but considerably more than Earth (e.g., Lognonné et al., 2020). A high-frequency class of Martian seismic events is strongly scattering. Driel et al. (2021) suggested that seismic waves from this event travel within the fractured crust, and Menina et al. (2023) found that the heterogeneous Martian crust as a whole is a significant source of the scattering. Events with ray paths through the Martian mantle do not exhibit the same level of scatter.

A previous study by Bozdağ et al. (2017) modeled large-scale seismic wave propagation on Mars using SPECFEM3D_GLOBE software. The model has a lateral resolution of 20 km and the shortest wave period is 10 s. This work shows the effect of large topographic features, including Valles Marineris and Hellas Planitia. However, computational limitations did not allow for the incorporation of effects from impact craters, which are mostly smaller than the model resolution (Robbins & Hynek, 2012; Watters et al., 2015). Additionally, the frequency content of only 0.1 Hz is not high enough to capture Martian seismic events. More than 90% of Martian events have a frequency content greater than 2.4 Hz, and some extend beyond 10 Hz (Driel et al., 2021; Lognonné et al., 2023). In this study, we use 3D numerical simulation on SPECFEM3D_Cartesian to investigate how Mars' topography in the vicinity of the InSight lander influences seismic wave propagation through a crater. Our study differs from that of Bozdağ et al. (2017) in that we use an impact as a source and wave propagation is modeled at 2 Hz frequency instead of 0.1 Hz. We propagate seismic waves through crater topography, incorporating crustal seismic models beneath InSight to study how the seismic energy of the body and surface waves changes with propagation distance. Our goal is not to replicate the seismic signals in Figure 1, as this task would be impossible given the unknown layer heterogeneity and fracturing of Mars' crust. Rather, we aim to show that surface wave energy is significantly more affected by crater topography than body wave energy, providing a potential contributing factor for why surface waves on Mars generated by meteorite impacts have lower amplitudes compared to body waves.

## 2. Numerical Model

SPECFEM3D_Cartesian is an open-source software that utilizes spectral element method (SEM) to simulate 3D seismic wave propagation (Komatitsch & Tromp, 2002; Komatitsch et al., 2005). One of the advantages of SEM is its ability to handle sharp edges in the model (van Wijk et al., 2004) which is important to capture Mars' strong topographic features. SPECFEM3D also utilizes the SCOTCH library (Pellegrini & Roman, 1996) to partition the model into small parts to run on multiple CPUs simultaneously, significantly reducing computation time. Nonetheless, 3D modeling is computationally expensive which limits the model size, resolution, and wave frequency. Because of these limitations, our model size (120 km) is smaller than the distances of some real Martian impact events (more than 3,400 km; Kim et al., 2022). However, the model will be applicable to the four impact events that originated within 100 km of InSight (Daubar et al., 2023; Drilleau et al., 2023; Garcia et al., 2022).

We use mesh sizes (i.e., resolution) of 250 and 500 m for the shallow and deep layers, respectively. The mesh sizes are selected to maintain >4 grid points per wavelength (De Basabe & Sen, 2007). Doubling layers are used at the transition between the two mesh sizes at 2 km below the low-velocity top layer. The model's top boundary is implemented as a free surface. An absorbing boundary condition (Xie et al., 2016) is implemented on the side and bottom of the model. The seismic model comprises three layers representing the crust, lower crust, and mantle. The thicknesses, P- and S-wave velocities, and quality factors (Q) are compiled from published studies (Driel et al., 2021; Kawamura et al., 2022; Knapmeyer-Endrun et al., 2021; Lognonné et al., 2020) and are summarized in Table 1.

In SPECFEM3D, surface topography can be incorporated into the seismic simulation (Komatitsch et al., 2016). We use the topography of Mars extracted from its digital elevation model (DEM) with a resolution of 463 m (Smith et al., 2001). The selected area covers 120 × 120 km and is located north of the InSight lander (Figure 2). This section was selected as there is a large crater just north of the lander. The elevation of the study area from the
<table><caption>**Table 1**
Seismic Properties of the Models Used in This Study</caption><thead><tr><th>Layer</th><th>Thickness (km)</th><th>v<sub>p</sub> (m/s)</th><th>v<sub>s</sub> (m/s)</th><th>Density (kg/m<sup>3</sup>)</th><th>Q<sub>μ</sub></th><th>Q<sub>x</sub></th></tr></thead><tbody><tr><td>1</td><td>9</td><td>3,600</td><td>2,100</td><td>2,900</td><td>2,500</td><td>3,500</td></tr><tr><td>2</td><td>11</td><td>5,200</td><td>2,900</td><td>2,900</td><td>2,500</td><td>3,500</td></tr><tr><td>3</td><td>5</td><td>7,700</td><td>4,200</td><td>3,400</td><td>2,500</td><td>3,500</td></tr></tbody></table>

Note. Layer 1 represents the top layer and layer 3 is the bottom layer.

DEM is normalized to the average elevation of this area (approximately -2,600 m). The normalized elevation is then used in the 3D models. Because the element size and the DEM resolution are different, the elevation used in the models is interpolated based on the location of the element and the available elevation data nearby. The study area is located in the northern lowland of Mars. According to the DEM, the selected area is a plain with few craters. There are one large and two smaller craters near the receiver line. The large crater is located in the middle of the area approximately 10 km in diameter and 500 m deep. The two smaller craters are 5 km in diameter and 400 m deep.

Impact craters are complicated structures. Complex craters on Mars can have a central peak (e.g., Melosh, 1989) and morphologically distinct ejecta deposits (e.g., Barlow et al., 2000; Boyce et al., 2012; Cao et al., 2023). During the cratering process, the area experiences significant shock pressure. The shock pressure propagation dissipates exponentially with distance (Holsapple, 1993). The pressure wave decays into an elastic wave at a distance comparable to 10 times the crater radius for meter-size small impacts on the Moon (Rajšić et al., 2021). Comparably, the amount of irreversible damage caused by the shock wave propagation through compaction of pore space, compression of the matrix, and further fragmentation and fracturing also decays exponentially with distance. Previous work simulated the accumulation of plastic strain and demonstrated that there is significantly less damage made at radial distances larger than 1–2 radii away from the impact point, with a lesser spread directly beneath the crater and a larger spread closer to the free surface (Collins et al., 2004). To account for the difference in crustal mechanical properties between a cratered site and a non-cratered area, we specified a damaged zone depth and implemented it in the simulation as an artificial crater depth. We tested our wave propagation for three artificially assumed crater depths: (a) crater depths as measured using MOLA-DEM image (Figure 2), (b) twice and (c) half the crater depth as measured from MOLA-DEM.

In total, seven models are used in this study to explore the effect of topography on seismic signals. The models can be grouped as:

1. Homogeneous model (one layer) with and without topography. The properties of Layer 2 in Table 1 and a thickness of 25 km are used for the homogeneous models. This model is used as a baseline to understand the effect of the seismic discontinuities beneath the InSight lander.

2. Three-layered model (Table 1) with and without topography and intrinsic attenuation ($Q_i$), highlighting the effect of large-scale seismic discontinuities on wave propagation.

3. For the above models, we vary crater depth by enhancing or reducing topography to study its influence on wave scattering. The enhanced topography model is created by doubling the crater depths, while the reduced topography halves these.

A vertical force point source with a Ricker wavelet with a central frequency of 2 Hz is located on the surface. We chose this frequency because it is lower than the recordings of the S0986c impact (2–5 Hz) which occurred 85 km from the InSight lander (Garcia et al., 2022), but higher than distant events (e.g., 1000a and 1094b; 7,460 and 3,460 km, respectively) of which the frequency content is less than 1 Hz (Kim et al., 2022). An array of 11 receivers is placed along an east-west transect with 10 km spacing. The nearest receiver is located 10 km west of the source, and the furthest 110 km (Figure 2).

## 3. Results

We begin by modeling wave propagation in an elastic three-layer system, then incorporate topography, and finally add intrinsic attenuation. The vertical component of the wavefields 110 km from the source is shown in Figure 3a. The Rayleigh (R-) wave is identified based on the elliptical motion in the hodogram (Figure 3b). P-wave phases are identified as the first arrivals, assisted by snapshots of the simulations (Figure 4) and a TauP model (Crotwell et al., 1999). It is clear from both the waveforms and the hodograms that incorporating topography reduces the R-wave amplitude and increases

<figure><img src="image_5.png" /><figcaption>**Figure 2.** Normalized elevation of the study area. The green square shows the location of the InSight lander. Yellow triangles and red star are locations for the modeled receivers and source, respectively.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** (a) Modeled waveforms recorded in the Z-direction (arbitrary unit; AU) for the receiver at 110 km. Waveforms are for three models: the layered model, the layered model with topography, and the layered model with topography and intrinsic attenuation. Inset (I) shows the first arrival P-wave phase. Insets (II) and (III) highlight changes in the R-wave and coda phases, respectively. (b) Hodograms (plots of amplitudes in X- and Z-directions) of the R-wave for the three models. The color represents the recorded time for each data point.</figcaption></figure>

the amount of scattered events represented in the coda. By contrast, intrinsic attenuation reduces the amplitude of the entire waveform and hodogram without significantly altering the waveform shape (cod a). When examining all receiver distances, the nature of the first arrivals of P-wave phases varies depending on the source-receiver (epicentral) distance: (a) direct P-waves traveling in layer 1 are the first arrivals for epicentral distances less than 50 km, and (b) a package of transmitted P-waves reflected from the 20 km interface and P-waves refracted from the 9 km interface are the first-arrivals for epicentral distances greater than 50 km.

Figure 5 compares the R- and P-wave seismic energies with distance from the source. In addition to the models previously introduced, we also present results for homogeneous models, that is, models without layering and models where the crater depth is enhanced by 100% or reduced by 50%. Seismic energy for P- and R-wave phases are calculated in a 2-s window around their respective arrival time. The energy is calculated by summing the squared values of amplitudes from X-, Y-, and Z-directions. The dominant decrease in energy with distance is due to geometric spreading and intrinsic attenuation (where applicable), while changes in energy due to the scattering from layers and craters are imprinted on top of this decay. Geometric spreading for R-waves is slower than for P-waves, as surface-wave energy spreads as 1/distance and body-waves as 1/distance squared. The amount of energy in the R-wave is four orders of magnitude greater than the P-wave energy over the first 100 km from the source in this model. The energy in the homogeneous models (labeled “hom”) shows less energy in the wave-forms recorded at the surface because layering traps energy near the surface. We will discuss the effect of the craters in more detail, but the first observation in the simple homogeneous model is that the R-wave energy decays when passing the largest crater at ~50 km from the source.

The P-wave energy plotted in Figure 5 corresponds to different arrivals: direct and reflected P-waves. The homogeneous models enable analysis of energy changes in the direct P-waves. For the layered models, the first P-
<figure><img src="image_7.png" /><figcaption>**Figure 4.** (a) Side view snapshots at *t* = 12.5 s of a simulation showing (1) a package of direct and reflected P-wave from the 9 km interface, (2) reflected P-wave from the 20 km interface, (3) refracted P-wave, and (4) Rayleigh (R-) wave phases. (b) Side view snapshot at *t* = 30 s showing (5) body waves generated from scattered R-waves by the crater. The colors represent Z-direction displacement in arbitrary unit. The dashed lines indicate the layer interfaces at 9 and 20 km. Animation for the whole simulation is available online which can be accessed via the link referenced in the Data Availability Statement. (c) A snapshot of a top view of the vertical component of the wavefield in a layered model with topography 27.5 s after the impact. The color scale is adjusted to observe low-amplitude scattered R-waves (black arrows). The green arrow indicates the R-wave. The orange and blue arrows indicate P- and S-wave phases, respectively, or their reflected/refracted phases. Animation for the whole simulation is available online at Charoensawan (2024).</figcaption></figure>

wave arrival is a direct P-wave before 50 km epicentral distance. After this distance, the reflected P-wave from the 20 km interface arrives before the direct wave because of the higher velocity of the second layer. This causes the jump in the P-wave energy for all layered models as the first arrival P-waves transition from direct (before 50 km distance) to reflected P-wave (beyond 50 km distance). Coincidentally, the largest crater is located at this distance (Figure 2), but it is clear that the crater is not responsible for the energy jump because this feature is also presented in the layered model without topography. In general, topography and intrinsic attenuation have little to no effect on both direct (homogeneous models) and reflected (layered models) P-wave energy.

Figure 6 highlights the effect of the crater topography on P-wave energy by normalizing the energy to models without topography. The P-wave energy in the homogeneous model shows that the enhanced crater reduces direct P-wave energy abruptly by more than 30%, but wavefront healing causes a recovery to 95%. In this homogeneous
<figure><img src="image_8.png" /><figcaption>**Figure 5.** (a) R-wave energy and (b) P-wave energy (in AU) with distance from the source. The solid lines are energies from the layered models and the dashed lines are from homogeneous models.</figcaption></figure>

model, the ray paths are straight lines intersecting the crater. For the layered models, it is uncertain how much the crater contributes to the energy fluctuation because the location of the crater at ~50 km distance coincides with the jump in energy in Figure 5b. However, it is clear that P-wave energy is lost only in the model with intrinsic attenuation.

Figure 7 presents the R-wave energy as a function of the epicentral distance normalized to the models without topography. These data clearly show that the effect of topography is more significant on the R-waves than on the P-wave. e.g., the R-wave energy for the homogeneous with enhanced topography has a maximum energy drop of more than 70% at its peak before wavefront healing occurs, while the maximum drop for P-wave is less than 30%. The maximum drop in energy occurs as the waveform enters the crater. Other than the enhanced topography model and the models with intrinsic attenuation, the layered models show approximately 40% decay of R-wave energy at the final distance of 110 km (i.e., past the crater) compared to the P-wave energy which shows almost no decay apart from the decay of the intrinsic attenuation. The maximum R-wave energy decrease is proportional to crater depth with a 40% and 20% energy decrease for the enhanced and reduced topography models, respectively. The R-wave energy starts to partially recover with distance to the crater due to the arrival of surface-to-body wave scattered energy from the crater as it reflects from the 20 km interface (Figure 4). The recovery rate is inverse to the crater depth. In the reduced topography model, the energy recovers slightly over the remaining distance. In contrast, the energy recovers rapidly for the enhanced topography model. In the enhanced topography layered model, the energy exceeds its original value due to additional contributions from surface-to-body wave scattering.

<figure><img src="image_9.png" /><figcaption>**Figure 6.** Normalized P-wave energy from Figure 5 versus receiver distance from (a) all layered models normalized to the layered model without topography, and (b) the homogeneous model with enhanced topography normalized to the homogeneous model without topography.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Figure 7.** Normalized R-wave energy from Figure 5 versus receiver distance from (a) all layered models normalized to the layered model without topography, and (b) the homogeneous model with enhanced topography normalized to the homogeneous model without topography.</figcaption></figure>

Topography not only reduces the R-wave amplitude but also affects the coda wave energy decay rate. We compare energy envelopes from two layered models: one with and one without topography (Figure 8). The envelope is calculated by summing the squared amplitudes of all three components and then using a 2-s window moving average on the seismic energy. The coda after the arrival of the R-wave (58–75 s) is a combination of body and scattered surface waves. The energy for the model without topography fluctuates more sharply and its coda decreases faster than that of the model with topography. In a scenario where there are more craters nearby, the scattered R-wave from the nearby craters will travel to the receivers after the direct R-wave. These scattered waves add energy to the coda wave, reducing the coda energy decay rate (Figure 8).

**4. Discussion**

Wave propagation simulations in this study show how scattering from topography disproportionally attenuates R-waves. The influence of craters on wave propagation is summarized in Figure 9. As Rayleigh waves travel through a layered medium with topography (labeled 1 and 2), three effects are observed: R-wave energy is transmitted or forward scattered by the crater (labeled 3). For the transmitted R-wave, the scattering results in an initial reduction of energy, but the wave later undergoes a wavefront healing process (Hung et al., 2001), which

<figure><img src="image_11.png" /><figcaption>**Figure 8.** (a) Comparison between energy envelopes (AU) for the receiver at 110 km distance for the layered model with and without topography. (b) Arrival times of direct P-wave phases and reflected phases from 9 km (v9) and 20 km (v20) phases from the TauP simulation. The three non-reflection P-wave phases (blue lines) indicate (i) refraction from the 20 km interface, (ii) refraction from the 9 km interface, and (iii) direct P-wave.</figcaption></figure>
<figure><img src="image_12.png" /></figure>

**Figure 9.** Diagram showing the pathway of R-wave and first-arrival P-wave propagation for our modeled topography. R-waves propagate from the source in all directions (1, 2). Craters scatter R-wave, resulting in lower energy transmitted R-wave (3). Part of the scattered R-wave converted to body waves (4) traveling within the crust. Some of the body waves are reflected by the subsurface interfaces back to the surface (5), and some transmit to the deeper part of the crust (6). Energy radiated in directions other than the source-receive line interacts with craters elsewhere resulting in a scattering of R-waves that travel to the receiver (7). The first arrival P-wave for epicentral distance greater than 50 km is a reflected wave from the 20 km interface and does not interact with the crater (8).

refers to the diffraction of energy into shadow zones (herein caused by craters). Topography causes R-waves to scatter and convert to body waves (labeled 4). Body waves reflect (labeled 5) and transmit (labeled 6) at layer boundaries. Reflected body waves and R-waves scattered off nearby craters (labeled 7) are recorded at the receiver. As a result, more seismic energy is recorded at the surface in layered models than in homogeneous models.

Due to computational limitations, the models used in this study are relatively small (120 km by 120 km by 25 km). Out of the four impact events that occurred within 100 km of InSight including S0793a, S0986c, S1034a and S1160a (Daubar et al., 2023; Garcia et al., 2022), surface waves are only detected from S0986c and S1034a (Drilleau et al., 2023). Surface waves are also detected in the impact event S1094b which originated 3,500 km from InSight (Kim et al., 2022), outside the modeled area. R-wave propagation for impacts at long epicentral distances would be affected significantly more than what we show here given that there are a greater number of craters and other topographic features that would cause scattering attenuation of R-waves (e.g., Dundas et al., 2023; Garcia et al., 2022; Pan et al., 2020; Watters et al., 2015). In reality, wave scattering from Mars' complex topography is likely to be substantial as many more craters and topographic structures exist at sub-MOLA-DEM resolution as seen from CTX and HiRISE images (e.g., Dundas et al., 2023; Garcia et al., 2022; Pan et al., 2020; Watters et al., 2015). The surface imagery (including DEM) provides only apparent crater depth but not effective depth. Mars craters can be partially filled with sediments (Pan et al., 2019, 2020) and/or have deep-seated shock-damaged zones (Lagain et al., 2022). In either case, the crater's effective depth will be deeper than the observed depth from the DEM. Finally, many other topographic

heterogeneities—such as shallow layering, crater ejecta, fractured zones, and cliffs—also characterize Mars' surface (Golombek et al., 2017; Pan et al., 2020). Our model size also limits incorporating large-scale topography such as Hellas Planitia crater, which is so large that it affects the crust thickness resulting in an increase in the velocity of long-period surface waves as they propagate through the crater (Bozdağ et al., 2017). A higher elastic impedance contrast generally leads to stronger scattering (Wu & Aki, 1985). Thus, we hypothesize that on Mars a strong elastic impedance contrast exists between the now-dry and impact fractured rock of the craters and the surrounding regolith, and that this results in greater R-wave scattering than on Earth, which in contrast has a relatively smoother topography and subsurface fractured zones are water-saturated.

In contrast to R-waves, surface topography has a much smaller effect on both direct and reflected P-waves (Figure 5b). For the direct P-wave, Figure 6b shows that the energy loss of approximately 30% through scattering at the crater is localized and the net loss behind the crater is minimal (approximately 5%). This observation on body waves is similarly reported by Takemura et al. (2015) and Wang et al. (2019) as they observe a limited, localized effect of Earth topography on synthetic P-waves. For the reflected P-wave, Figure 6a shows that the energies from all models without intrinsic attenuation are almost identical after 70 km distance. This is because the reflected P-waves have traveled in the underlying higher-velocity layers. The crater is not in the path of these reflected P-wave ray paths (Figure 9) thus, the reflected energy is not influenced by the topography. It should be noted that the crater lies at the distance where first-arrival P-waves transition from direct to reflected paths. This causes the energy jump (as shown in Figure 7b) to superimpose on the crater scattering, resulting in the P-wave energy fluctuation at 40–70 km in Figure 6a. For future study, relocating the source so that the crater is further than the direct and reflected P-wave crossover distance should resolve this issue. Although seismic wave scattering for impacts on the Moon is not directly studied here, the implications to the propagation of surface waves of the highly cratered and fractured moon crust (Xiao & Werner, 2015) will be affected, resulting in the reduction of surface waves.

Although the coda in seismic events is dominated by shear waves (Aki, 1992), surface waves also play a role as they decay slower due to geometrical spreading and their lower frequency when compared to body waves (Maeda et al., 2008). Previous studies have used the radiative transfer model to constrain Mars' crustal scattering and attenuation properties of the medium (e.g., Menina et al., 2021; Onodera et al., 2023). However, our study shows
that topographic scattering also affects coda waves—particularly the contribution from surface waves—which can add to the scattering effect from a heterogeneous medium. Our observations imply that the scattering of surface waves from topography can look the same as body-wave scattering from the internal heterogeneity of the Martian crust (e.g., layering and fractures). Neglecting surface wave scattering from topography may lead to overestimating the medium's scattering properties or underestimating the intrinsic attenuation because of the slow coda wave decay rate. Therefore, coda analysis should incorporate the topographic scattering effect into the model to better estimate the medium properties.

As explained earlier, the goal of our study is not to reproduce the real seismic data from Figure 1 given the unknown crustal heterogeneity and the fact that much of the topography cannot be handled by the models. We do want to highlight our assumption about the meteorite impact source. The source used in these models is a force point, which is a good approximation to an impact source directed in a downward direction. However, meteoroids impact Mars at an oblique angle (e.g., Garcia et al., 2022). In our study, we do not discuss the coupling of the air blast or shock wave such as those reported for the S0986 event, 85 km away from InSight (Garcia et al., 2022). Such energy can couple into the ground and generate an additional source of Rayleigh waves (Karakostas et al., 2018), even if the air burst itself of distant meteors (>500 km) is attenuated by the Martian atmosphere (Garcia et al., 2017; Lognonné et al., 2016). Future work should incorporate such energy into the modeling.

Additionally, our models assume horizontally uniform velocity layers. Studies hypothesized that the shallow (9 km) layer could be a local feature around InSight Lander (e.g., Kim et al., 2022; Menina et al., 2023; Wieczorek et al., 2022). More recently, a low velocity (vs. ~1.5 km/s) layer to a depth of 1–2 km has been identified but was not included in the modeling (Carrasco et al., 2023; Drilleau et al., 2023; Shi et al., 2023). The crustal model is created based on the 2-layer, thin crust model presented in Knapmeyer-Endrun et al. (2021). However, there are other studies (e.g., Durán et al., 2022; Kim et al., 2021) that present results supporting the 3-layer, thick crust hypothesis. Other recent studies suggest a 4-layer crustal model, incorporating a shallow (1–2 km), low-velocity layer in addition to the previous 3-layer model (Carrasco et al., 2023; Drilleau et al., 2023). These thick crust models have lower impedance interfaces, which reduces the reflected energy. In the context of this study, the reflected P-wave amplitude and the R-wave recovery from reflected waves would be weaker in the low-impedance crust scenarios.

Lastly, the modeled seismic signals presented in this study still show high-amplitude surface waves even with crater scattering, unlike what was observed on Mars. In addition to the effect of craters not incorporated into the model discussed previously, we suspected that the discrepancy is also caused by a near-surface scattering layer, such as regolith or fractured heterogeneous crust, which was also not incorporated into the model. Regolith was hypothesized to scatter surface waves on the Moon (e.g., Goins et al., 1981; Latham et al., 1972) and Mars' crust is reported to be highly scattering (e.g., Driel et al., 2021; Menina et al., 2023). Craters (either unfilled or filled with very low velocity/density regolith) also present areas of high impedance contrast, causing a strong scattering. The combination of the scattering layer and the craters, neither is common in Earth's crust, results in a drastically different seismic waveform recorded on Earth and Mars. We further hypothesized that this scattering feature is likely limited to the shallow part of Mars' crust. This allows the scattering to preferentially affect surface waves while having minimal effect on reflected P-waves as shown in this study.

## 5. Conclusions

In this study, we investigate the effect of Martian craters on seismic waves using spectral element wave propagation simulations. We simulate seismic wave propagation due to an impact event using Mars' topographic data, crustal velocity models, and a force point source. We then estimate body and surface wave energy using seismograms recorded at different epicentral distances. Martian craters scatter Rayleigh waves, converting the wave energy into body waves. Although some energy is recovered through subsurface reflections and wavefront healing, topography causes surface waves to be more strongly attenuated than body waves. For most events on Mars, the propagation distance to the only seismometer is beyond the limits of our computational capabilities. In reality, surface waves from more distant events than modeled here will encounter more craters than what were included in our models. This, combined with additional scattering from the damage zone beneath each crater, helps explain the lack of surface wave energy observed in most Martian seismic records.
## Acknowledgments

The authors would like to acknowledge the InSight project science team for valuable discussions. The authors also wish to acknowledge the use of New Zealand eScience Infrastructure (NeSI) high performance computing facilities, consulting support and/or training services as part of this research. New Zealand's national facilities are provided by NeSI and funded jointly by NeSI's collaborator institutions and through the Ministry of Business, Innovation and Employment's Research Infrastructure program. URL https://www.nesi.org.nz. CN's research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (80NM0018D0004). Open access publishing facilitated by The University of Auckland, as part of the Wiley - The University of Auckland agreement via the Council of Australian University Librarians.

## Data Availability Statement

The Mars topography data used for creating the spectral element models are available from the NASA Planetary Data System (Smith et al., 2003). The SPECFEM3D Cartesian software is used to simulate seismic wave propagation is archived on Zenodo (Komatitsch et al., 2024). Model parameters, synthetic waveforms and simulation snapshots can be accessed at Charoensawan (2024).

## References

Adam, L., Batzle, M., Lewallen, K. T., & van Wijk, K. (2009). Seismic wave attenuation in carbonates. *Journal of Geophysical Research*, 114*(B6). https://doi.org/10.1029/2008JB005890

Aki, K. (1992). Scattering conversions P to S versus S to P. *Bulletin of the Seismological Society of America*, 82(4), 1969–1972. https://doi.org/10.1785/BSSA0820041969

Aki, K., & Chouet, B. (1975). Origin of coda waves: Source, attenuation, and scattering effects. *Journal of Geophysical Research* (1896-1977), 80(23), 3322–3342. https://doi.org/10.1029/JB080i023p03322

Barlow, N. G., Boyce, J. M., Costard, F. M., Craddock, R. A., Garvin, J. B., Sakimoto, S. E., et al. (2000). Standardizing the nomenclature of Martian impact crater ejecta morphologies. *Journal of Geophysical Research*, 105(E11), 26733–26738. https://doi.org/10.1029/2000je001258

Bean, C., Lokmer, I., & O'Brien, G. (2008). Influence of near-surface volcanic structure on long-period seismic signals and on moment tensor inversions: Simulated examples from Mount Etna. *Journal of Geophysical Research*, 113(B8), B08308. https://doi.org/10.1029/2007JB005468

Boyce, J. M., Wilson, L., Mouginis-Mark, P. J., Hamilton, C. W., & Tornabene, L. L. (2012). Origin of small pits in Martian impact craters. *Icarus*, 221(1), 262–275. https://doi.org/10.1016/j.icarus.2012.07.027

Bozdağ, E., Ruan, Y., Metthez, N., Khan, A., Leng, K., Van Driel, M., et al. (2017). Simulations of seismic wave propagation on Mars. *Space Science Reviews*, 211(1-4), 571–594. https://doi.org/10.1007/s11214-017-0350-z

Cao, W., Xiao, Z., Luo, F., Ma, Y., & Xu, R. (2023). Comparison of topographic roughness of layered deposits on Mars. *Remote Sensing*, 15(9), 2272. https://doi.org/10.3390/rs15092272

Carrasco, S., Knapmeyer-Endrun, B., Margerin, L., Xu, Z., Joshi, R., Schimmel, M., et al. (2023). Constraints for the martian crustal structure from Rayleigh waves ellipticity of large seismic events. *Geophysical Research Letters*, 50(16), e2023GL104816. https://doi.org/10.1029/2023GL104816

Charoensawan, J. (2024). Model parameters for article submitted to jgr:planet, 2024 [dataset]. *The University of Auckland*. https://doi.org/10.17608/K6.auckland.25565967

Collins, G. S., Melosh, H. J., & Ivanov, B. A. (2004). Modeling damage and deformation in impact simulations. *Meteoritics & Planetary Sciences*, 39(2), 217–231. https://doi.org/10.1111/j.1945-5100.2004.tb00337.x

Crotwell, H. P., Owens, T. J., & Ritsema, J. (1999). The TauP toolkit: Flexible seismic travel-time and ray-path utilities. *Seismological Research Letters*, 70(2), 154–160. https://doi.org/10.1785/gssrl.70.2.154

Daubar, I. J., Fernando, B. A., Garcia, R. F., Grindrod, P. M., Zenhäusern, G., Wójcicka, N., et al. (2023). Two seismic events from InSight confirmed as new impacts on Mars. *The Planetary Science Journal*, 4(9), 175. https://doi.org/10.3847/PSJ/ace9b4

De Basabe, J. D., & Sen, M. K. (2007). Grid dispersion and stability criteria of some common finite-element methods for acoustic and elastic wave equations. *Geophysics*, 72(6), T81–T95. https://doi.org/10.1190/1.2785046

Driel, M., Ceylan, S., Clinton, J., Giardini, D., Horleston, A., Margerin, L., et al. (2021). High-frequency seismic events on Mars observed by InSight. *Journal of Geophysical Research: Planets*, 126(2), e2020JE006670. https://doi.org/10.1029/2020JE006670

Drilleau, M., Beucler, r., Shi, J., Knapmeyer-Endrun, B., Garcia, R. F., Ansan, V., et al. (2023). Structure of the martian crust below insight from surface waves and body waves generated by nearby meteoroid impacts. *Geophysical Research Letters*, 50(23), e2023GL104601. https://doi.org/10.1029/2023GL104601

Dundas, C. M., Mellon, M. T., Posiolova, L. V., Miljković, K., Collins, G. S., Tornabene, L. L., et al. (2023). A large new crater exposes the limits of water ice on Mars. *Geophysical Research Letters*, 50(2), e2022GL100747. https://doi.org/10.1029/2022gl100747

Durán, C., Khan, A., Ceylan, S., Zenhäusern, G., Stähler, S., Clinton, J., & Giardini, D. (2022). Seismology on Mars: An analysis of direct, reflected, and converted seismic body waves with implications for interior structure. *Physics of the Earth and Planetary Interiors*, 325, 106851. https://doi.org/10.1016/j.pepi.2022.106851

Garcia, R., Brissaud, Q., Rolland, L., Martin, R., Komatitsch, D., Spiga, A., et al. (2017). Finite-difference modeling of acoustic and gravity wave propagation in Mars atmosphere: Application to infrasounds emitted by meteor impacts. *Space Science Reviews*, 211(1-4), 547–570. https://doi.org/10.1007/s11214-016-0324-6

Garcia, R., Daubar, I., Beucler, E., Posiolova, L., Collins, G., Lognonné, P., et al. (2022). Newly formed craters on Mars located using seismic and acoustic wave data from InSight. *Nature Geoscience*, 15(10), 1–7. https://doi.org/10.1038/s41561-022-01014-0

Giardini, D., Lognonné, P., Banerdt, W., Pike, W., Christensen, U., Ceylan, S., et al. (2020). The seismicity of Mars. *Nature Geoscience*, 13, 1–8. https://doi.org/10.1038/s41561-020-0539-8

Gillet, K., Margerin, L., Calvet, M., & Monnereau, M. (2017). Scattering attenuation profile of the moon: Implications for shallow moonquakes and the structure of the megaregolith. *Physics of the Earth and Planetary Interiors*, 262, 28–40. https://doi.org/10.1016/j.pepi.2016.11.001

Goins, N. R., Dainty, A., & Toksöz, M. (1981). Lunar seismology: The internal structure of the moon. *Journal of Geophysical Research*, 86(B6), 5061–5074. https://doi.org/10.1029/jb086ib06p05061

Golombek, M., Kipp, D., Warner, N., Daubar, I. J., Fergason, R., Kirk, R. L., et al. (2017). Selection of the InSight landing site. *Space Science Reviews*, 211(1-4), 5–95. https://doi.org/10.1007/s11214-016-0321-9

Holsapple, K. A. (1993). The scaling of impact processes in planetary sciences. *Annual Review of Earth and Planetary Sciences*, 21(1), 333–373. https://doi.org/10.1146/annurev.ea.21.050193.002001

Hung, S.-H., Dahlen, F. A., & Nolet, G. (2001). Wavefront healing: A banana-doughnut perspective. *Geophysical Journal International*, 146(2), 289–312. https://doi.org/10.1046/j.1365-246x.2001.01466.x

Jacob, A., Plasman, M., Perrin, C., Fuji, N., Lognonné, P., Xu, Z., et al. (2022). Seismic sources of InSight marsquakes and seismotectonic context of Elysium Planitia, Mars. *Tectonophysics*, 837, 229434. https://doi.org/10.1016/j.tecto.2022.229434

Jousset, P., Neuberg, J., & Jolly, A. (2004). Modelling low-frequency volcanic earthquakes in a viscoelastic medium with topography. *Geophysical Journal International*, 159(2), 776–802. https://doi.org/10.1111/j.1365-246X.2004.02411.x
Karakostas, F., Rakoto, V., Lognonné, P., Larmat, C., Daubar, I., & Miljković, K. (2018). Inversion of meteor Rayleigh waves on earth and modeling of air coupled Rayleigh waves on Mars. *Space Science Reviews*, *214*, 1–33.

Kawamura, T., Clinton, J. F., Zenhäusern, G., Ceylan, S., Horleston, A. C., Dahmen, N. L., et al. (2022). S1222a - The largest marsquake detected by InSight. *Geophysical Research Letters*, *n/a(n/a), e2022GL101543*. https://doi.org/10.1029/2022GL101543

Kim, D., Banerdt, W. B., Ceylan, S., Giardini, D., Lekić, V., Lognonné, P., et al. (2022). Surface waves and crustal structure on Mars. *Science*, *378*(6618), 417–421. https://doi.org/10.1126/science.abq7157

Kim, D., Lekić, V., Irving, J. C. E., Schmerr, N., Knapmeyer-Endrun, B., Joshi, R., et al. (2021). Improving constraints on planetary interiors with PPS receiver functions. *Journal of Geophysical Research: Planets*, *126*(11), e2021JE006983. https://doi.org/10.1029/2021JE006983

Knapmeyer-Endrun, B., Panning, M., Bissig, F., Joshi, R., Khan, A., Kim, D., et al. (2021). Thickness and structure of the martian crust from InSight seismic data. *Science*, *373*(6553), 438–443. https://doi.org/10.1126/science.abf8966

Komatitsch, D., & Tromp, J. (2002). Introduction to the spectral element method for three-dimensional seismic wave propagation. *Geophysical Journal International*, *139*(3), 806–822. https://doi.org/10.1046/j.1365-246x.1999.00967.x

Komatitsch, D., Tromp, J., Garg, R., Gharti, H. N., Nagaso, M., Oral, E., et al. (2024). Specfem/specfem3d: Specfem3d v4.1.1. *Zenodo*. https://doi.org/10.5281/zenodo.10823181

Komatitsch, D., Tsuboi, S., & Tromp, J. (2005). The spectral-element method in seismology. *Seismic Earth: Array Analysis of Broadband Seismograms*, *157*, 205–227. https://doi.org/10.1029/157GM13

Komatitsch, D., Xie, Z., Bozdağ, E., Sales de Andrade, E., Peter, D., Liu, Q., & Tromp, J. (2016). Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion. *Geophysical Journal International*, *206*(3), 1467–1478. https://doi.org/10.1093/gji/ggw224

Lagain, A., Bouley, S., Zanda, B., Miljković, K., Rajšić, A., Baratoux, D., et al. (2022). Early crustal processes revealed by the ejection site of the oldest Martian meteorite. *Nature Communications*, *13*(1), 3782. https://doi.org/10.1038/s41467-022-31444-8

Latham, G., Ewing, M., Dorman, J., Lammlein, D., Press, F., Toksőz, N., et al. (1972). Moonquakes and lunar tectonism. *The Moon*, *4*(3–4), 373–382. https://doi.org/10.1007/BF00562004

Latham, G., Ewing, M., Dorman, J., Nakamura, Y., Press, F., Toksőz, N., et al. (1973). Lunar structure and dynamics - Results from the Apollo passive seismic experiment. *The Moon*, *7*(3–4), 396–421. https://doi.org/10.1007/BF00564643

Latham, G., Ewing, M., Press, F., Sutton, G., Dorman, J., Nakamura, Y., et al. (1970). Passive seismic experiment. *Science*, *167*(3918), 455–457. https://doi.org/10.1126/science.167.3918.455

Lognonné, P., Banerdt, W., Clinton, J., Garcia, R., Giardini, D., Knapmeyer-Endrun, B., et al. (2023). Mars seismology. *Annual Review of Earth and Planetary Sciences*, *51*(1), 643–670. https://doi.org/10.1146/annurev-earth-031621-073318

Lognonné, P., Banerdt, W., Giardini, D., Pike, W., Christensen, U., Laudet, P., et al. (2019). Seis: Insight's seismic experiment for internal structure of Mars. *Space Science Reviews*, *215*(1), 12. https://doi.org/10.1007/s11214-018-0574-6

Lognonné, P., Banerdt, W., Pike, W., Giardini, D., Christensen, U., Garcia, R., et al. (2020). Constraints on the shallow elastic and anelastic structure of Mars from InSight seismic data. *Nature Geoscience*, *13*(3), 213–220. https://doi.org/10.1038/s41561-020-0536-y

Lognonné, P., Karakostas, F., Rolland, L., & Nishikawa, Y. (2016). Modeling of atmospheric-coupled Rayleigh waves on planets with atmosphere: From Earth observation to Mars and Venus perspectives. *Journal of the Acoustical Society of America*, *140*(2), 1447–1468. https://doi.org/10.1121/1.4960788

Maeda, T., Sato, H., & Nishimura, T. (2008). Synthesis of coda wave envelopes in randomly inhomogeneous elastic media in a half-space: Single scattering model including Rayleigh waves. *Geophysical Journal International*, *172*(1), 130–154. https://doi.org/10.1111/j.1365-246X.2007.03603.x

Melosh, H. J. (1989). *Impact cratering: A geologic process*. Oxford University Press; Oxford: Clarendon Press.

Menina, S., Margerin, L., Kawamura, T., Heller, G., Drilleau, M., Xu, Z., et al. (2023). Stratification of heterogeneity in the lithosphere of Mars from envelope modeling of event S1222a and near impacts: Interpretation and implications for very-high-frequency events. *Geophysical Research Letters*, *50*(7), e2023GL103202. https://doi.org/10.1029/2023GL103202

Menina, S., Margerin, L., Kawamura, T., Lognonné, P., Marti, J., Drilleau, M., et al. (2021). Energy envelope and attenuation characteristics of high-frequency (HF) and very-high-frequency (VF) Martian events. *Bulletin of the Seismological Society of America*, *111*(6), 3016–3034. https://doi.org/10.1785/0120201127

O'Brien, G. S., & Bean, C. J. (2009). Volcano topography, structure and intrinsic attenuation: Their relative influences on a simulated 3D visco-elastic wavefield. *Journal of Volcanology and Geothermal Research*, *183*(1), 122–136. https://doi.org/10.1016/j.jvolgeores.2009.03.004

Onodera, K., Maeda, T., Nishida, K., Kawamura, T., Margerin, L., Sabrina, M., et al. (2023). Seismic scattering and absorption properties of Mars estimated through coda analysis on a long-period surface wave of S1222a marsquake. https://doi.org/10.22541/essoar.167422916.68888746/v1

Pan, L., Quantin-Nataf, C., Breton, S., & Michaut, C. (2019). The impact origin and evolution of Chryse Planitia on Mars revealed by buried craters. *Nature Communications*, *10*(1), 4257. https://doi.org/10.1038/s41467-019-12162-0

Pan, L., Quantin-Nataf, C., Tauzin, B., Michaut, C., Golombek, M., Lognonné, P., et al. (2020). Crust stratigraphy and heterogeneities of the first kilometers at the dichotomy boundary in western Elysium Planitia and implications for InSight lander. *Icarus*, *338*, 113511. https://doi.org/10.1016/j.icarus.2019.113511

Pellegrini, F., & Roman, J. (1996). Scotch: A software package for static mapping by dual recursive bipartitioning of process and architecture graphs. In H. Liddell, A. Colbrook, B. Hertzberger, & P. Sloot (Eds.), *High-performance computing and networking* (pp. 493–498). Springer Berlin Heidelberg.

Rajšić, A., Miljković, K., Collins, G., Wünnemann, K., Daubar, I., Wójcicka, N., & Wieczorek, M. (2021). Seismic efficiency for simple crater formation in the Martian top crust analog. *Journal of Geophysical Research: Planets*, *126*(2), e2020JE006662. https://doi.org/10.1029/2020je006662

Ripperger, J., Igel, H., & Wasserman, J. (2003). Seismic wave simulation in the presence of real volcano topography. *Journal of Volcanology and Geothermal Research*, *128*(1), 31–44. (Putting Volcano Seismology in a Physical Context. In memory of Bruno Martinelli). https://doi.org/10.1016/S0377-0273(03)00245-2

Robbins, S. J., & Hynek, B. M. (2012). A new global database of Mars impact craters 1 km: 1. Database creation, properties, and parameters. *Journal of Geophysical Research*, *117*(E5), E05004. https://doi.org/10.1029/2011JE003966

Schmerr, N., Matzel, E., & Ford, S. (2011). The effect of free-surface topography on seismic waves in the moon. In *42nd annual lunar and planetary science conference*.1961.

Shi, J., Plasman, M., Knapmeyer-Endrun, B., Xu, Z., Kawamura, T., Lognonné, P., et al. (2023). High-frequency receiver functions with event s1222a reveal a discontinuity in the Martian shallow crust. *Geophysical Research Letters*, *50*(5), e2022GL101627. https://doi.org/10.1029/2022gl101627
Smith, D. E., Zuber, M., Neumann, G., Guinness, E., & Slavney, S. (2003). Mars global surveyor laser altimeter mission experiment gridded data record, mgs-m-mola-5-megdr-l3-v1.0 [dataset]. NASA Planetary Data System. https://doi.org/10.17189/1519460

Smith, D. E., Zuber, M. T., Frey, H. V., Garvin, J. B., Head, J. W., Muhleman, D. O., et al. (2001). Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars. *Journal of Geophysical Research*, **106**(E10), 23689–23722. https://doi.org/10.1029/2000JE001364

Soderblom, J. M., Evans, A. J., Johnson, B. C., Melosh, H. J., Miljković, K., Phillips, R. J., et al. (2015). The fractured moon: Production and saturation of porosity in the lunar highlands from impact cratering. *Geophysical Research Letters*, **42**(17), 6939–6944. https://doi.org/10.1002/2015GL065022

Stutzmann, E., Schimmel, M., Lognonné, P., Horleston, A., Ceylan, S., van Driel, M., et al. (2021). The polarization of ambient noise on Mars. *Journal of Geophysical Research: Planets*, **126**(1), e2020JE006545. https://doi.org/10.1029/2020JE006545

Takemura, S., Furumura, T., & Maeda, T. (2015). Scattering of high-frequency seismic waves caused by irregular surface topography and small-scale velocity inhomogeneity. *Geophysical Journal International*, **201**(1), 459–474. https://doi.org/10.1093/gji/ggv038

van Wijk, K., Komatitsch, D., Scales, J. A., & Tromp, J. (2004). Analysis of strong scattering at the micro-scale. *Journal of the Acoustical Society of America*, **115**(3), 1006–1011. https://doi.org/10.1121/1.1647480

Wang, N., Shen, Y., Bao, X., & Flinders, A. (2019). Locating shallow seismic sources with waves scattered by surface topography: Validation of the method at the Nevada test site. *Journal of Geophysical Research: Solid Earth*, **124**(7), 7040–7051. https://doi.org/10.1029/2018JB017291

Watters, W. A., Geiger, L. M., Fendrock, M., & Gibson, R. (2015). Morphometry of small recent impact craters on Mars: Size and terrain dependence, short-term modification. *Journal of Geophysical Research: Planets*, **120**(2), 226–254. https://doi.org/10.1002/2014JE004630

Wieczorek, M. A., Broquet, A., McLennan, S. M., Rivoldini, A., Golombek, M., Antonangeli, D., et al. (2022). InSight constraints on the global character of the Martian crust. *Journal of Geophysical Research: Planets*, **127**(5), e2022JE007298. https://doi.org/10.1029/2022JE007298

Wu, R.-S., & Aki, K. (1985). Scattering characteristics of elastic waves by an elastic heterogeneity. *Geophysics*, **50**(4), 582–595. https://doi.org/10.1190/1.1441934

Xiao, Z., & Werner, S. C. (2015). Size-frequency distribution of crater populations in equilibrium on the moon. *Journal of Geophysical Research: Planets*, **120**(12), 2277–2292. https://doi.org/10.1002/2015JE004860

Xie, Z., Matzen, R., Cristini, P., Komatitsch, D., & Martin, R. (2016). A perfectly matched layer for fluid-solid problems: Application to ocean-acoustics simulations with solid ocean bottoms. *Journal of the Acoustical Society of America*, **140**(1), 165–175. https://doi.org/10.1121/1.4954736

Xu, Z., Froment, M., Garcia, R., Beucler, E., Onodera, K., Kawamura, T., et al. (2022). Modeling seismic recordings of high-frequency guided infrasound on Mars. *The Journal of Geophysical Research Planets*, **127**(11), e2022JE007483. https://doi.org/10.1029/2022JE007483