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# Properties of Interplanetary Fast Shocks Close to the Martian Environment

Hui Huang, Jianpeng Guo, Christian Mazelle, Emmanuel Penou, Haibo Lin, Dan Zhao

► To cite this version:

Hui Huang, Jianpeng Guo, Christian Mazelle, Emmanuel Penou, Haibo Lin, et al. Properties of Interplanetary Fast Shocks Close to the Martian Environment. The Astrophysical Journal, 2021, 914, 10.3847/1538-4357/abf82b. insu-03672429

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# Properties of Interplanetary Fast Shocks Close to the Martian Environment

Hui Huang¹, Jianpeng Guo¹, Christian Mazelle², Emmanuel Penou², Haibo Lin¹, and Dan Zhao¹

¹Planetary and Space Physics Group, Department of Astronomy, Beijing Normal University, Beijing 100875, People's Republic of China; jpguo@bnu.edu.cn

²IRAP CNRS-University of Toulouse-UPS-CNES, Toulouse, France

Received 2021 March 27; revised 2021 April 13; accepted 2021 April 13; published 2021 June 9

## Abstract

Magnetic field and plasma measurements from the Mars Atmosphere and Volatile EvolutionN mission in orbit around Mars are analyzed for interplanetary fast shock properties and drivers from 2014 October to 2018 November. We identified 52 fast shocks, including 39 fast forward (FF) shocks and 13 fast reverse (FR) shocks. Most (79%) of the FF shocks are driven by stream interaction regions (SIRs) with only a few cases being driven by interplanetary coronal mass ejections, and all of the FR shocks are driven by SIRs. A total of 92% of the identified shocks are quasi-perpendicular shocks. On average, the shock strengths of SIR-driven forward and reverse shocks are comparable, and they are greater than that of ICME-driven forward shocks. The shock strengths show no systematic dependence on the shock locations relative to the Martian bow shock. We find no evidence that the shock shapes are affected by Mars and its bow shock as an obstacle in the propagating medium. The results can help us understand the nature of interplanetary shocks propagating in different environments.

*Unified Astronomy Thesaurus concepts: Heliosphere (711); Solar wind (1534); Shocks (2086); Mars (1007); Interplanetary shocks (829)*

## 1. Introduction

A shock may form when the speed of its driver relative to the upstream medium exceeds the upstream magnetosonic speed. When the upstream flow speed in the shock frame is larger than the fast magnetosonic speed, the shock is referred to as a fast shock. In interplanetary (IP) space, the most frequently observed shocks are fast shocks, the focus of this study. The fast shocks are generally divided into two types with respect to the solar wind frame of reference. One is the fast forward (FF) shocks that propagate away from the Sun, and the other is the fast reverse (FR) shocks that propagate toward the Sun but are carried out by the bulk flow of solar wind. It is well known that the two major drivers of the IP shocks are interplanetary coronal mass ejections (ICMEs; reviewed by, e.g., Crooker et al. 1997; Kilpua et al. 2017) and stream interaction regions (SIRs; reviewed by, e.g., Balogh et al. 1999; Richardson 2018). Specifically, when an ICME is sufficiently faster than the preceding solar wind, an FF shock develops ahead of the ICME. Being a region of high pressure, an SIR is bounded by a pair of forward-reverse pressure waves, which commonly steepen into FF and FR shocks at large heliocentric distances.

In situ observations of fast IP shocks in the past decades have resulted in significant advances in our understanding of their statistical properties as well as their radial evolution. It is found that most of the shocks near the Sun appear to be driven by ICMEs, and the SIR-driven shocks begin to form at about 0.4 au and increase in number with heliocentric distance (Lai et al. 2012). At 1 au, ICMEs are the major drivers of FF shocks in all solar cycle phases except at solar minimum (Hewish et al. 1985; Berdichevsky et al. 2000; Oh et al. 2007; Kilpua et al. 2015), and nearly all FR shocks are driven by SIRs (Kilpua et al. 2015). Occasionally, the ICME-driven FR shocks occur in cases where the ICMEs are overexpanding (Whang 1988; Gosling et al. 1995). The SIR-driven FF shocks propagate to the ecliptic plane, while the SIR-driven FR shocks propagate poleward (Riley et al. 2012). As a result, at latitudes beyond 30° the SIR-driven shocks are almost exclusively FR shocks

(Balogh et al. 1995), and in the ecliptic plane the SIR-driven FF shocks occur more frequently than FR shocks do (Jian et al. 2006, 2008a, 2008b; Huang et al. 2019). At heliocentric distances between 3 au and 10 au, the FR shocks mainly driven by SIRs are prevalent (Richardson & Wang 2005). The shocks on average grow stronger as they propagate from the Sun to about 5 au, and then they level off or decrease near 10 au, with shock strength at 10 au comparable to that near 1 au (Echer 2019a). The shocks preferentially have a quasi-perpendicular propagation to the magnetic field direction at distances within about 5 au (Richardson & Cane 2010a; Echer 2019b), and they preferentially have an oblique propagation at larger distances, near about 10 au (Echer 2019a).

The fast shocks are of interest because they are connected to some fundamental plasma physical processes in the heliosphere, such as plasma heating and acceleration and plasma waves ahead of the shocks (Blanco-Cano et al. 2016; Wilson et al. 2017). They are also important drivers of space weather disturbances in the Earth's and other planetary environments. For instance, Jakosky et al. (2015a) reported an IP shock that arrived at Mars on 2015 March 8 and led to a significant enhancement of the ion escape rate. This phenomenon was also observed during the 2017 September event (Lee et al. 2018). There have been several efforts toward characterizing IP shock parameters near planetary orbits (Echer 2019b; Huang et al. 2019). Nevertheless, owing to the limited upstream solar wind measurements, the properties of IP shocks that occurred upstream of planetary bow shocks have received little attention in the literature. Mars does not have a global intrinsic dipole magnetic field, and moreover it has a weak gravitational field, both of which allow the neutral exosphere to extend far beyond the Martian bow shock. As a result, the solar wind directly interacts with the Martian exosphere, and thus the atmospheric neutrals are ionized in the solar wind. The newly ionized ions are accelerated by the electric field and gyrate around the magnetic field in the upstream solar wind. Both the anisotropy of the pick-up ion distributions (typically the ring-beam distribution) and their relative streaming with the solar wind
drive instabilities that excite waves and disturb the local plasma parameters and fields (Ruhunusiri et al. 2015; Romanelli et al. 2016; Halekas et al. 2020; Romeo et al. 2021). In addition to the pick-up ions, there exist a number of other ion populations in the upstream region (including the foreshock), such as reflected ions from the bow shock (Mazelle et al. 2004 and references therein). The solar wind is slightly slowed down by mass loading upstream from Mars (Szegő et al. 2000; Halekas et al. 2017). It means that when an IP shock enters the Martian exosphere, the medium of propagation becomes different from the normal solar wind condition. The properties of the shocks propagating close to the Martian environment are not yet fully understood. In addition, it is unclear whether the local shape of the shock varies in response to the presence of an obstacle in the propagating medium, such as Mars and its bow shock. The purpose of this paper is to analyze IP shocks close to the Martian environment, which provides fresh perspectives on the issues noted above.

The Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft (Jakosky et al. 2015b) arrived at Mars in 2014 September and was inserted into a 4.5 hr elliptical orbit around Mars, with periapsis at 150 km, apoapsis at 6200 km, and a 75° inclination during the nominal mission phase. It spends a portion of its orbit in the upstream solar wind. During periods of the mission when apoapsis is located upstream of the bow shock, it provides a large number of measurements of the solar wind. The orbit does not extend far beyond the bow shock, and thus the in situ measurements of the plasma and magnetic field present a unique opportunity to characterize IP shocks in the medium outside of and close to the bow shock. In this work, we catalog IP shocks observed by MAVEN from 2014 October to 2018 November and analyze their parameters and drivers. Also, we examine the potential effects of the Martian bow shock on IP shock shapes in a statistical sense.

This paper is outlined as follows: Section 2 describes the MAVEN data. Section 3 presents the calculation method of shock parameters and introduces the identification criteria for IP shocks and their drivers. In Section 4, we investigate the shock properties and how the properties depend on the drivers in a statistical sense, and examine the potential impacts of Mars on the shock shapes. The last section presents the summary.

## 2. MAVEN Data

The primary data used in this work are from three instruments: the Solar Wind Ion Analyzer (SWIA; Halekas et al. 2015), the Solar Wind Electron Analyzer (SWEA; Mitchell et al. 2016) and the Magnetometer (MAG; Connerney et al. 2015). The proton moments (the proton velocity, density, and temperature) are computed from the Fine 3D velocity distributions measured by SWIA under the assumption that all ions are protons. Since even a small alpha particle population leads to an artificially large temperature moment due to their higher energy per charge (Halekas et al. 2017), appropriate routines, as described later, are used to separately compute proton and alpha particle temperatures when attempting a more quantitative calculation of the upstream parameters of IP shocks. But it has been difficult to separate these two ion species from the SWIA energy spectrum in the downstream regions for some shocks, and thus the downstream parameters are computed under the assumption that all ions are protons. The ion energy spectra are also derived from the Fine 3D data. The plasma electron moments, including the electron velocity,

density, and temperature, and the electron energy spectra are calculated from the 3D velocity distributions measured by SWEA. The magnetic field data are from the MAG. SWIA and SWEA data with a temporal resolution of 8 s and MAG data with a temporal resolution of 1 s are used. In addition, the fluxes of electrons from 20 keV to 1000 keV and ions from 20 keV to 6000 keV measured by the solar energetic particle instrument (SEP; Larson et al. 2015) are utilized in the identification of shock drivers. The MAVEN data are utilized in the MSO coordinate system, in which X points from Mars toward the Sun, Y points in the opposite direction of the Mars orbital velocity component perpendicular to X, and Z completes the right-handed system.

## 3. Methodology and Data Analysis

### 3.1. Shock Parameters

To analyze and quantify the shock parameters, the upstream and downstream time intervals of a shock need to be determined in the first step. In practice, however, the ideal analysis interval set has proved difficult to find (Berdichevsky et al. 2000). Following earlier works of Kilpua et al. (2015) and Huang et al. (2019), we analyze the upstream and downstream conditions over a fixed analysis interval, i.e., 8 minutes. The upstream analysis interval begins 1 minute away from the shock and extends to 9 minutes away from it, and the downstream analysis interval begins 2 minutes away from the shock and extends to 10 minutes away from it. For each analysis interval, a careful examination is conducted to eliminate the periods with magnetic structures, discontinuities, or fluctuations that could contaminate the estimation of shock parameters. In some cases, the shocks are encountered by MAVEN just after the outbound bow shock crossings or just before inbound bow shock crossings, and thus the intervals of upstream and downstream might be less than 8 minutes. The optimal upstream and downstream intervals are chosen to ensure that they are far from the shock ramp and include a sufficient number of data points. It should be noted that the selected intervals cannot be ideal for all shocks and therefore may result in errors in the estimation of the shock parameters.

The most important parameters of IP shocks are the fast magnetosonic Mach number $M_f$, the shock angle $\theta_{Bn}$, i.e., the angle between the shock normal and the upstream magnetic field, and the upstream plasma beta $\beta^{up}$. Hereafter, the superscript “up” and “down” correspond to the upstream and downstream of the shock, respectively. $M_f$ can efficiently describe the strength of the shock, $\theta_{Bn}$ determines whether the shock is quasi-perpendicular or quasi-parallel, and $\beta^{up}$ characterizes the upstream conditions. The methods we have used in the calculation of these parameters are described below.

The upstream fast magnetosonic Mach number of the shock $M_f$ is calculated by the formula:

$$M_f = \frac{V_{sh} \cdot n - V_p^{up} \cdot n}{V_f^{up}} \quad (1)$$

where $V_{sh}$ is the shock velocity, $n$ is the shock normal, $V_p^{up}$ is the upstream proton velocity, and $V_f^{up}$ is the upstream fast magnetosonic speed in the MSO coordinate system.
The term $V_{\text{sh}} \cdot n$ in Equation (1) is calculated from the mass flux conservation equation across the shock:

$$V_{\text{sh}} \cdot n = \frac{N_{p}^{\text{down}} V_{p}^{\text{down}} - N_{p}^{\text{up}} V_{p}^{\text{up}}}{N_{p}^{\text{down}} - N_{p}^{\text{up}}} \cdot n \quad (2)$$

where $N_p$ is the proton number density and $V_p$ is the proton velocity. For FF shocks, the shock speed $V_{\text{sh}} = V_{\text{sh}} \cdot n$; for FR shocks, $V_{\text{sh}} = -V_{\text{sh}} \cdot n$. The shock normal $n$ is estimated using the mixed mode method (i.e., the MD3 method in Abraham-Shrauner & Yun 1976):

$$n = \pm \frac{(\mathbf{B}^{\text{down}} - \mathbf{B}^{\text{up}}) \times ((\mathbf{B}^{\text{down}} - \mathbf{B}^{\text{up}}) \times (V_{p}^{\text{down}} - V_{p}^{\text{up}}))}{|\mathbf{B}^{\text{down}} - \mathbf{B}^{\text{up}}| \times ((\mathbf{B}^{\text{down}} - \mathbf{B}^{\text{up}}) \times (V_{p}^{\text{down}} - V_{p}^{\text{up}}))} \quad (3)$$

where $B$ is the magnetic field. The term $n$ is the normal direction pointing upstream, and the sign of $n$ is determined using conditions of the proton velocity. In the MSO coordinate system, the $x$ component $n_x$ should be less than 0 for FF shocks, but larger than 0 for FR shocks. Once the shock normal $n$ is determined, we can analyze other shock parameters, such as the tangential component of the magnetic field $B_t = \sqrt{|\mathbf{B}|^2 - (\mathbf{B} \cdot n)^2}$, and the normal component of the proton velocity $U_n = V_p \cdot n - V_{\text{sh}} \cdot n$ in the shock frame. As discussed later, the downstream to upstream ratios of $B_t$ and $U_n$ can also be used to describe the compression ratios at shocks.

The term $V_f^{\text{up}}$ in Equation (1) is calculated by

$$V_f^{\text{up}} = \sqrt{\frac{1}{2}[(V_A^{\text{up2}} + V_{cs}^{\text{up2}}) + \sqrt{(V_A^{\text{up2}} + V_{cs}^{\text{up2}})^2 - 4V_A^{\text{up2}}V_{cs}^{\text{up2}} \cos^2 \theta_{\text{Bn}}}]} \quad (4)$$

where $V_{\text{cs}}^{\text{up}}$ is the upstream sound speed and $V_A^{\text{up}}$ is the upstream Alfvén speed. To compute the characteristic velocities $V_{\text{cs}}^{\text{up}}$ and $V_A^{\text{up}}$, we develop a method to compute separate proton and alpha particle moments, instead of using the general treatment assuming that all ions are protons, which returns artificially large proton temperature estimates and therefore incorrect $V_f^{\text{up}}$. Specifically, the method uses the Fine 3D distributions, bisects the measured distribution at the minimum in count rate between the proton and alpha peaks, and calculates separate moments for the two portions of the distribution, namely proton density $N_p$, proton temperature $T_p$, alpha particle density $N_\alpha$ and alpha particle temperature $T_\alpha$. We should note here that the calculation assumes the presence of only two particle populations (protons and alpha particles). The electron density $N_e$ is generally overestimated due to the influence of the spacecraft photoelectrons, and thus is estimated by setting $N_e = N_p + N_\alpha$. Accordingly, the upstream sound speed $V_{\text{cs}}^{\text{up}}$ is computed as $V_{\text{cs}}^{\text{up}} = \sqrt{\frac{1}{m_p}(\gamma_i(N_p^{\text{up}}T_p^{\text{up}} + N_\alpha^{\text{up}}T_\alpha^{\text{up}}) + \gamma_e(N_e^{\text{up}}T_e^{\text{up}})}{N_p^{\text{up}} + 4N_\alpha^{\text{up}}}}$ ($\gamma$ is the polytropic index, $m_p$ is the proton mass, and $T_e$ is the electron temperature; the temperatures are in units of eV). We take the polytropic index $\gamma_i = 2$ for ions by taking them to have only two degrees of freedom, one of which is for the guiding center motion along the magnetic field lines and the other one is for the perpendicular gyromotion with a fixed Larmor radius

(Fairfield 1971; Tatrallyay et al. 1984). We also take $\gamma_e = 1$ for electrons, whose thermal speed is much faster than the ion acoustic wave phase speed and, hence, they behave more like an isothermal gas (Sittler & Scudder 1980; Chen et al. 1984; Gary 1993). The upstream Alfvén speed $V_A^{\text{up}}$ is determined by $V_A^{\text{up}} = \frac{B^{\text{up}}}{\sqrt{\mu_0 m_p (N_p^{\text{up}} + 4N_\alpha^{\text{up}})}}$ ($\mu_0$ is the vacuum permeability).

The shock angle $\theta_{\text{Bn}}$ is the acute angle between the shock normal and the upstream magnetic field. It is calculated by

$$\theta_{\text{Bn}} = \frac{180}{\pi} \arccos \left( \frac{|\mathbf{B}^{\text{up}} \cdot \mathbf{n}|}{|\mathbf{B}^{\text{up}}||\mathbf{n}|} \right) \quad (5)$$

The upstream plasma beta $\beta^{\text{up}}$ is defined as the ratio of plasma to magnetic pressure. It is calculated by

$$\beta^{\text{up}} = \frac{N_p^{\text{up}} T_p^{\text{up}} + N_\alpha^{\text{up}} T_\alpha^{\text{up}} + N_e^{\text{up}} T_e^{\text{up}}}{B^{\text{up2}}/2\mu_0} \quad (6)$$

## 3.2. Identification of Shocks and Their Drivers

We search for the shock candidates by visually surveying 3 hr plots of the temporal variations of solar wind plasma and magnetic field observations. When there are sharp increases in proton speed $V_p$, proton density $N_p$, proton temperature $T_p$, and interplanetary magnetic field (IMF) magnitude $B$, along with a broadening of ion energy spectra, the discontinuity is classified as a potential FF shock. When there is a sharp increase in proton speed $V_p$ but decreases in the other parameters, the discontinuity is classified as a potential FR shock. For some ambiguous events, we check for the presence of the expected discontinuities in the electron moments and electron energy spectra. Assuming that the candidates are fast shocks, the times of the shocks are determined using 1 s resolution magnetic field data, and then the shock parameters are computed using the methods described above.

To confirm the hypothesis that the candidates are IP fast shocks, we require the following criteria to be satisfied: (1) for every case, we clearly identify the two crossings of the Martian bow shock closer to the planet during the orbit, (2) the upstream and downstream normal components of the proton velocity, i.e., $U_n^{\text{up}}$ and $U_n^{\text{down}}$, have negative values in the shock frame, (3) the $V_{\text{sh}}$ is larger than 0, and (4) the fast magnetosonic Mach number $M_f$ is greater than 1. Based on these criteria, we identify 52 fast shocks, including 39 FF shocks and 13 FR shocks. It should be noted that a fast shock can only exist when the relative speed between the shock and the upstream medium is larger than the upstream fast magnetosonic speed, i.e, the fast magnetosonic Mach number $M_f > 1$. However, several factors would lead to errors in the calculations of $M_f$. First, we obtain the proton and alpha particle moments by assuming the presence of only two particle populations, but in fact other populations such as solar wind heavy ions and ion populations that originate locally in the Martian environment also contribute. Second, the method used to determine the shock normal $n$ can result in errors (Schwartz 1998), and in turn affect the values of $M_f$. In addition, the selection of the analysis interval affects the shock parameters and therefore $M_f$. For these reasons, some candidates with $M_f < 1$ may be fast shocks, but they are excluded in this work. So we do not claim to have identified all of the IP fast shocks that were present.

Figures 1(a) and (b) show two examples of IP shocks encountered by MAVEN: an FF shock and an FR shock. The
<figure><img src="image_4.png" /><figcaption>**Figure 1.** An FF shock (a) and an FR shock (b) observed by MAVEN. From top to bottom: the MAVEN spacecraft position in units of $R_M$, ion energy spectra, electron energy spectra, proton speed ($V_p$), proton density ($N_p$), proton temperature ($T_p$), magnetic field strength ($B$), electron speed ($V_e$), electron density ($N_e$), and electron temperature ($T_e$). Red vertical lines mark the shocks. The intervals between two black dashed lines before and after the shock correspond to the shock upstream (downstream) and downstream (upstream), respectively.</figcaption></figure>

FF shock was observed around 20:05 UT on 2016 July 19. It is clearly distinguished by sharp increases in proton speed $V_p$, density $N_p$, temperature $T_p$, and magnetic field magnitude $B$. Moreover, the ion spectra are significantly broadened and strengthened across the shock from the upstream to the downstream. Similar variations are present in the electron moments and energy spectra. The FR shock was observed

around 19:06 UT on 2015 August 20. It is characterized by an abrupt increase in proton speed and decreases in density, temperature, and magnetic field magnitude. The ion energy spectra are broadened across the shock from the upstream to the downstream. Similar variations are also found in the electron moments and energy spectra except for electron speed and temperature.
To identify the drivers of the shocks, we examine the plasma and magnetic field observations over a period of 1–3 days behind (ahead of) the FF (FR) shocks. Our preliminary analysis shows that the shocks are mainly driven by ICMEs and SIRs, as expected. The ICMEs are distinguished by three or more of the following features: enhanced magnetic field magnitude *B*, smoothly changing magnetic field direction, declining proton speed *V*<sub>p</sub> profile, low proton temperature *T*<sub>p</sub>, low plasma β, bidirectional streaming of electrons, and SEP ions and electrons (Zurbuchen & Richardson 2006; Richardson & Cane 2010b). When Mars and Earth (or STEREO-A) are approximately aligned along the same nominal Parker spiral field line, the ICMEs observed at 1 au are likely to arrive at Mars. In such cases, the measurements from WIND, ACE, and STEREO-A are also examined to ensure identification of ICMEs. The SIRs are identified by the signatures including a compression of magnetic field magnitude *B*, an increase of proton speed *V*<sub>p</sub>, an increase of proton density *N*<sub>p</sub>, and an enhancement of proton temperature *T*<sub>p</sub> (Huang et al. 2019). In addition to examining the solar wind data, we refer to the available SIR list compiled by Huang et al. (2019). Among the 39 FF shocks, 7 shocks are driven by ICMEs, 31 shocks are driven by SIRs, and the remaining one seems not to be followed by an ICME or an SIR observed in situ. The 13 FR shocks are all driven by SIRs.

Table 1 lists all 52 fast shocks encountered by MAVEN upstream from the Martian bow shock between 2014 October and 2018 November, which are categorized into several groups based on their types (FF or FR) and their drivers. The catalog includes the shock arrival time, the downstream to upstream ratio of magnetic field magnitude $B^{\text{down}}/B^{\text{up}}$, proton speed difference $\Delta V_p$, downstream to upstream ratio of proton density $N_p^{\text{down}}/N_p^{\text{up}}$, downstream to upstream ratio of proton temperature $T_p^{\text{down}}/T_p^{\text{up}}$, downstream to upstream ratio of proton entropy $S_p^{\text{down}}/S_p^{\text{up}}$ (here $S_p = T_p/N_p^{2/3}$), shock normal unit vector **n** ($n_x, n_y, n_z$), downstream to upstream ratio of the tangential component of magnetic field $B_t^{\text{down}}/B_t^{\text{up}}$, downstream to upstream ratio of the normal component of proton velocity in the shock frame $U_n^{\text{down}}/U_n^{\text{up}}$, the normal component of proton velocity in the shock frame $U_n^{\text{up}}$, shock angle $\theta_{Bn}$, shock speed $V_{sh}$, upstream plasma beta $\beta^{\text{up}}$, upstream sound speed $V_{\text{cs}}^{\text{up}}$, upstream Aflévén speed $V_A^{\text{up}}$, upstream fast magnetosonic speed $V_f^{\text{up}}$, sonic Mach number $M_{cs}$, Aflévén Mach number $M_A$, and fast magnetosonic Mach number $M_f$. It should be mentioned that in most cases the shock arrival time is readily identified from a step function–like increase or decrease in magnetic field magnitude *B*. In other cases where a relatively sharp transition occurs in *B*, the transition midpoint is taken as the shock arrival time. The number of SIR-driven shocks is much larger than that of ICME-driven shocks. This is attributed to the fact that the solar activity was relatively quiet during the declining phase of solar cycle 24 and there were fewer CMEs and therefore fewer ICME-driven shocks. The SIR-driven FF shocks occurred ~2.5 times more frequently than SIR-driven FR shocks. This is consistent with the previous statistical results near the solar ecliptic plane (Jian et al. 2006, 2008a, 2008b; Huang et al. 2019).

The upstream parameters of the shocks, including magnetic field magnitude $B^{\text{up}}$, proton speed $V_p^{\text{up}}$, proton density $N_p^{\text{up}}$, proton temperature $T_p^{\text{up}}$, and electron temperature $T_e^{\text{up}}$, together with the shock observation position $P_x, P_y, P_z$ (in units of the radius of Mars $R_M$), are given in Table 2.

# 4. Statistical Results

## 4.1. Shock Strength Parameters

The fast magnetosonic Mach number $M_f$ is an important parameter for the energy being processed by a shock, and provides a measure of the shock strength (Kivelson & Russell 1995). In addition, the downstream to upstream ratios of the magnetic field magnitude $B^{\text{down}}/B^{\text{up}}$ and proton density $N_p^{\text{down}}/N_p^{\text{up}}$ are often used as indicators of the shock strength (Burton et al. 1996; Echer et al. 2003; Oh et al. 2007; Kilpua et al. 2015). This raises an interesting question whether or not other compression ratio parameters, such as the downstream to upstream ratio of the tangential component of magnetic field $B_t^{\text{down}}/B_t^{\text{up}}$, the inverse of the downstream to upstream ratio of the normal component of proton velocity in the shock frame $U_n^{\text{up}}/U_n^{\text{down}}$, and the downstream to upstream ratio of proton temperature $T_p^{\text{down}}/T_p^{\text{up}}$, could also represent the shock strength. To address this issue, we investigate the relationships among all the pairs of these parameters. The results are displayed in Figure 2. As we can see, all pairs of these parameters are positively correlated, and the correlation coefficients are higher than 0.6, except for the relationship between $M_f$ and $B_t^{\text{down}}/B_t^{\text{up}}$ and that between $M_f$ and $N_p^{\text{down}}/N_p^{\text{up}}$ (or $U_n^{\text{up}}/U_n^{\text{down}}$). Note that $U_n^{\text{up}}/U_n^{\text{down}}$ is equal to $N_p^{\text{down}}/N_p^{\text{up}}$, owing to the mass flux conservation across the shock (Figure 2(c)). As mentioned earlier, the proton temperature is not accurate, and there exist multiple uncertainty factors that affect the reliable calculation of the fast magnetosonic Mach number. Thus, $T_p^{\text{down}}/T_p^{\text{up}}$ and $M_f$ are not appropriate parameters to represent the shock strength in this study. Since the component of the magnetic field along the shock normal remains constant and the tangential component is enhanced across the fast shock, it is reasonable to believe that $B_t^{\text{down}}/B_t^{\text{up}}$ is more suitable for characterizing the compression ratio of the shock than $B^{\text{down}}/B^{\text{up}}$. Here, $B_t^{\text{down}}/B_t^{\text{up}}$ is selected as the main criterion for assessing whether or not other shock parameters can properly describe the shock strength. We note that $N_p^{\text{down}}/N_p^{\text{up}}$ and $U_n^{\text{up}}/U_n^{\text{down}}$ are well correlated with $B_t^{\text{down}}/B_t^{\text{up}}$ (see Figures 2(b) and 2(k)). In conclusion, $B_t^{\text{down}}/B_t^{\text{up}}$, $N_p^{\text{down}}/N_p^{\text{up}}$, and $U_n^{\text{up}}/U_n^{\text{down}}$ can provide a better representation of the shock strength.

## 4.2. Spatial Distribution of Shock Strengths

We analyze the spatial distribution of the identified shocks in cylindrical MSO coordinates, and examine the dependence of the shock strengths on the location of the shock. The results are displayed in Figure 3, in which the locations of the shocks can be determined by two parameters, namely the solar zenith angle (SZA) and the distance from the shock to the modeled bow shock (BS) that represents the average location of the BS. Figure 3(a1) shows an example of an identified shock with an SZA of 64°, indicated by a colored dot at (1.099, 2.282). This shock was encountered at 12:29 on 2018 January 1, when MAVEN was located at (1.099, 0.783, 2.143) in the MSO coordinate system. The dot color represents the shock strength characterized by $N_p^{\text{down}}/N_p^{\text{up}}$. As shown in Figure 3(a2), the distance of this shock to the BS is marked by a line, which passes through the shock point ($P_{x_s}, P_{y_s}$) and is parallel to the BS normal vector. The intersection of the line with the surface of the BS (BS<sub>x</sub>, BS<sub>y</sub>) is located at (0.729, 1.944). The distance of the shock to the BS is about 0.501 $R_M$. Similarly, the spatial distribution of all 52 identified shocks, together with the shock strengths, are shown in Figures 3(a3) and (a4). Figure 3(b)
<table><caption>Table 1
List of Shocks Observed by MAVEN (2014.10–2018.11)</caption><thead><tr><th>No.</th><th>Time</th><th>B<sup>down</sup><br>gup</th><th>ΔV<sub>p</sub></th><th>N<sup>down</sup><sub>p</sub><br>N<sup>up</sup><sub>p</sub></th><th>T<sup>down</sup><sub>p</sub><br>T<sup>up</sup><sub>p</sub></th><th>S<sup>down</sup><sub>p</sub><br>S<sup>up</sup><sub>p</sub></th><th>n<sub>x</sub></th><th>n<sub>y</sub></th><th>n<sub>z</sub></th><th>B<sup>down</sup><sub>p</sub><br>B<sup>up</sup><sub>p</sub></th><th>U<sup>down</sup><sub>n</sub><br>U<sup>up</sup><sub>n</sub></th><th>U<sup>up</sup><sub>n</sub></th><th>θ<sub>Bn</sub></th><th>V<sub>sh</sub></th><th>β<sup>up</sup></th><th>V<sup>up</sup><sub>cs</sub></th><th>V<sup>up</sup><sub>A</sub></th><th>V<sup>up</sup><sub>f</sub></th><th>M<sub>cs</sub></th><th>M<sub>A</sub></th><th>M<sub>f</sub></th></tr></thead><tbody><tr><td colspan="21">FF Shocks Driven by Unclear Drivers</td></tr><tr><td>1</td><td>2015.12.29 13:32:28</td><td>1.19</td><td>9.1</td><td>1.21</td><td>1.03</td><td>0.90</td><td>-0.94</td><td>-0.34</td><td>0.00</td><td>1.19</td><td>0.83</td><td>-58.3</td><td>84.0</td><td>341.7</td><td>2.95</td><td>42.9</td><td>30.9</td><td>49.3</td><td>1.36</td><td>1.89</td><td>1.18</td></tr><tr><td colspan="21">FF Shocks Driven by ICMEs</td></tr><tr><td>2</td><td>2016.07.20 18:13:20</td><td>1.44</td><td>24.9</td><td>1.24</td><td>1.18</td><td>1.02</td><td>-0.80</td><td>0.48</td><td>0.35</td><td>1.67</td><td>0.81</td><td>-126.4</td><td>51.0</td><td>625.4</td><td>3.61</td><td>76.3</td><td>44.8</td><td>83.6</td><td>1.66</td><td>2.82</td><td>1.51</td></tr><tr><td>3</td><td>2016.07.27 00:55:34</td><td>1.22</td><td>8.1</td><td>1.18</td><td>1.07</td><td>0.96</td><td>-0.96</td><td>-0.25</td><td>-0.08</td><td>1.29</td><td>0.85</td><td>-72.1</td><td>60.6</td><td>414.0</td><td>0.91</td><td>42.6</td><td>50.7</td><td>62.4</td><td>1.69</td><td>1.42</td><td>1.16</td></tr><tr><td>4</td><td>2016.08.14 16:38:51</td><td>1.56</td><td>26.9</td><td>1.63</td><td>1.17</td><td>0.84</td><td>-0.95</td><td>0.30</td><td>0.02</td><td>1.84</td><td>0.61</td><td>-48.4</td><td>51.0</td><td>367.6</td><td>3.27</td><td>42.1</td><td>28.2</td><td>46.7</td><td>1.15</td><td>1.72</td><td>1.03</td></tr><tr><td>5</td><td>2016.09.23 00:20:00</td><td>1.57</td><td>20.5</td><td>2.73</td><td>1.38</td><td>0.71</td><td>-0.63</td><td>0.05</td><td>0.77</td><td>1.69</td><td>0.37</td><td>-51.1</td><td>62.4</td><td>295.0</td><td>6.53</td><td>48.4</td><td>23.7</td><td>49.5</td><td>1.06</td><td>2.16</td><td>1.03</td></tr><tr><td>6</td><td>2017.07.17 02:11:34</td><td>1.56</td><td>16.9</td><td>1.36</td><td>1.09</td><td>0.89</td><td>-0.81</td><td>-0.53</td><td>0.24</td><td>1.98</td><td>0.73</td><td>-59.7</td><td>44.4</td><td>321.6</td><td>2.15</td><td>36.0</td><td>28.6</td><td>38.9</td><td>1.66</td><td>2.09</td><td>1.53</td></tr><tr><td>7</td><td>2017.07.22 00:38:10</td><td>1.36</td><td>13.2</td><td>1.51</td><td>1.14</td><td>0.86</td><td>-0.75</td><td>-0.06</td><td>-0.66</td><td>1.39</td><td>0.66</td><td>-38.0</td><td>74.0</td><td>257.4</td><td>7.57</td><td>34.5</td><td>15.3</td><td>37.7</td><td>1.10</td><td>2.49</td><td>1.01</td></tr><tr><td>8</td><td>2018.03.10 00:10:39</td><td>1.54</td><td>18.4</td><td>1.62</td><td>1.16</td><td>0.84</td><td>-0.93</td><td>-0.03</td><td>-0.36</td><td>1.56</td><td>0.62</td><td>-57.3</td><td>78.1</td><td>380.7</td><td>1.17</td><td>42.1</td><td>45.1</td><td>52.0</td><td>1.36</td><td>1.27</td><td>1.10</td></tr><tr><td colspan="21">FF Shocks Driven by SIRs</td></tr><tr><td>9</td><td>2015.02.25 23:51:23</td><td>1.65</td><td>13.3</td><td>1.63</td><td>1.34</td><td>0.96</td><td>-0.33</td><td>-0.80</td><td>0.51</td><td>1.70</td><td>0.61</td><td>-79.4</td><td>73.7</td><td>172.1</td><td>1.57</td><td>43.1</td><td>42.1</td><td>60.2</td><td>1.84</td><td>1.88</td><td>1.32</td></tr><tr><td>10</td><td>2015.10.02 03:17:00</td><td>1.92</td><td>19.5</td><td>1.72</td><td>1.32</td><td>0.92</td><td>-0.89</td><td>-0.33</td><td>0.33</td><td>1.99</td><td>0.58</td><td>-54.6</td><td>73.2</td><td>324.3</td><td>5.04</td><td>36.6</td><td>19.2</td><td>40.1</td><td>1.49</td><td>2.85</td><td>1.36</td></tr><tr><td>11</td><td>2016.02.14 03:45:36</td><td>1.65</td><td>33.1</td><td>2.23</td><td>1.38</td><td>0.81</td><td>-0.97</td><td>0.12</td><td>-0.23</td><td>1.73</td><td>0.45</td><td>-59.6</td><td>68.9</td><td>424.6</td><td>3.60</td><td>45.9</td><td>30.2</td><td>46.5</td><td>1.30</td><td>1.97</td><td>1.28</td></tr><tr><td>12</td><td>2016.02.22 01:20:03</td><td>1.68</td><td>27.5</td><td>1.91</td><td>1.26</td><td>0.82</td><td>-0.74</td><td>-0.50</td><td>0.46</td><td>1.70</td><td>0.52</td><td>-70.1</td><td>78.6</td><td>342.4</td><td>4.24</td><td>51.7</td><td>32.0</td><td>51.8</td><td>1.36</td><td>2.19</td><td>1.35</td></tr><tr><td>13</td><td>2016.03.11 06:53:04</td><td>1.85</td><td>30.8</td><td>1.41</td><td>1.23</td><td>0.98</td><td>-0.80</td><td>-0.49</td><td>0.36</td><td>2.12</td><td>0.71</td><td>-119.2</td><td>56.4</td><td>400.5</td><td>2.02</td><td>40.6</td><td>32.8</td><td>41.8</td><td>2.94</td><td>3.64</td><td>2.85</td></tr><tr><td>14</td><td>2016.06.06 18:01:23</td><td>2.92</td><td>55.0</td><td>2.89</td><td>2.15</td><td>1.06</td><td>-0.72</td><td>-0.67</td><td>0.19</td><td>3.86</td><td>0.35</td><td>-89.4</td><td>47.4</td><td>299.4</td><td>8.11</td><td>43.6</td><td>19.8</td><td>44.1</td><td>2.05</td><td>4.50</td><td>2.02</td></tr><tr><td>15</td><td>2016.06.12 06:24:36</td><td>1.34</td><td>21.4</td><td>1.48</td><td>1.16</td><td>0.89</td><td>-0.99</td><td>0.09</td><td>0.07</td><td>1.35</td><td>0.68</td><td>-64.4</td><td>77.8</td><td>427.3</td><td>2.01</td><td>44.2</td><td>39.4</td><td>54.8</td><td>1.46</td><td>1.63</td><td>1.18</td></tr><tr><td>16</td><td>2016.06.23 04:17:31</td><td>1.43</td><td>9.0</td><td>1.45</td><td>1.05</td><td>0.81</td><td>-0.60</td><td>-0.34</td><td>0.73</td><td>1.44</td><td>0.69</td><td>-54.0</td><td>84.0</td><td>289.8</td><td>1.86</td><td>39.6</td><td>35.3</td><td>49.6</td><td>1.36</td><td>1.53</td><td>1.09</td></tr><tr><td>17</td><td>2016.07.07 11:25:18</td><td>1.41</td><td>16.3</td><td>1.39</td><td>1.17</td><td>0.94</td><td>-0.97</td><td>-0.25</td><td>-0.02</td><td>1.61</td><td>0.72</td><td>-65.6</td><td>52.6</td><td>383.1</td><td>2.75</td><td>37.3</td><td>28.5</td><td>44.2</td><td>1.76</td><td>2.30</td><td>1.48</td></tr><tr><td>18</td><td>2016.07.19 20:05:26</td><td>2.72</td><td>54.0</td><td>2.70</td><td>1.77</td><td>0.92</td><td>-0.95</td><td>-0.20</td><td>0.24</td><td>2.74</td><td>0.37</td><td>-91.5</td><td>83.4</td><td>422.7</td><td>3.25</td><td>42.1</td><td>28.0</td><td>50.4</td><td>2.17</td><td>3.27</td><td>1.82</td></tr><tr><td>19</td><td>2016.08.02 03:44:17</td><td>2.29</td><td>31.7</td><td>2.18</td><td>1.31</td><td>0.78</td><td>-0.90</td><td>-0.37</td><td>0.24</td><td>2.49</td><td>0.46</td><td>-63.2</td><td>64.5</td><td>365.1</td><td>4.39</td><td>42.2</td><td>24.0</td><td>48.5</td><td>1.50</td><td>2.63</td><td>1.30</td></tr><tr><td>20</td><td>2016.08.22 13:15:18</td><td>1.48</td><td>21.5</td><td>1.89</td><td>1.34</td><td>0.88</td><td>-0.81</td><td>-0.56</td><td>0.19</td><td>1.64</td><td>0.53</td><td>-68.8</td><td>56.4</td><td>362.3</td><td>1.77</td><td>50.5</td><td>45.5</td><td>53.0</td><td>1.36</td><td>1.51</td><td>1.30</td></tr><tr><td>21</td><td>2016.12.25 22:05:54</td><td>1.92</td><td>28.4</td><td>2.10</td><td>1.50</td><td>0.92</td><td>-0.75</td><td>-0.44</td><td>0.49</td><td>1.96</td><td>0.48</td><td>-77.0</td><td>76.7</td><td>303.1</td><td>4.43</td><td>39.3</td><td>23.5</td><td>45.4</td><td>1.96</td><td>3.27</td><td>1.70</td></tr><tr><td>22</td><td>2017.01.07 13:31:46</td><td>1.61</td><td>25.9</td><td>1.77</td><td>1.16</td><td>0.79</td><td>-0.93</td><td>-0.37</td><td>0.06</td><td>1.90</td><td>0.56</td><td>-75.9</td><td>51.7</td><td>387.0</td><td>1.59</td><td>39.2</td><td>37.4</td><td>54.1</td><td>1.94</td><td>2.03</td><td>1.40</td></tr><tr><td>23</td><td>2017.01.26 02:22:27</td><td>1.40</td><td>14.8</td><td>1.54</td><td>1.29</td><td>0.97</td><td>-0.47</td><td>-0.71</td><td>0.53</td><td>1.49</td><td>0.65</td><td>-66.4</td><td>62.6</td><td>249.2</td><td>2.31</td><td>41.1</td><td>33.3</td><td>42.8</td><td>1.61</td><td>2.00</td><td>1.55</td></tr><tr><td>24</td><td>2017.02.02 22:44:37</td><td>2.95</td><td>73.1</td><td>2.84</td><td>3.03</td><td>1.51</td><td>-0.80</td><td>0.34</td><td>0.50</td><td>2.95</td><td>0.35</td><td>-134.3</td><td>88.4</td><td>402.4</td><td>2.03</td><td>40.4</td><td>35.3</td><td>45.0</td><td>3.32</td><td>3.80</td><td>2.98</td></tr><tr><td>25</td><td>2017.02.23 07:08:34</td><td>2.45</td><td>95.1</td><td>2.59</td><td>2.00</td><td>1.06</td><td>-0.93</td><td>-0.37</td><td>-0.08</td><td>2.65</td><td>0.39</td><td>-157.8</td><td>65.9</td><td>427.4</td><td>7.07</td><td>41.9</td><td>19.9</td><td>42.0</td><td>3.76</td><td>7.94</td><td>3.76</td></tr><tr><td>26</td><td>2017.03.14 23:35:16</td><td>1.20</td><td>35.5</td><td>1.77</td><td>1.35</td><td>0.92</td><td>-0.80</td><td>-0.03</td><td>0.60</td><td>1.50</td><td>0.57</td><td>-78.4</td><td>36.4</td><td>336.3</td><td>5.39</td><td>44.2</td><td>23.9</td><td>50.0</td><td>1.78</td><td>3.28</td><td>1.57</td></tr><tr><td>27</td><td>2017.07.24 16:10:57</td><td>1.97</td><td>52.1</td><td>2.60</td><td>1.88</td><td>0.99</td><td>-0.75</td><td>0.31</td><td>-0.59</td><td>2.32</td><td>0.38</td><td>-67.0</td><td>54.1</td><td>343.5</td><td>4.60</td><td>58.9</td><td>34.8</td><td>64.1</td><td>1.14</td><td>1.93</td><td>1.04</td></tr><tr><td>28</td><td>2017.08.14 18:23:06</td><td>1.72</td><td>38.7</td><td>2.05</td><td>1.63</td><td>1.01</td><td>-0.92</td><td>0.05</td><td>0.38</td><td>1.78</td><td>0.49</td><td>-81.0</td><td>72.7</td><td>381.9</td><td>4.81</td><td>36.9</td><td>20.6</td><td>38.2</td><td>2.19</td><td>3.93</td><td>2.12</td></tr><tr><td>29</td><td>2018.01.01 12:29:09</td><td>2.20</td><td>22.5</td><td>1.66</td><td>1.25</td><td>0.89</td><td>-0.89</td><td>-0.44</td><td>-0.08</td><td>2.20</td><td>0.60</td><td>-62.1</td><td>89.5</td><td>383.1</td><td>14.97</td><td>38.8</td><td>12.0</td><td>40.6</td><td>1.60</td><td>5.16</td><td>1.53</td></tr><tr><td>30</td><td>2018.01.17 06:13:58</td><td>2.86</td><td>47.6</td><td>2.72</td><td>2.78</td><td>1.43</td><td>-0.74</td><td>-0.30</td><td>-0.61</td><td>2.86</td><td>0.37</td><td>-100.2</td><td>86.8</td><td>325.7</td><td>3.82</td><td>37.6</td><td>23.9</td><td>43.9</td><td>2.67</td><td>4.19</td><td>2.28</td></tr><tr><td>31</td><td>2018.02.08 20:16:29</td><td>1.69</td><td>14.0</td><td>1.76</td><td>1.26</td><td>0.86</td><td>-0.69</td><td>-0.67</td><td>0.28</td><td>1.72</td><td>0.57</td><td>-43.1</td><td>78.2</td><td>250.9</td><td>6.52</td><td>35.7</td><td>16.7</td><td>36.2</td><td>1.21</td><td>2.58</td><td>1.19</td></tr><tr><td>32</td><td>2018.03.01 19:12:48</td><td>1.43</td><td>16.4</td><td>1.43</td><td>1.11</td><td>0.87</td><td>-0.83</td><td>-0.50</td><td>-0.27</td><td>1.60</td><td>0.70</td><td>-67.5</td><td>55.2</td><td>360.8</td><td>5.58</td><td>48.8</td><td>24.3</td><td>54.4</td><td>1.38</td><td>2.77</td><td>1.24</td></tr><tr><td>33</td><td>2018.03.09 19:37:40</td><td>1.53</td><td>20.0</td><td>1.70</td><td>1.19</td><td>0.83</td><td>-0.81</td><td>0.26</td><td>-0.53</td><td>1.62</td><td>0.59</td><td>-44.2</td><td>65.8</td><td>310.2</td><td>3.70</td><td>38.3</td><td>23.6</td><td>38.6</td><td>1.15</td><td>1.87</td><td>1.14</td></tr><tr><td>34</td><td>2018.03.12 23:00:33</td><td>2.58</td><td>33.0</td><td>2.61</td><td>1.63</td><td>0.86</td><td>-0.73</td><td>0.03</td><td>-0.68</td><td>2.88</td><td>0.38</td><td>-83.2</td><td>61.7</td><td>353.9</td><td>5.67</td><td>48.0</td><td>24.2</td><td>53.1</td><td>1.73</td><td>3.43</td><td>1.57</td></tr><tr><td>35</td><td>2018.06.20 19:40:23</td><td>1.88</td><td>22.1</td><td>1.98</td><td>1.49</td><td>0.95</td><td>-0.71</td><td>-0.35</td><td>-0.61</td><td>1.90</td><td>0.50</td><td>-59.3</td><td>80.7</td><td>251.3</td><td>9.56</td><td>35.6</td><td>14.7</td><td>37.8</td><td>1.67</td><td>4.04</td><td>1.57</td></tr><tr><td>36</td><td>2018.08.03 07:00:51</td><td>1.31</td><td>8.3</td><td>1.34</td><td>1.12</td><td>0.92</td><td>-0.77</td><td>-0.35</td><td>-0.53</td><td>1.31</td><td>0.74</td><td>-39.4</td><td>88.2</td><td>269.6</td><td>2.55</td><td>37.8</td><td>29.7</td><td>39.3</td><td>1.04</td><td>1.33</td><td>1.00</td></tr><tr><td>37</td><td>2018.08.12 04:47:00</td><td>1.76</td><td>17.3</td><td>2.35</td><td>1.39</td><td>0.79</td><td>-0.53</td><td>-0.48</td><td>0.69</td><td>2.82</td><td>0.43</td><td>-62.9</td><td>33.2</td><td>230.4</td><td>8.44</td><td>44.7</td><td>18.1</td><td>48.1</td><td>1.41</td><td>3.47</td><td>1.31</td></tr><tr><td>38</td><td>2018.09.11 04:36:24</td><td>2.91</td><td>33.7</td><td>2.07</td><td>2.00</td><td>1.23</td><td>-0.88</td><td>-0.46</td><td>0.12</td><td>2.98</td><td>0.48</td><td>-77.5</td><td>76.5</td><td>352.0</td><td>3.57</td><td>35.3</td><td>22.3</td><td>40.6</td><td>2.19</td><td>3.48</td><td>1.91</td></tr><tr><td>39</td><td>2018.11.03 14:21:41</td><td>1.77</td><td>22.7</td><td>1.47</td><td>1.11</td><td>0.86</td><td>-0.85</td><td>-0.26</td><td>0.45</td><td>1.79</td><td>0.68</td><td>-72.9</td><td>77.7</td><td>356.5</td><td>5.52</td><td>41.1</td><td>21.6</td><td>44.4</td><td>1.77</td><td>3.37</td><td>1.64</td></tr><tr><td colspan="21">FR Shocks Driven by SIRs</td></tr></tbody></table>
<table><caption>Table 1
(Continued)</caption><thead><tr><th>No.</th><th>Time</th><th><i>B</i><sup>down</sup>/<i>B</i><sup>up</sup></th><th>Δ<i>V</i><sub>p</sub></th><th><i>N</i><sub>p</sub><sup>down</sup>/<i>N</i><sub>p</sub><sup>up</sup></th><th><i>T</i><sub>p</sub><sup>down</sup>/<i>T</i><sub>p</sub><sup>up</sup></th><th><i>S</i><sub>p</sub><sup>down</sup>/<i>S</i><sub>p</sub><sup>up</sup></th><th><i>n</i><sub>x</sub></th><th><i>n</i><sub>y</sub></th><th><i>n</i><sub>z</sub></th><th><i>B</i><sub>t</sub><sup>down</sup>/<i>B</i><sup>up</sup></th><th><i>U</i><sub>h</sub><sup>down</sup>/<i>U</i><sub>h</sub><sup>up</sup></th><th><i>U</i><sub>n</sub><sup>up</sup></th><th><i>θ</i><sub>Bn</sub></th><th><i>V</i><sub>sh</sub></th><th><i>β</i><sup>up</sup></th><th><i>V</i><sub>cs</sub><sup>up</sup></th><th><i>V</i><sub>A</sub><sup>up</sup></th><th><i>V</i><sub>f</sub><sup>up</sup></th><th><i>M</i><sub>cs</sub></th><th><i>M</i><sub>A</sub></th><th><i>M</i><sub>f</sub></th></tr></thead><tbody><tr><td>40</td><td>2015.01.02 23:27:55</td><td>1.43</td><td>-18.8</td><td>1.47</td><td>1.14</td><td>0.88</td><td>0.76</td><td>-0.15</td><td>0.63</td><td>1.54</td><td>0.68</td><td>-78.4</td><td>60.8</td><td>293.1</td><td>2.31</td><td>64.1</td><td>46.9</td><td>77.7</td><td>1.22</td><td>1.67</td><td>1.01</td></tr><tr><td>41</td><td>2015.07.27 15:59:34</td><td>1.78</td><td>-87.1</td><td>2.91</td><td>2.03</td><td>1.00</td><td>0.99</td><td>0.09</td><td>0.06</td><td>2.07</td><td>0.34</td><td>-133.7</td><td>54.2</td><td>352.1</td><td>8.60</td><td>60.3</td><td>25.2</td><td>63.3</td><td>2.22</td><td>5.31</td><td>2.11</td></tr><tr><td>42</td><td>2015.08.20 19:06:20</td><td>1.79</td><td>-54.5</td><td>1.82</td><td>1.19</td><td>0.80</td><td>0.69</td><td>0.72</td><td>0.00</td><td>2.19</td><td>0.55</td><td>-132.2</td><td>49.8</td><td>250.1</td><td>2.62</td><td>66.8</td><td>46.7</td><td>71.1</td><td>1.98</td><td>2.83</td><td>1.86</td></tr><tr><td>43</td><td>2016.01.14 00:00:15</td><td>1.85</td><td>-43.7</td><td>1.74</td><td>1.25</td><td>0.86</td><td>0.91</td><td>0.40</td><td>0.10</td><td>1.86</td><td>0.58</td><td>-128.6</td><td>81.6</td><td>365.9</td><td>1.83</td><td>65.8</td><td>57.3</td><td>67.1</td><td>1.95</td><td>2.24</td><td>1.92</td></tr><tr><td>44</td><td>2016.06.07 20:44:07</td><td>1.55</td><td>-22.3</td><td>1.64</td><td>1.16</td><td>0.83</td><td>0.67</td><td>0.14</td><td>-0.73</td><td>1.56</td><td>0.61</td><td>-88.9</td><td>80.9</td><td>237.3</td><td>1.70</td><td>65.9</td><td>58.8</td><td>81.6</td><td>1.35</td><td>1.51</td><td>1.09</td></tr><tr><td>45</td><td>2016.07.03 23:44:40</td><td>1.60</td><td>-47.8</td><td>1.81</td><td>1.22</td><td>0.82</td><td>0.99</td><td>0.10</td><td>-0.06</td><td>1.99</td><td>0.55</td><td>-106.1</td><td>46.6</td><td>368.6</td><td>2.35</td><td>66.3</td><td>50.4</td><td>73.1</td><td>1.60</td><td>2.11</td><td>1.45</td></tr><tr><td>46</td><td>2016.08.03 07:37:02</td><td>1.45</td><td>-20.1</td><td>1.52</td><td>0.98</td><td>0.75</td><td>0.51</td><td>0.86</td><td>0.09</td><td>1.47</td><td>0.66</td><td>-118.5</td><td>76.3</td><td>136.2</td><td>1.47</td><td>78.8</td><td>74.4</td><td>102.0</td><td>1.50</td><td>1.59</td><td>1.16</td></tr><tr><td>47</td><td>2016.08.18 21:58:32</td><td>1.41</td><td>-23.3</td><td>1.49</td><td>1.16</td><td>0.89</td><td>0.83</td><td>0.22</td><td>-0.51</td><td>1.77</td><td>0.67</td><td>-123.8</td><td>43.0</td><td>309.1</td><td>0.87</td><td>65.3</td><td>86.8</td><td>104.6</td><td>1.90</td><td>1.43</td><td>1.18</td></tr><tr><td>48</td><td>2016.09.18 04:51:18</td><td>1.65</td><td>-81.7</td><td>2.24</td><td>1.17</td><td>0.68</td><td>0.72</td><td>0.70</td><td>0.02</td><td>1.67</td><td>0.45</td><td>-144.1</td><td>80.6</td><td>289.0</td><td>1.83</td><td>84.2</td><td>67.6</td><td>105.5</td><td>1.71</td><td>2.13</td><td>1.37</td></tr><tr><td>49</td><td>2017.01.26 21:15:50</td><td>1.50</td><td>-36.0</td><td>1.48</td><td>1.12</td><td>0.86</td><td>0.66</td><td>0.68</td><td>-0.31</td><td>1.58</td><td>0.68</td><td>-134.2</td><td>66.0</td><td>221.9</td><td>2.34</td><td>96.1</td><td>67.1</td><td>96.2</td><td>1.40</td><td>2.00</td><td>1.40</td></tr><tr><td>50</td><td>2018.03.21 04:18:00</td><td>1.22</td><td>-37.0</td><td>1.75</td><td>1.17</td><td>0.81</td><td>0.41</td><td>0.45</td><td>-0.79</td><td>1.28</td><td>0.57</td><td>-96.9</td><td>60.4</td><td>136.2</td><td>2.10</td><td>67.6</td><td>52.9</td><td>78.4</td><td>1.43</td><td>1.83</td><td>1.24</td></tr><tr><td>51</td><td>2018.07.23 10:08:42</td><td>1.78</td><td>-38.1</td><td>1.74</td><td>1.36</td><td>0.94</td><td>0.80</td><td>0.17</td><td>-0.58</td><td>2.30</td><td>0.58</td><td>-118.3</td><td>45.3</td><td>265.9</td><td>3.98</td><td>67.7</td><td>38.2</td><td>77.2</td><td>1.75</td><td>3.10</td><td>1.53</td></tr><tr><td>52</td><td>2018.11.04 13:07:23</td><td>2.52</td><td>-35.0</td><td>1.96</td><td>1.30</td><td>0.83</td><td>0.91</td><td>0.17</td><td>-0.38</td><td>3.01</td><td>0.51</td><td>-93.9</td><td>54.3</td><td>360.5</td><td>13.57</td><td>64.9</td><td>20.1</td><td>66.9</td><td>1.45</td><td>4.67</td><td>1.40</td></tr></tbody></table>

Note. The units of Δ<i>V</i><sub>p</sub>, <i>U</i><sub>n</sub><sup>up</sup>, <i>V</i><sub>sh</sub>, <i>V</i><sub>cs</sub><sup>up</sup>, <i>V</i><sub>A</sub><sup>up</sup>, and <i>V</i><sub>f</sub><sup>up</sup> are km s<sup>-1</sup>. The unit of <i>θ</i><sub>Bn</sub> is degrees.
<table><caption>Table 2
Shock Upstream Parameters and Shock Positions</caption><thead><tr><th>No.</th><th>Time</th><th>B<sup>up</sup></th><th>V<sup>up</sup><sub>p</sub></th><th>N<sup>up</sup><sub>p</sub></th><th>T<sup>up</sup><sub>p</sub></th><th>T<sup>up</sup><sub>e</sub></th><th>P<sub>x</sub></th><th>P<sub>y</sub></th><th>P<sub>z</sub></th></tr></thead><tbody><tr><td colspan="10">FF Shocks Driven by Unclear Drivers</td></tr><tr><td>1</td><td>2015.12.29 13:32:28</td><td>2.24</td><td>300</td><td>2.34</td><td>6.05</td><td>10.75</td><td>0.261</td><td>2.323</td><td>-1.550</td></tr><tr><td colspan="10">FF Shocks Driven ICMEs</td></tr><tr><td>2</td><td>2016.07.20 18:13:20</td><td>3.36</td><td>600</td><td>2.46</td><td>31.21</td><td>16.07</td><td>2.300</td><td>1.362</td><td>-0.236</td></tr><tr><td>3</td><td>2016.07.27 00:55:34</td><td>5.82</td><td>364</td><td>5.87</td><td>8.69</td><td>5.87</td><td>1.755</td><td>1.250</td><td>-0.816</td></tr><tr><td>4</td><td>2016.08.14 16:38:51</td><td>2.25</td><td>333</td><td>2.82</td><td>6.89</td><td>9.27</td><td>2.553</td><td>-0.387</td><td>-0.003</td></tr><tr><td>5</td><td>2016.09.23 00:20:00</td><td>1.51</td><td>376</td><td>1.90</td><td>6.53</td><td>14.09</td><td>0.816</td><td>-2.503</td><td>0.421</td></tr><tr><td>6</td><td>2017.07.17 02:11:34</td><td>2.06</td><td>334</td><td>2.34</td><td>5.81</td><td>5.07</td><td>0.727</td><td>-1.461</td><td>-1.783</td></tr><tr><td>7</td><td>2017.07.22 00:38:10</td><td>1.27</td><td>292</td><td>3.14</td><td>4.42</td><td>6.29</td><td>0.172</td><td>-0.986</td><td>-2.630</td></tr><tr><td>8</td><td>2018.03.10 00:10:39</td><td>4.21</td><td>340</td><td>4.01</td><td>7.04</td><td>6.57</td><td>1.689</td><td>0.646</td><td>0.707</td></tr><tr><td colspan="10">FF Shocks Driven SIRs</td></tr><tr><td>9</td><td>2015.02.25 23:51:23</td><td>3.84</td><td>347</td><td>3.72</td><td>6.56</td><td>10.36</td><td>1.194</td><td>-0.913</td><td>-1.670</td></tr><tr><td>10</td><td>2015.10.02 03:17:00</td><td>1.96</td><td>317</td><td>4.73</td><td>5.72</td><td>5.71</td><td>0.040</td><td>0.141</td><td>2.665</td></tr><tr><td>11</td><td>2016.02.14 03:45:36</td><td>2.19</td><td>374</td><td>2.34</td><td>7.17</td><td>13.06</td><td>0.172</td><td>0.221</td><td>-2.752</td></tr><tr><td>12</td><td>2016.02.22 01:20:03</td><td>2.13</td><td>376</td><td>1.95</td><td>7.93</td><td>18.95</td><td>0.596</td><td>0.252</td><td>-2.766</td></tr><tr><td>13</td><td>2016.03.11 06:53:04</td><td>3.64</td><td>360</td><td>5.36</td><td>8.86</td><td>6.00</td><td>1.331</td><td>-0.111</td><td>-1.963</td></tr><tr><td>14</td><td>2016.06.06 18:01:23</td><td>1.46</td><td>305</td><td>2.47</td><td>4.60</td><td>14.13</td><td>-0.203</td><td>2.617</td><td>-0.976</td></tr><tr><td>15</td><td>2016.06.12 06:24:36</td><td>3.40</td><td>364</td><td>3.37</td><td>5.57</td><td>12.87</td><td>0.892</td><td>2.337</td><td>0.603</td></tr><tr><td>16</td><td>2016.06.23 04:17:31</td><td>2.98</td><td>368</td><td>3.20</td><td>6.06</td><td>8.33</td><td>0.161</td><td>2.054</td><td>-1.286</td></tr><tr><td>17</td><td>2016.07.07 11:25:18</td><td>2.25</td><td>330</td><td>2.93</td><td>3.16</td><td>9.01</td><td>2.174</td><td>1.603</td><td>0.557</td></tr><tr><td>18</td><td>2016.07.19 20:05:26</td><td>1.99</td><td>349</td><td>2.29</td><td>6.78</td><td>8.56</td><td>2.301</td><td>1.397</td><td>-0.200</td></tr><tr><td>19</td><td>2016.08.02 03:44:17</td><td>2.34</td><td>345</td><td>4.25</td><td>7.30</td><td>8.27</td><td>2.329</td><td>-0.562</td><td>1.155</td></tr><tr><td>20</td><td>2016.08.22 13:15:18</td><td>3.53</td><td>372</td><td>2.73</td><td>9.22</td><td>12.29</td><td>1.610</td><td>-1.861</td><td>1.393</td></tr><tr><td>21</td><td>2016.12.25 22:05:54</td><td>1.86</td><td>303</td><td>2.82</td><td>5.24</td><td>9.98</td><td>0.813</td><td>0.938</td><td>2.486</td></tr><tr><td>22</td><td>2017.01.07 13:31:46</td><td>2.70</td><td>341</td><td>2.37</td><td>5.81</td><td>7.49</td><td>1.133</td><td>0.499</td><td>2.550</td></tr><tr><td>23</td><td>2017.01.26 02:22:27</td><td>3.19</td><td>347</td><td>4.19</td><td>5.80</td><td>9.40</td><td>1.568</td><td>-0.719</td><td>2.188</td></tr><tr><td>24</td><td>2017.02.02 22:44:37</td><td>2.01</td><td>336</td><td>1.48</td><td>5.14</td><td>9.81</td><td>1.079</td><td>-0.481</td><td>2.621</td></tr><tr><td>25</td><td>2017.02.23 07:08:34</td><td>1.79</td><td>291</td><td>3.62</td><td>6.79</td><td>11.44</td><td>0.540</td><td>-2.112</td><td>-0.111</td></tr><tr><td>26</td><td>2017.03.14 23:35:16</td><td>1.94</td><td>327</td><td>3.07</td><td>5.10</td><td>12.19</td><td>-0.276</td><td>-2.532</td><td>1.325</td></tr><tr><td>27</td><td>2017.07.24 16:10:57</td><td>2.46</td><td>350</td><td>2.27</td><td>9.18</td><td>23.15</td><td>0.067</td><td>-0.873</td><td>-2.707</td></tr><tr><td>28</td><td>2017.08.14 18:23:06</td><td>1.50</td><td>325</td><td>2.42</td><td>4.55</td><td>7.36</td><td>0.079</td><td>-2.244</td><td>-1.396</td></tr><tr><td>29</td><td>2018.01.01 12:29:09</td><td>1.26</td><td>359</td><td>5.10</td><td>5.19</td><td>7.10</td><td>1.099</td><td>0.783</td><td>2.143</td></tr><tr><td>30</td><td>2018.01.17 06:13:58</td><td>1.57</td><td>311</td><td>2.00</td><td>3.99</td><td>8.32</td><td>1.004</td><td>1.679</td><td>2.032</td></tr><tr><td>31</td><td>2018.02.08 20:16:29</td><td>1.22</td><td>318</td><td>2.48</td><td>4.23</td><td>5.84</td><td>1.804</td><td>0.026</td><td>2.177</td></tr><tr><td>32</td><td>2018.03.01 19:12:48</td><td>1.58</td><td>363</td><td>1.95</td><td>8.20</td><td>9.94</td><td>1.592</td><td>0.973</td><td>0.750</td></tr><tr><td>33</td><td>2018.03.09 19:37:40</td><td>1.68</td><td>318</td><td>2.36</td><td>5.16</td><td>6.35</td><td>1.762</td><td>0.549</td><td>0.855</td></tr><tr><td>34</td><td>2018.03.12 23:00:33</td><td>1.64</td><td>386</td><td>2.08</td><td>8.70</td><td>11.20</td><td>1.743</td><td>-0.704</td><td>1.850</td></tr><tr><td>35</td><td>2018.06.20 19:40:23</td><td>1.78</td><td>281</td><td>6.93</td><td>2.84</td><td>8.43</td><td>-0.452</td><td>2.459</td><td>1.233</td></tr><tr><td>36</td><td>2018.08.03 07:00:51</td><td>3.17</td><td>299</td><td>5.30</td><td>4.05</td><td>8.79</td><td>2.050</td><td>1.205</td><td>-1.015</td></tr><tr><td>37</td><td>2018.08.12 04:47:00</td><td>1.76</td><td>333</td><td>4.26</td><td>7.70</td><td>8.51</td><td>2.380</td><td>1.182</td><td>0.490</td></tr><tr><td>38</td><td>2018.09.11 04:36:24</td><td>1.83</td><td>327</td><td>3.14</td><td>5.01</td><td>5.66</td><td>2.067</td><td>-0.471</td><td>-1.796</td></tr><tr><td>39</td><td>2018.11.03 14:21:41</td><td>2.97</td><td>329</td><td>8.60</td><td>5.34</td><td>9.74</td><td>0.253</td><td>0.606</td><td>-2.667</td></tr><tr><td colspan="10">FR Shocks Driven SIRs</td></tr><tr><td>40</td><td>2015.01.02 23.27:55</td><td>2.88</td><td>486</td><td>1.67</td><td>22.10</td><td>10.82</td><td>1.413</td><td>0.823</td><td>-2.228</td></tr><tr><td>41</td><td>2015.07.27 15:59:34</td><td>1.25</td><td>492</td><td>1.06</td><td>15.88</td><td>21.02</td><td>1.260</td><td>1.881</td><td>0.697</td></tr><tr><td>42</td><td>2015.08.20 19:06:20</td><td>3.24</td><td>564</td><td>2.07</td><td>25.89</td><td>14.36</td><td>1.634</td><td>1.062</td><td>0.565</td></tr><tr><td>43</td><td>2016.01.14 00:00:15</td><td>3.48</td><td>562</td><td>1.61</td><td>21.76</td><td>18.90</td><td>0.895</td><td>2.084</td><td>-1.721</td></tr><tr><td>44</td><td>2016.06.07 20:44:07</td><td>3.89</td><td>532</td><td>1.92</td><td>22.02</td><td>17.31</td><td>-0.036</td><td>2.705</td><td>-0.787</td></tr><tr><td>45</td><td>2016.07.03 23:44:40</td><td>4.49</td><td>489</td><td>3.50</td><td>20.29</td><td>17.86</td><td>1.895</td><td>2.042</td><td>0.146</td></tr><tr><td>46</td><td>2016.08.03 07:37:02</td><td>4.28</td><td>587</td><td>1.43</td><td>34.30</td><td>22.07</td><td>1.303</td><td>1.016</td><td>-1.019</td></tr><tr><td>47</td><td>2016.08.18 21:58:32</td><td>4.41</td><td>514</td><td>1.17</td><td>13.78</td><td>24.66</td><td>2.463</td><td>-1.327</td><td>0.763</td></tr><tr><td>48</td><td>2016.09.18 04:51:18</td><td>5.31</td><td>661</td><td>2.75</td><td>38.81</td><td>14.33</td><td>1.291</td><td>-2.189</td><td>0.106</td></tr><tr><td>49</td><td>2017.01.26 21:15:50</td><td>6.32</td><td>637</td><td>3.84</td><td>53.82</td><td>14.84</td><td>1.084</td><td>-0.133</td><td>2.666</td></tr><tr><td>50</td><td>2018.03.21 04:18:00</td><td>2.69</td><td>610</td><td>1.09</td><td>28.29</td><td>15.42</td><td>1.782</td><td>-0.457</td><td>1.376</td></tr><tr><td>51</td><td>2018.07.23 10:08:42</td><td>2.64</td><td>494</td><td>2.15</td><td>22.25</td><td>13.48</td><td>1.664</td><td>2.133</td><td>0.702</td></tr><tr><td>52</td><td>2018.11.04 13:07:23</td><td>1.53</td><td>520</td><td>2.54</td><td>21.63</td><td>14.60</td><td>0.487</td><td>-0.568</td><td>-2.585</td></tr></tbody></table>

Note. The units of the physical parameters are as follows: B<sup>up</sup> (nT), V<sup>up</sup><sub>p</sub> (km s<sup>-1</sup>), N<sup>up</sup><sub>p</sub> (cm<sup>-3</sup>), T<sup>up</sup><sub>p</sub> (eV), T<sup>up</sup><sub>e</sub> (eV), P<sub>x</sub> (R<sub>M</sub>), P<sub>y</sub> (R<sub>M</sub>), and P<sub>z</sub> (R<sub>M</sub>).
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Relationships among all of the pairs of the shock parameters, including the ratios of downstream to upstream proton density ($N_p^{down}/N_p^{up}$), magnetic field magnitude ($B^{down}/B^{up}$), tangential component of magnetic field ($B_t^{down}/B_t^{up}$) and proton temperature ($T_p^{down}/T_p^{up}$), the inverse of the downstream to upstream ratio of the normal component of proton velocity in the shock frame ($U_n^{up}/U_n^{down}$), and fast magnetosonic Mach number ($M_p$). The linear fit results are also superimposed on each one.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>(a) SZA of the IP shock</figcaption></figure>

(a1)

<figure><img src="image_7.png" /></figure>

(a3)

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>Distance from the IP shock to the BS</figcaption></figure>

<figure><img src="image_12.png" /></figure>

(a4)

<figure><img src="image_13.png" /></figure>

<figure><img src="image_14.png" /></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /><figcaption>**Figure 3.** (a) Spatial distribution of the identified shocks and their strengths characterized by $N_p^{down}/N_p^{up}$ in cylindrical coordinates. The green and blue solid lines respectively mark the bow shock location and the magnetic pile-up boundary from the empirical model of Trotignon et al. (2006). (b) Dependencies of the shock strengths on SZA and the distance to the BS for all IP shocks, ICME-driven FF shocks, and SIR-driven FF and FR shocks.</figcaption></figure>

exhibits the dependencies of the shock strengths on SZA and the distance to the BS for all shocks, ICME-driven FF shocks, and SIR-driven FF and FR shocks. The SZA ranges from 0° to 100°,

and the distance ranges from 0 to $1.2 R_M$. It is immediately clear that the shock strengths show no systematic dependence on either SZA or the distance to the BS.
<figure><img src="image_18.png" /><figcaption>**Figure 4.** Dependencies of the upstream magnetic field magnitude $B^{\text{up}}$, proton moments ($V_p^{\text{up}}$, $N_p^{\text{up}}$, and $T_p^{\text{up}}$) and electron temperature $T_e^{\text{up}}$ of the identified FF shocks on SZA (left) and the distance from the shock to the BS (right).</figcaption></figure>

We further examine the dependencies of the upstream magnetic field magnitude $B^{\text{up}}$, proton moments ($V_p^{\text{up}}$, $N_p^{\text{up}}$, and $T_p^{\text{up}}$) and electron temperature $T_e^{\text{up}}$ of the identified FF shocks on SZA and the distance from the shock to the BS, which are illustrated in Figure 4. We can see that these parameters are virtually independent of SZA and the distance to the BS.

Therefore, the spatial dependence of the IP shock propagating medium should be statistically negligible.

### 4.3. Shock Statistical Properties

To investigate the statistical properties of the shocks and how the properties depend on the drivers, we classify the
identified shocks into three groups: ICME-driven FF shocks, SIR-driven FF shocks, and SIR-driven FR shocks. The shock with an unclear driver is probably the flank of an ICME-associated shock (Gopalswamy et al. 2010; Janvier et al. 2014), and here is put into the group of ICME-driven FF shocks.

Figure 5 shows the probability distribution of the shock parameters, including the ratio of downstream to upstream tangential component of magnetic field $B_t^{\text{down}}/B_t^{\text{up}}$, the ratio of downstream to upstream proton density $N_p^{\text{down}}/N_p^{\text{up}}$, the fast magnetosonic Mach number $M_f$, the solar wind speed jump at the shock $|\Delta V_p|$, the shock speed $V_{\text{sh}}$, the upstream fast magnetosonic speed $V_f^{\text{up}}$, the upstream plasma beta $\beta^{\text{up}}$, the normal component of the upstream solar wind velocity in the shock frame $U_n^{\text{up}}$, and the shock angle $\theta_{\text{Bn}}$. As we can see from Figures 5(a) and (b), the shock strength represented by the median value of $B_t^{\text{down}}/B_t^{\text{up}}$ or $N_p^{\text{down}}/N_p^{\text{up}}$ for SIR-driven FF shocks is quite comparable to that for SIR-driven FR shocks, but both are larger than that for ICME-driven FF shocks, which is opposite to that observed by WIND near 1 au during the period from 1995 to 2013 (Kilpua et al. 2015). The relatively weak shock strength for ICME-driven FF shocks might be explained in terms of $|\Delta V_p|$ and $U_n^{\text{up}}$. The median value of $|\Delta V_p|$ is about $18 \text{ km s}^{-1}$ for ICME-driven FF shocks, which is lower than that for SIR-driven FF shocks, $26 \text{ km s}^{-1}$. The median value of $U_n^{\text{up}}$ is about $-58 \text{ km s}^{-1}$ for ICME-driven FF shocks, compared to $-69 \text{ km s}^{-1}$ for SIR-driven FF shocks. The negative sign of $U_n^{\text{up}}$ indicates that the plasma flows from the upstream to the downstream.

The median value of $V_f^{\text{up}}$ is about $78 \text{ km s}^{-1}$ for SIR-driven FR shocks, which is much faster than the $45 \text{ km s}^{-1}$ value for SIR-driven FF shocks. The median value of $U_n^{\text{up}}$ is about $-119 \text{ km s}^{-1}$ for SIR-driven FR shocks, compared to $-69 \text{ km s}^{-1}$ for SIR-driven FF shocks. As mentioned above, however, the shock strength for both classes of events are quite similar. This implies that a higher $V_f^{\text{up}}$ corresponds with a higher $|U_n^{\text{up}}|$ for a fast shock, which is consistent with Equation (1). Therefore, the forming condition for an SIR-driven FR shock is generally harder to satisfy than that for an SIR-driven FF shock near the Martian environment. This may partly explain why SIR-driven FR shocks were less frequently observed. Note that the low occurrence of SIR-driven FR shocks near the solar ecliptic plane is also partly due to the fact that the propagation directions of SIR-driven FR shocks are mainly poleward, while those of SIR-driven FF shocks are mainly toward the ecliptic plane (Jian et al. 2006; Balogh et al. 1995).

The mean and median values of the shock angle $\theta_{\text{Bn}}$ are similar among the three groups, and they are larger than $45^\circ$. Only four shocks have $\theta_{\text{Bn}}$ less than $45^\circ$. This means that the quasi-perpendicular IP shocks are predominant in the upstream of the BS, which is reasonably consistent with our expectation from the observations at 1 au (Kilpua et al. 2015).

## 4.4. Potential Impacts of Mars on the IP Shock Shape

We know that the shape of IP shocks can be modulated by the upstream medium conditions. However, it is unclear whether the local shape of the shock varies in response to the presence of an obstacle in the solar wind, such as Mars and its BS. Assuming that the local shape of an IP shock is significantly modified by the Martian BS, one may expect that the angle between the shock normal direction and the BS normal direction at the shock tends to become very small. To examine the assumption, we analyze the distributions of such

angles for all IP shocks, ICME-driven FF shocks, and SIR-driven FF and FR shocks, which are shown in Figure 6. For the identified shocks, the distribution of the angles appears to be uniform. This means that, from a statistical point of view, we find no evidence that the local shape of the IP shocks are affected by the BS when they travel past Mars.

It should be mentioned that the properties of IP shocks, such as the shock speed and the shock strength, will be more or less modified when they propagate very close to the Martian environment, owing to their passing across a large number of boundary surfaces, e.g., the foreshock boundary (Mazelle et al. 2018), and regions of different density, velocity, and magnetic field strength. In general, the upstream conditions are already different from the pristine solar wind (far from Mars) when getting closer and closer to Mars due to the increasing local implantation of pick-up ions. This process adds a new ion population to the solar wind with a very different velocity distribution function (VDF). This strong microscopic difference will therefore lead to very different macroscopic properties (density, velocity, temperature, and energy, of course) for this new population. Typically, mass loading by pick-up ions will slow the solar wind flow (Szegő et al. 2000). Of course, the general influence on the solar wind parameters will depend on the relative density of the added ion population. In particular, a large part of the upstream region is inside the foreshock region where the backstreaming ions produced by reflection at the BS where the IMF intersects the shock surface will add again another new ion population with a very different VDF and therefore different macroscopic properties. This will lead to another source of mass loading with this foreshock ion population and the deceleration of the solar wind, as shown for the Earth (Cao et al. 2009). In addition, some extreme upstream conditions, such as hot flow anomalies characterized by greatly heated solar wind plasmas and substantial flow deflection (Shuvalov et al. 2019, and references therein) and magnetic holes (Madanian et al. 2020, and references therein), may also be present near the Martian BS. It is likely that the shock speed and the shock strength dramatically change as a shock propagates in these upstream conditions with extreme values of the plasma and magnetic parameters (i.e., the upstream Alfvén speed, the plasma $\beta$, and the magnetic field strength; Lugaz et al. 2015). The details of how the shock properties evolve with the upstream conditions near the Martian environment are beyond the scope of this study, but they are worth evaluating on a case-by-case basis in the future.

## 5. Summary

MAVEN provides simultaneous high-resolution measurements of plasma and magnetic field, allowing for the characterization of interplanetary shocks in the medium upstream from the Martian bow shock. In the present study, we conduct a comprehensive survey of interplanetary shocks and their drivers using MAVEN data from 2014 October to 2018 November, covering the declining phase of solar cycle 24, and investigate the shock properties and how the properties depend on the drivers in a statistical sense. In addition, we examine the potential impacts of Mars on the shock shapes. The main conclusions can be summarized as follows:

1. A total of 52 shocks are identified: 39 FF shocks and 13 FR shocks. Most (79%) of the FF shocks are driven by SIRs with only a few cases being driven by ICMEs. All
<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

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<figure><img src="image_44.png" /></figure>

<figure><img src="image_45.png" /><figcaption>**Figure 5.** Distribution of shock parameters for ICME-driven FF shocks (left), SIR-driven FF shocks (middle), and SIR-driven FR shocks (right). From top to bottom: (a) the ratio of downstream to upstream tangential component of magnetic field $B_t^{down}/B_t^{up}$, (b) the ratio of downstream to upstream proton density $N_p^{down}/N_p^{up}$, (c) the fast magnetosonic Mach number $M_f$, (d) the solar wind speed jump at the shock $|\Delta V_p|$, (e) the shock speed $V_{sh}$, (f) the upstream fast magnetosonic speed $V_f^{up}$, (g) the upstream plasma beta $\beta^{up}$, (h) the normal component of the upstream solar wind velocity in the shock frame $U_n^{up}$, and (i) the shock angle $\theta_{Bn}$. The mean and median values are given in each panel.</figcaption></figure>
<figure><img src="image_46.png" /><figcaption>**Figure 6.** Distributions of the angles between the shock normal direction and the BS normal direction at all IP shocks, ICME-driven FF shocks, and SIR-driven FF and FR shocks.</figcaption></figure>

of the FR shocks are driven by SIRs. A total of 92% of the identified shocks are quasi-perpendicular shocks.

2. Besides the downstream to upstream ratios of the magnetic field magnitude $B^{\text{down}}/B^{\text{up}}$ and proton density $N_{p}^{\text{down}}/N_{p}^{\text{up}}$, the downstream to upstream ratio of the tangential component of magnetic field $B_{t}^{\text{down}}/B_{t}^{\text{up}}$ and the inverse of the downstream to upstream ratio of the normal component of proton velocity $U_{n}^{\text{up}}/U_{n}^{\text{down}}$ can also provide a good measure of the shock strength.

3. On average, the shock strengths for SIR-driven forward and reverse shocks are comparable, and they are stronger than that of ICME-driven forward shocks. The shock

strengths show no systematic dependence on the shock locations relative to the bow shock.

4. From a statistical point of view, we find no evidence that the local shape of the IP shocks are affected by Mars and its bow shock as an obstacle in the propagating medium.

This work is supported by the Strategic Priority Research Program of Chinese Academy of Sciences, grant No. XDB 41000000, the pre-research Project on Civil Aerospace Technologies No. D020104 funded by the Chinese National Space Administration, the National Natural Science Foundation of China (NSFC; 42074212, 41674147), and the Key Research
Program of the Institute of Geology and Geophysics, CAS, grant IGGCAS-201904. Parts of this work for the observations obtained with the SWEA instrument are supported by the French space agency CNES. The MAVEN data are publicly available through the PDS Planetary Plasma Interactions Node (https://pds-ppi.igpp.ucla.edu/).

## ORCID iDs

Hui Huang https://orcid.org/0000-0001-7098-551X

Jianpeng Guo https://orcid.org/0000-0003-1707-2716

Dan Zhao https://orcid.org/0000-0001-8962-5397

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