Mercury’s Lobate Scarps Reveal that Polygonal Impact Craters Form on Contractional Structures

Analysis of polygonal impact craters (PICs) can be used to investigate the presence and orientations of subtle and/or buried faults and fractures across the solar system that may otherwise be unobservable in spacecraft images. Although this technique has been vetted for the analysis of extensional structures, no previous work has investigated if PICs also form on contractional thrust faults. This determination, which we investigated in this work, is critical for accurate tectonic setting interpretations from PICs. Mercury shows an abundance of thrust-fault-related landforms, making it an ideal laboratory to perform this investigation. In this work, we found that Mercury’s thrust faults, and their overlying folds and fractures, cause some complex craters ∼20 km or larger to form PICs. However, in most cases, craters form as circular impact craters on these structures. When PIC straight rim segments do form, they parallel the lobate scarp thrust faults and fold hinges. Some PICs likely formed as a result of an impact’s interaction with the thrust fault itself, while others may have interacted with fold hinge joints. The parallel relationship between PICs and shortening structures is consistent with the well-established relationship between PICs and extensional structures. Therefore, in addition to extensional fractures, contractional features should also be taken into consideration when utilizing PICs to interpret tectonic settings on bodies across the solar system.


Introduction
Polygonal impact craters (PICs), craters with one or more straight edges along their rims, have been identified on planetary bodies across the solar system (Figure 1) and form when an impact event occurs in a target with preexisting faults or fractures (Fielder 1961;Shoemaker 1962Shoemaker , 1963;;Roddy 1978;Öhman et al. 2005;Beddingfield et al. 2016;Beddingfield & Cartwright 2020).Because PIC straight rim segments in many cases align with subimage resolution and/or subregolith fracture systems, they can provide crucial information for deciphering the tectonic histories of planetary bodies.For example, PICs have been used to more completely infer globalscale deformation patterns on the Saturnian moons Iapetus (Singer & McKinnon 2011) and Dione (e.g., Beddingfield et al. 2016) and the Uranian moon Miranda (Beddingfield & Cartwright 2020).However, only the association and relationship between PICs and extensional tectonic structures have been previously established.The association of PICs with contractional tectonic landforms has not been investigated on any planetary body or by utilizing physical models.Therefore, the interpretation of global-scale deformation patterns inferred from PICs is limited by the lack of knowledge regarding the possible association and orientation relationship between PICs and faults that accommodates lithospheric shortening.
Mercury is known to exhibit PICs (e.g., Weihs et al. 2015), as well as craters superposed on shortening landforms, socalled lobate scarps and wrinkle ridges (e.g., Banks et al. 2015;Crane & Klimczak 2017).Both of these landform types are widely accepted to be the surface expressions of combinations of thrust faults and folds (Strom et al. 1975;Cordell & Strom 1977; Melosh & McKinnon 1988;Watters et al. 1998Watters et al. , 2001Watters et al. , 2004)).Their formation is widely attributed to global contraction, the process causing Mercury to shrink from the long, sustained cooling of the planet (e.g., McKinnon 2014;Byrne 2018).Extensional landforms such as normal faults and graben are also curiously absent on Mercury's surface aside from those observed within plains units inside basins (Watters et al. 2009a(Watters et al. , 2009b;;Blair et al. 2013).Therefore, Mercuryʼs surface represents an ideal test bed to investigate how impact cratering processes interact with preexisting contractional structures.In this work, we investigated if there is a relationship between PICs and lobate scarps to gain invaluable insight into how contractional structures affect crater morphologies.
Furthermore, the origin of PICs across the surface of Mercury remains uncertain because a general relationship between thrust faults and PICs has not been determined.Quantifying this relationship is therefore needed to use PICs as a tool to investigate Mercuryʼs tectonic history.Detection and characterization of the orientations of subtle fracture systems would help discriminate between different tectonic processes on the innermost planet.For example, tidal despinning-the slowing of rotation to lock Mercury in its current 3:2 spin-orbit resonance with the Sun-is proposed to have formed a global fracture pattern (Klimczak et al. 2015); however, structural artifacts from this event and other early processes were likely overprinted by shortening landforms driven by global contraction, the volumetric reduction of Mercury due to long, sustained planetary cooling (Solomon 1977).Overprinting would have included the reactivation of favorably oriented fracture sets (Klimczak et al. 2015) but not the destruction of those unfavorably oriented.Those sets remain hidden but could be expressed during PIC formation.Therefore, characterization of PICs provides insight into how other tectonic processes, along with global contraction, played a role in shaping the surface of Mercury.

Controls on Impact Crater Morphologies
Differences in impactor and target material properties influence the resulting impact crater morphologies.For a given impactor and impact velocity, the diameter of an impact crater will be larger on planets and satellites with lower gravity and lower target material density (e.g., De Pater & Lissauer 2010).Higher-velocity impacts will form craters with larger diameters, as will an increase in the density or size of the impactor.Impact crater geometries depend on other factors, including the angle of impact (e.g., Herrick & Forsberg-Taylor 2003), whether or not impacts are clustered (e.g., O' Keefe & Ahrens 1982;Schultz & Gault 1985b;Cochrane & Ghail 2006), the topography of the target area (e.g., Gifford & Maxwell 1979), the layering of the target material (Quaide & Oberbeck 1968), erosion (Ronca & Salisbury 1966), postimpact tectonic modification (e.g., Pappalardo & Collins 2005;Watters & Johnson 2010), and the presence of preexisting subvertical structures within the target material (e.g., Eppler et al. 1983;Kumar & Kring 2008).In addition to target material properties, crater geometries may also be affected by properties of the projectile including the porosity, composition, and shape (e.g., Schultz & Gault 1985a;Melosh 1989;Osinski & Pierazzo 2013).
Circular impact craters (CICs) are inferred to result from impact events in target material with uniform, multidirectional strength properties (e.g., Melosh 1989).This material could be nontectonized and so uniformly strong, or prefractured, if the fractures are widely or closely spaced relative to the size of the resulting crater (e.g., Fulmer & Roberts 1963).Additionally, CICs can form in a fractured target if the the fracture system is highly complex or covered by a thick layer of noncohesive sediment that limits interactions between the impactor and the underlying bedrock (e.g., Fulmer & Roberts 1963).In contrast, the only known cause for the formation of PICs is the presence of preexisting subvertical structures within the target material (e.g., Fielder 1965;Eppler et al. 1983;Öhman et al. 2005, 2008;Öhman 2009;Aittola et al. 2010).PICs exhibit straight rim segments, which reflect the orientations of preexisting fractures in the target material (e.g., Fielder 1961;Shoemaker 1962Shoemaker , 1963;;Roddy 1978;Öhman et al. 2005).Consequently, CICs and PICs are excellent tools to distinguish between nontectonized and tectonized terrains on the surfaces of both silicate-rich and ice-rich surfaces across the solar system (e.g., Öhman et al. 2006;Beddingfield et al. 2016;Beddingfield & Cartwright 2020;Robbins & Riggs 2023).

Models of PIC Formation in Extensional Settings
Four PIC formation models have been investigated previously, each requiring the target material to contain preexisting fractures, which we refer to as models A, B, C, and D. Descriptions of these models are provided in detail by Öhman (2009), so we only summarize them here.According to model A, simple PICs are structurally controlled during the excavation stage of the transient crater (e.g., Schultz 1976;Eppler et al. 1983).The cavity expands in a direction oriented 45°to the surrounding fracture azimuths, forming PICs with azimuths that are offset by 45°to azimuths of the controlling fractures.This model is based on observations of two orthogonal fracture sets trending 45°to the straight crater rim segments of Barringer (Meteor) Crater located near Flagstaff, Arizona (Shoemaker 1963(Shoemaker , 1977;;Gault et al. 1974;Schultz 1976;Roddy 1978;Poelchau et al. 2008Poelchau et al. , 2009)).
In model B, simple PIC shapes form as excavation flow preferentially overturns material along preexisting fractures, causing the crater to preferentially expand perpendicular to the fracture azimuths.In this model, the final PIC azimuths parallel surrounding fracture azimuths (Kumar & Kring 2008).
In model C, complex PIC geometries are determined during the modification stage (e.g., Schultz 1976;Eppler et al. 1983).In this model, the craterʼs straight rim segments are a result of the transient crater walls slumping via modification-related normal faulting along preexisting target structures along the crater wall.Consequently, the crater expands in a direction parallel to surrounding fracture azimuths.Like model B for simple PICs, this activity results in a parallel PIC-fracture relationship for complex craters.
In model D, applicable to both simple and complex craters, PICs inherit their geometries from movement of material along preexisting structures during the excavation stage (Öhman 2009).Like models B and C, model D predicts that the final PIC azimuths parallel surrounding fracture azimuths.Model D is supported by observational evidence of an association between faults and PIC crater rims on planetary surfaces (e.g., Gault et al. 1974;Reimold et al. 1998).

PICs throughout the Solar System
PICs have been identified throughout the solar system, and the relationships between PIC straight rim segment azimuths and controlling fracture azimuths have been investigated on many planetary bodies (e.g., Öhman 2009; Öhman et al. 2010).PICs are abundant on solid surfaces, and methods of automated detection of crater geometries are under investigation (Robbins & Riggs 2023).PIC azimuths on Mercury (Melosh & Dzurisin 1978;Strom & Sprague 2003) and Venus (Aittola et al. 2007(Aittola et al. , 2008(Aittola et al. , 2010;;Öhman 2009) have been found to parallel azimuths of surrounding linear structures.On Earth, many PICs have also been identified, and their orientations have been compared to those of surrounding structures for both simple craters (e.g., Öhman 2009) and complex craters (e.g., Morrison 1984).

PICs on Mercury in a Contractional Tectonic Setting
Mercury exhibits PICs on its surface (Figure 1(a)) that were first systematically documented by Herrick et al. (2011) in the production of a global catalog of Mercurian craters.Weihs et al. (2015) visually inspected craters in this catalog and marked those with at least two straight rim segments as being polygonal, with 33 of the 291 assessed craters meeting this criterion.A recent study of PICs on Mercury systematically mapped and analyzed over 7000 impact craters, finding nearly 29,000 straight rim segments longer than 10 km (Yazici & Klimczak 2021;Yazici et al. 2024).These authors found that, in contrast to previous work that estimated PICs to represent ∼11% of craters on Mercury (Weihs et al. 2015), 83% of craters in their study contained straight rim segments.Both studies noticed roughly east-west orientations in straight rim segments near the poles; however, Yazici et al. (2024) also noted a weak preference for north-south orientations closer to the equator.Both studies located a range of sizes for PICs, 20-400 km (Yazici et al. 2024) and 65-240 km (Weihs et al. 2015).
Because PICs utilize preexisting fractures during their formation, the orientations of PIC walls in the spatial context of lobate scarps would inform our understanding of how folding progresses on Mercury.PIC straight rim segments aligned with the orientation of shortening landforms could indicate that pure shear accommodates folding and that folding and fracturing are coincident.Alternatively, PIC walls oriented obliquely to the fold hinge could be used to infer prefolding stress directions that may have generated tectonic fabrics prior to folding.It is also possible that both scenarios exist, and thus fracturing both before and during folding could be evaluated.The spatial density of PICs with along-trend versus oblique-to-trend walls could be evaluated to determine the spatial variability in tectonic fabric and shear strain.It is widely anticipated that many fracturing processes, unrelated to lobate scarp formation, occurred globally and regionally across Mercury's surface.Stresses resulting in these fractures may have been derived from tidal despinning (Klimczak et al. 2015), polar wander due to the Caloris Basin mascon (Matsuyama & Nimmo 2009), mantle upwelling or downwelling (King 2008;Tosi et al. 2013), or any combination of these processes over time.If sufficient in magnitude, stresses from these processes also would have produced fractures that resulted in PIC formation.
All models of PIC formation emphasize the necessity of subvertical fractures, regardless of their orientations.For lobate scarps, underlying major fault structures are predicted to dip between 5° (Galluzzi et al. 2019;Crane 2020) and 45° (Galluzzi et al. 2015;Watters 2021) on Mercury, with the theory of faulting predicting thrust faults to have optimal dips of 30° ( Anderson 1951;Jaeger et al. 2009).The often rounded, asymmetric surface expressions of lobate scarps imply anticlinal folding above the underlying thrust faults.These folds on Earth are observed to contain fracture sets in various orientations relative to their limbs and hinges-not all of which are shallowly dipping (Figure 2; also see Figure 11 in Klimczak et al. 2019).Extension in the outer hinges causes near vertical shear fractures and jointing in these outer layers and shallowly dipping conjugate fracture sets in the inner hinges (Ramsay 1967;Cosgrove 2015).These joints may be accompanied by additional fractures caused by regional tectonic stresses, flexural slip, and intraunit stresses.Conjugate joint sets steeply dipping with orientations 60°from the hinge orientation may occur (Price & Cosgrove 1990) as well as nearly vertical joints perpendicular to the hinge (Reber et al. 2010), which may result from buckling (Eckert et al. 2014).Thus, horizontal compression and shortening, especially when in association with folding, do not limit the presence of steep fracture networks.
Although Mercury's lobate scarps form from strong, horizontally compressive stresses, the crests of these landforms often display graben or opening mode fractures, signs of outerarc extension, localized within the fold hinge (Byrne et al. 2018;Klimczak et al. 2019;Man et al. 2023).Where these fractures align with the overall trend of the landform, it may be interpreted that pure shear has dominated the strain history causing fracturing during folding (Ramsey 1968).However, fractures can also be observed crossing the hinge zone obliquely (Figure 2), implying that fractures accommodate regional stresses prior to folding (e.g., Ahmadhadi et al. 2008).

Data and Methods
We identified and investigated PICs on Mercury's lobate scarps by using a series of statistical tests.We utilized the R language to analyze rim azimuth distributions for each crater investigated.The steps discussed below are provided in additional detail in previous PIC studies (Beddingfield et al. 2016;Beddingfield & Cartwright 2020).For an overview of all steps outlined in the following subsections, see the flowchart in Figure 3. Due to the large number of craters analyzed in this study, the Appendix contains much of the information on crater and image data (Table A1), identified PICs (Figures A1-A3), statistical test information (Table A2), collected azimuth data for PICs and lobate scarps (Figures A4-A9), descriptions of lobate scarp proximities to craters (Table A3), and lobate scarp dip directions (Table A4).

Crater Selection Criteria
We assessed the craters identified by Crane & Klimczak (2017) that are in overprinting stratigraphic relationships with lobate scarps.As summarized in Crane & Klimczak (2017), craters that are superposed by faults and those that overprint faults were distinguished.These identified craters are based on the thrust-fault-related data set provided by Byrne et al. (2014) and the Kinczyk et al. (2020) data set of craters with diameters 20 km.For each impact crater that matched our selection criteria, we determined the crater rim azimuth distribution.
For this study, our impact crater selection criteria included the following.
Criterion 1.The crater must overprint, and not be cut by, the lobate scarp.This stratigraphic relationship indicates that the lobate scarp existed before the impact event took place.
Criterion 2. The crater rims must not be cut or offset significantly by faults (unrelated to the lobate scarp).This criterion is based on the fact that postimpact-forming faults that cut across craters alter their plan-view morphologies (Galluzzi et al. 2015) and therefore may affect the results in later steps that involve accessing the rim azimuth distributions of these craters.
Criterion 3.For a similar reason to criterion 2, the crater rims must not be notably cut by overprinting large craters.The presence of these overprinting craters would be associated with large sections of missing rims of the crater in question, making analyses of rim azimuths challenging in later steps.
Criterion 4. The crater must be ∼20 km or larger in diameter.Because such a large number of craters are present on Mercury's lobate scarps, we are investigating craters of this size, which provide us with a large data set to analyze for purposes of this work.Analyses of smaller craters are beyond the scope of this project and will be assessed in future work.

Image Selection and Processing
All impact craters that meet our selection criteria were identified by utilizing the MErcury Surface, Space ENvironment, GEochemistry and Ranging (MESSENGER) Mercury Dual Imaging System (MDIS) Global Basemap (∼116 m pixel −1 ), also called the Morphology Mosaic, published in 2016 and available through the United States Geological Survey Astrogeology branch (Murchie et al. 2016;Hawkins et al. 2007;Denevi et al. 2016) and the Mercury Application of JMARS (Christensen et al. 2009).We then analyzed all individual MDIS images that cover each crater of interest to further investigate the craters that meet the selection criteria.Each crater used in this study was subsequently assigned a unique label for organizational purposes in this study (Appendix Table A1).
We utilized the highest-resolution MDIS images available that cover each selected impact crater overprinting a lobate scarp (Appendix Table A1).In some cases, multiple MDIS images were acquired for analyzing individual crater and lobate scarp sets.For example, multiple images were needed if a single image did not cover the entire crater, or if multiple images were needed to investigate the crater and a sufficient length of the adjacent lobate scarp.Additionally, in some cases multiple images were needed if different lighting conditions were more favorable for analyzing the lobate scarp than for the crater.All images used are detailed in the Appendix (Table A1).These MDIS images were downloaded from the Planetary Data System website. 4 We utilized these images for measurements using the Quantum Geographic Information System software (QGIS Development Team 2021).
Processing and projection of MDIS images were conducted using the Integrated Software for Imagers and Spectrometers 3, version 4.2.0 (Anderson et al. 2004).The images were associated with a camera model for MDIS and augmented with spatial information (geometries of the spacecraft, Sun angle geometries, ground positions, etc.).Because the geometries of surface features are most accurate, with negligible distortion, at the projection center, we projected each overlying MDIS image to the coordinates at the center of each impact crater using a sinusoidal projection.This technique allowed for high-accuracy azimuth measurements to be taken along the crater rims, which was critical for this analysis.

Crater Rim Tracing
Each impact crater rim was manually traced, as illustrated in Figure 4. We utilized shadowing and lighting variations as high-elevation indicators associated with the crater rims.The resultant crater polygons from this tracing step were then converted to sets of multilines by splitting the continuous  polygon boundaries at their vertices.The numbers of vertices were determined based on the image resolutions (Table A1), where the distance between vertices is equivalent to the distance across a pixel.For each set of multilines, the azimuths of each individual segment were calculated.Each set of multiline segment azimuths and their associated lengths were exported to R for statistical analysis.
The crater rim tracing procedure was not affected by variations in image illumination angles.PICs are easier to recognize by eye in images with low illumination angles where prominent shadows are present along crater rims.However, studies have shown that, when rim azimuths are measured quantitatively, neither image resolution nor solar illumination effects due to lighting geometry have a strong effect on whether or not a crater is identified as a PIC (Binder & McCarthy 1972;Öhman et al. 2006).Measured rim azimuth distributions of impact craters taken on images with low illumination angles have been shown to be statistically similar to those taken on images with high illumination angles (Öhman et al. 2006).
None of the impact craters that we analyzed were notably cut by large extensional faults, lobate scarps, or large craters (see Section 3.1 above).In the majority of cases, the analyzed crater rims also were not cut by smaller features (Figure 4(a)).However, some craters that we analyzed were cut by small features, including faults or mass wasting features (Figure 4(b)) or small craters (Figure 4(c)).In these locations, the small sections of the crater rims erased by these features were excluded from our azimuth distributions (Figures 4(e) and (h)).

Lobate Scarp Tracing
Similar to our methodology for tracing crater rims, we also traced the structures associated with lobate scarps.We traced the thrust fault surface breaks exposed at the bases of the forelimbs, which are the steeper faces of the lobate scarps.We used shadowing and/or lighting of the surface topography as a guide.However, in some cases, identifying lobate scarp traces was more difficult than tracing impact crater rims due to their more shallow and subdued topography.In some images, shadows and variations in apparent surface brightness, caused by this more subdued topography, were less prominent and therefore more difficult to assess.Because the topography of lobate scarps includes a broad, gently dipping back limb and a steep forelimb, it was critical for us to utilize images with the appropriate lighting geometry.
Lobate scarps are mostly easily recognizable and traceable in images with lighting geometries that allow shadows to be cast along their steep sides, where the fault breaks the surface.Therefore, the direction of sunlight in an image must be from the direction of the shallow back limb in order for us to make use of this shadowing for purposes of tracing lobate scarps.To mitigate this issue, we investigated multiple MDIS images with different lighting geometries covering each lobate scarp (see Section 3.2 above).As mentioned in Section 3.2, multiple MDIS images were analyzed for the area covering each lobate scarp to obtain the images with the most ideal lighting geometry for each feature.In some cases, different images were used to trace the lobate scarp fault than what were used to trace the crater rim.The images determined to be the best for these measurements, and therefore utilized in this study, are listed in the Appendix (Table A1).
To compare lobate scarp azimuths to PIC azimuths in later steps, we investigated the segment of each lobate scarp immediately adjacent to the overprinting crater (Figure 4).Many lobate scarp segments that are immediately adjacent to the overprinting crater are covered by that crater's ejecta blanket (for example, the area south of the crater in Figure 4(a)).As a result, lobate scarp tracing was done along the segments that were not masked by ejecta and as close as possible to the crater (for example, the area north of the crater in Figure 4(a)).In the majority of cases, a single lobate scarp is associated with an analyzed crater (Figures 4(b), (c), (e), and (f)).However, in some cases, the measurable sections of two lobate scarps are equidistant from the crater (Figure 4(h)).In those cases, we incorporated both lobate scarps into our study, which we termed scarps A and B for each relevant study location (Figure 4(i)).
Like our crater rim tracing methodology, the resultant traced lobate scarp lines were converted to multiline sets, and the azimuths of each segment were calculated.For each lobate scarp, the set of azimuths and their associated lengths were exported to R for statistical analyses.

Chi-squared Tests
To identify PICs, we tested for uniform azimuth distributions for each analyzed impact crater by applying Pearsonʼs chisquared tests (e.g., Burt et al. 2009).For these tests, we selected alpha levels of 0.05.Therefore, if a resulting p-value of the Pearsonʼs chi-squared test is less than the alpha level of 0.05, then there is 95% confidence that the data are not uniformly distributed.For each impact crater trace, the set of multiline segment azimuths and lengths were utilized to test for a uniform distribution of crater rim azimuths, normalized for the lengths of each measurement, using Rʼs chisq.testfunction.
We binned each crater rim azimuth data into 8°and 16°bins.We then applied four chi-squared tests to each crater, shifting the data within the bins by 4°and 8°, respectively.This shifting method allowed us to detect PIC straight rim segments more accurately in the cases where the orientations of these segments fall close to a bin threshold and therefore may otherwise be split across two bins.This methodology also allowed us to account for straight rim segments of different lengths.If the result of a Pearsonʼs chi-squared test supported the null hypothesis, the azimuth distribution of that particular crater was considered to be uniform.In these scenarios, the crater was identified as a CIC.Alternatively, if the test result was significant, then the azimuth distribution was not considered to be uniform, and the analyzed crater was identified as a PIC.

Comparing PICs with Lobate Scarps
The prominent PIC rim azimuths (also referred to as "straight rim segments") were determined for all identified PICs.The prominent rim azimuth(s) of each PIC is (are) reflected by the mode(s) of the azimuth distributions.The modes for each PIC were determined using Rʼs dip.test function (Maechler & Ringach 2013), which applies the dip test of unimodality described by Hartigan et al. (1985).The modes of each lobate scarp azimuth distribution were also determined using this method.
We then compared the prominent PIC rim azimuth(s) with those of adjacent lobate scarps.We did not expect PIC straight rim segments to precisely reflect the orientations of the measured lobate scarp sections, even if the relationship between PICs and lobate scarps is truly parallel.We had this expectation because the lobate scarps were traced at some distance from the overprinting PICs (see Section 3.4), and the orientations of the lobate scarps can vary slightly across short distances (see the lobate scarps in Figures 4(a)-(h)).We accounted for this expected azimuth spatial variation by allowing for an acceptable range of differences in PIC and lobate scarp straight segment azimuths.As a threshold, we considered PIC straight rim segments to subparallel lobate scarps if the differences between their prominent azimuths fell into a category within five bins or less (out of 60 bins).Because each bin contains 6°of azimuths, this threshold is equivalent to <30°.

PICs on Lobate Scarps
As shown in Table 1, 29 PICs overprinting lobate scarps were identified out of the 163 craters analyzed in this study.Therefore, our results indicate that PICs can form on shortening landforms, in some cases.However, because <20% of the analyzed craters are PICs, we find that CIC formation is the most common outcome of impact events on shortening landforms.Of the identified PICs, 21 have one straight rim segment, while eight exhibit two straight segments.
We find that many PIC straight rim segments exhibit parallel relationships with adjacent lobate scarps.Of the 29 PICs identified in this study, 20 exhibit a parallel relationship with an adjacent lobate scarp.Four examples are shown in Figure 5.
See the information provided in the Appendix for additional details on other PICs that parallel adjacent lobate scarps (Figures A4-A9).As summarized in Table 1, five of the identified PICs exhibit azimuths between 0°and 6°of an adjacent lobate scarp.Four PICs exhibit azimuths between 6°a nd 12°, four between 12°and 18°, three between 18°and 24°, and four between 24°and 30°.

CICs on Lobate Scarps
Most impact events that occur on lobate scarps do not form as PICs and instead were identified as CICs.There are multiple possible explanations for this result.Perhaps the craters that form as CICs did so because of one or more of the following reasons.
(1) The impact event occurred too far away from the fault surface break and/or folding-associated fractures.In this case, these structures may not be close enough to influence the orientation of the resulting rim during crater formation.Or, few to no fracture sets are present in the anticline overlying the thrust fault.(2) The craters formed too directly on top of the thrust fault.In this case, the associated thrust and many of the associated steep fractures would be oriented perpendicularly to the crater rim, which is not optimal for influencing rim development.Additionally, large portions of the crater rims may have formed too far from the lobate scarp in this scenario and therefore were not affected by the underlying fault and fractures.
(3) The craters are too large relative to the lobate scarp, such that they excavated into the footwall of the thrust.
(4) The craters are too small relative to the lobate scarp and Note.All craters that have at least one straight rim segment are shown.Information on all 163 craters analyzed is provided in the Appendix.therefore did not interact with the underlying thrust fault or fractures.
(5) Our methodology is conservative; therefore, some straight rim segments may not have been identified.For example, straight rim segments and PICs may not have been identified if the crater is highly degraded, the straight segment does not take up a large enough portion of the crater rim, or the MDIS image resolution is low relative to the crater size.We investigated the above possible explanations for CICs on lobate scarps by comparing the study location characteristics of identified PICs with those of CICs (Table 2, Figure 7).We did not find a notable relationship between crater diameter and crater shape (Figure 6).Identified PICs range in diameter from ∼20 to 81 km, with the average being 37 km.In comparison, diameters of CICs range from ∼20 to 138 km with an average of 43 km.
We also investigated more specific relationships between craters and adjacent lobate scarps (Figure 7; Tables A3 and   A4).We categorized lobate scarps with a surface thrust fault that (1) intersects the crater through the crater center, (2) intersects the crater along the crater edge, and (3) does not intersect the crater.In the latter case, while the crater overprints the lobate scarp, the associated surface thrust fault does not directly underlie the crater.Therefore, the crater in question is instead overprinting a subsurface thrust fault in these locations.
We found a small difference in percentage of PICs and CICs that are associated with crater center intersections with lobate scarp surface thrust faults.These cases are associated with 41% of identified PICs and 62% of identified CICs.We also found only a small difference in the percentage of PICs and CICs associated with nearby surface thrust faults but without direct intersections with these faults.These configurations are associated with 31% of PICs and 43% of CICs.We found a notable difference in crater geometries that have edge intersections with surface thrust faults.In these scenarios, 41% of identified PICs are associated with at least one lobate scarp surface thrust fault that skims the crater edge, while only 10% of CICs exhibit this configuration.Therefore, our results Note.Values are provided that show the percentage of PICs associated with lobate scarps that run approximately through the crater center and crater edge and outside the crater edge (none).See Figure 7 for an illustration of these geometries.The percentages along each column, for PICs and CICs, add up to over 100% because some craters are associated with multiple lobate scarps.For additional information on these descriptions, see the caption of Figure 7. Also, see Appendix Table A3 for the data used to derive these results.A3.The surface thrust faults associated with the lobate scarps are shown in gray.The values indicate the percentage of particular configurations between the craters and lobate scarp surface thrust faults (center, edge, or none) with the identified crater geometry (PIC vs. CIC).The percentages for PICs and CICs each total more than 100% because some craters were associated with multiple lobate scarps.Our results indicate that, when an impact event occurs on top of a surface thrust fault, the resulting crater will be more likely to form a PIC than a CIC if the center of the impact is offset from the surface thrust fault (see red crater).In this scenario, 41% of PICs identified exhibit this configuration with at least one lobate scarp surface thrust fault.In comparison, only 10% of CICs exhibit this configuration.In Figure 5 indicate that in the presence of shortening structures, PICs are most likely to form when the impact event occurs so that the resulting crater center is offset from the lobate scarp surface thrust fault.However, we also find that PICs form in other configurations (center and none in Figure 7).Perhaps PICs on structures accommodating shortening form when an impact event causes the crater walls to interact with the shallow subsurface portion of thrust faults.Alternatively, perhaps these PICs form as a result of interactions with secondary structures instead of the main thrust fault.For example, perhaps the presence of extensional fractures, thought to form in response to lobate scarp formation (Figure 2; e.g., Engelder & Geiser 1980;Klimczak et al. 2019), resulted in some impact events occurring in these contractional terrains to form as PICs.In other words, on shortening landforms, PICs may be most likely to form when the crater edge overprints a surface thrust fault and/or overprints the fractures associated with the thrust's overlying fold.

Implications for PICs and Lobate Scarps
Our results indicate that impact events commonly produce PICs when the impact center location is slightly offset from the lobate scarp surface thrust fault (see red PIC illustration in Figure 7).This geometry allows the resulting crater rim to interact with the fault.Some past studies conclude that complex PICs form from normal faulting during the modification stage of crater formation (model C in Section 2.2; e.g., Schultz 1976;Eppler et al. 1983), while other studies instead conclude that they form from thrust faulting during the excavation stage (model D in Section 2.2; Öhman 2009; see Section 2.2).Öhman (2009) makes the argument that the fact that the straight rim segments of PICs are topographic highs indicates that thrusting is necessary, thereby supporting model D.
However, in this work, we note an example of a PIC where crater wall slumping appears to be associated with the formation of an impact crater straight rim segment.In this example, one part of the crater rim appears to have partially formed a straight rim segment but exhibits "failed" slumping (Figure 8).Perhaps this crater represents an example of an intermediate step of PIC straight rim segment formation during the crater modification phase.This slumping may be the result of backsliding against the original thrust motion of the fault plane due to the back limb of the lobate scarp being unsupported after crater formation, similar to slip sheets and collapse folds observed on Earth (Perucca et al. 2016;Harrison & Falcon 1934, 1936).These observations support model C, that modification stage normal faulting forms complex PIC straight rim segments.Based on our observations coupled with the logic described by Öhman (2009), we make the interpretation that both the excavation (model D) and modification (model C) stages of complex PIC crater formation contribute to the formation of the straight rim segments in the presence of thrust faults.
As described in Section 4.3, perhaps the presence of joints associated with folding during lobate scarp formation explains the formation of PICs in other configurations ("center" and "none" categories illustrated in Figure 7).These PICs, which commonly show parallel relationships with adjacent lobate scarps, form as a result of the existence of small joints that trend parallel to the underling thrust fault or fold hinge.Additionally, perhaps the parallel relationships in these scenarios between PICs and lobate scarps indicate that joints related to anticline formation more often form parallel than obliquely to the fold axes of Mercury's lobate scarps.
Folding in the brittle parts of the lithosphere is widely known to be accommodated by fractures (e.g., Engelder & Geiser 1980), and many fracture orientations within folds exist (e.g., Klimczak et al. 2019).Therefore, perhaps these particular PICs are highlighting the internal structural architecture of these thrust-fault-related landforms.Perhaps PIC straight rim segments that are aligned with lobate scarp orientations indicate that pure shear accommodates folding and that folding, fracturing, and faulting are coincident within lobate scarps on Mercury.
Perhaps PICs with straight rim segments that are oriented obliquely to adjacent lobate scarps are reflecting fractures unrelated to the lobate scarp.Perhaps they are instead reflecting prefolding and/or postfolding stress directions that generated tectonic fabrics prior to or following lobate scarp formation.Alternatively, these PICs may be reflecting joints associated with anticline formation but with orientations that formed obliquely to the underlying thrust fault.In future studies, the locations and orientations of PICs with straight rim segments that are oblique to the lobate scarp could be evaluated to investigate the orientations of additional stress directions in these locations.

Comparison with Extensional Settings
Similar to our results for contractional settings, both CICs and PICs form in targets that exhibit extensional fractures and faults.There are many known causes for the formation of CICs in extensional settings, which have been noted on many planetary bodies and in physical laboratory experiments.For example, within the pervasively fractured Wispy Terrain on Dione, 76% of the impact craters analyzed were classified as PICs, while 24% were classified as CICs.In Dione's more subtly fractured "Non-Wispy Terrain," percentages of PICs are as little as 20% in some locations, where fractures were inferred (Beddingfield et al. 2016).Within Miranda's cratered terrain, which exhibits a large number of fractures of various sizes, only 29% of the identified craters were identified as PICs (Beddingfield & Cartwright 2020).However, the locations of fractures in these terrains relative to each crater analyzed are not as well constrained as those for Dione's Wispy Terrain.Therefore, the true percentage of PICs overprinting extensional features may be higher.
Many characteristics of prefractured target material have been attributed to the formation of CICs.As summarized in Fulmer & Roberts (1963), CICs are shown to form in fractured material if the target consists of a complex set of closely spaced fractures, very widely spaced fractures, or unconsolidated material (Fulmer & Roberts 1963).For example, joints and normal faults both form in response to extensional stresses on planetary bodies.If joints or normal faults are covered by a thick layer of regolith, comparable to or greater than the depth of the impact crater, then we would expect an impact event to form a CIC instead of a PIC.
CICs may also be more likely to form if the impact event creates a crater that is too large or too small relative to the fracture sizes and/or spacing (see Öhman et al. 2005 for a full summary).As summarized in Öhman et al. (2005), in many extensional settings, PICs are somewhat constrained to specific crater diameter ranges.For example, Schultz (1976) concluded that lunar PICs more often exhibit diameters of >1 and <15 km.Similarly, in the Argyre region on Mars, the majority of identified PICs fall within the 10-35 km diameter size range (Öhman et al. 2006).
The explanations for the presence of overprinting CICs along with PICs in extensional target material may provide explanations for the abundant CICs that we identified in contractional settings this work.If similar relationships between CICs and tectonic structures hold true for thrust faulting, then our finding of a large number of CICs relative to PICs is not surprising.In the case of lobate scarps on Mercury, thrust faults are more widely spaced than many of the extensional terrains on planetary bodies noted above.Therefore, we would expect a lower ratio of PICs relative to CICs on lobate scarps relative to extensional terrains.However, additional studies that investigate the relationships between CICs and the characteristics of contractional terrains are needed.

Applications for Future PIC Interpretations
Our results show that, in addition to extensional structures, contractional structures should be considered as possible explanations for the presence of PICs on bodies across the solar system.Our new knowledge of the parallel relationship between PICs and contractional structures can be applied to better interpret tectonic settings and global stress mechanisms on rocky and icy bodies where PICs are present, as described in Section 4.4.
For example, future analyses of other PICs elsewhere on Mercury could be used to obtain a more complete understanding of the extent and orientations of tectonic features, including the possible existence of contractional structures, that are difficult to discern in available spacecraft images.Detection and characterization of the orientations of subtle tectonic systems could help further discriminate between different tectonic processes.For example, tidal despinning-the slowing of rotation to lock Mercury in its current 3:2 spin-orbit resonance with the Sun-is proposed to have formed a global fracture pattern (Klimczak et al. 2015).If tidal despinning was overprinted by global contraction-the volumetric reduction of Mercury due to long, sustained planetary cooling (e.g., Solomon 1977)-it would utilize and reactivate favorably oriented fracture sets (Klimczak et al. 2015).Therefore, characterization of additional PICs in future work would provide insight into how other tectonic processes, along with global contraction, played a role in shaping the surface of Mercury.Future analyses may also provide insight into the tectonic setting related to Caloris Basin.
Consideration of contractional features in future PIC work could lead to more refined interpretations of global stress mechanisms on many icy bodies where PICs have been identified (see Section 2.3).For example, global stress events such as orbital recession, despinning, volume contraction, nonsynchronous rotation, and true polar wander may create regions of compression in some locations and tension in others (e.g., Collins et al. 2009).However, only extensional tectonic structures associated with regions of tension have been considered when interpreting PICs.For example, previous analyses of PIC locations and orientations on Dione yielded an inferred fracture pattern across the surface that points to satellite despinning and volume expansion (Beddingfield et al. 2016).Using our results, new analyses of these craters could be used to better interpret PICs in regions that would be in compression during these events (see stress maps provided by Collins et al. 2009 and references within).

Conclusions
We conclude that the presence of thrust faults and their associated folds and fractures can result in the formation of PICs for complex craters ∼20 km in diameter or larger.Additionally, we conclude that PIC straight rim segment azimuths exhibit parallel relationships with the controlling thrust fault azimuths, which are also parallel to their overlying fold hinges.These relationships between craters and shortening structures are like the relationships between craters and normal faults and joints observed in laboratory work and on solid planetary surfaces of rocky and icy bodies.
While PICs do form on thrust faults, we find that in most cases CICs form on thrust faults.In extensional settings, CICs are also known to form when overprinting and/or adjacent to normal faults and joints.However, the specific occurrences of PICs relative to CICs in extensional settings is not well constrained; therefore, we are not able to determine if the ratios of PICs to CICs on thrust faults are like those formed by normal faults.Additionally, only some of the PIC straight rim segments identified in this work may have formed as a result of the presence of the lobate scarp thrust fault itself.In addition to the thrust fault, some PICs may have formed in response to interactions with joints related to the formation of the lobate scarp fold.Future work is needed to further investigate this possibility and therefore determine if some PICs overlying lobate scarps can be utilized to better constrain fractured rock masses associated with lobate scarps.Additional work is also needed to determine if the relationship between PICs and lobate scarps holds true for craters with diameters smaller than 20 km.Note.For additional details on lobate scarp dip directions, see Table A4.Annotated portions of MDIS images covering each PIC identified are shown in Figure A1 for craters 1-22, Figure A2 for craters 33-134, and Figure A3 for craters 140-159.Lobate scarps are visible in some of these images; however, in many cases, the scarps are most visible some distance from each crater due to overprinting of the scarps by impact ejecta.See Figure 5 for context images (with lower resolutions) that show PICs with their adjacent lobate scarps in single MDIS images.

Figure 2 .
Figure 2. Examples of anticline fractures that may result from folding above thrust faults on Mercury.

Figure 4 .
Figure 4. Illustrations of the methodology for analyzing crater rim and nearby lobate scarp azimuths.Only the closest visible sections of each lobate scarp analyzed were investigated to better compare with PIC straight rim segments, as described in Section 3.4.(a) An example of the most common scenario in this study, where an impact crater (crater 3), uncut by extensional faults, other lobate scarps, or craters, overprints a single lobate scarp.(b) The traced crater (orange) and the section of the lobate scarp immediately adjacent to the crater (green) shown in panel (a).(c) Rose diagrams illustrating the azimuth distributions of the crater and lobate scarp traced in panel (b).(d) An uncommon example in this study, showing a crater (crater 1) that has visibly offset rim segments and is overprinting a lobate scarp.(e) The traced crater (orange) and the section of the lobate scarp immediately adjacent to the crater (green) from panel (d).(f) Rose diagrams illustrating the azimuth distributions of the crater and lobate scarp traced in panel (e).(g) An uncommon example in this study, showing a large crater (crater 2) with rim segments that are overprinted by smaller craters.Two nearby lobate scarps are equidistant to the large crater.(h) The traced crater (orange) and the sections of the two lobate scarps that are equidistant to the crater (green and cyan) shown in panel (g).(i) Rose diagrams illustrating the azimuth distributions of the crater and lobate scarps traced in panel (h).

Figure 5 .
Figure 5. Example illustrations of our results, showing that PICs with straight rim segments parallel adjacent lobate scarps.(a) Crater 13.(b) Crater 140.(c) Crater 134.(d) Crater 4. For a full illustration of our results for all PICs identified, see the annotated rose diagrams in Figures A4-A9.For images of all PICs identified, see FiguresA1-A3.See TableA1for coordinate and image information.See Table1for information on azimuth modes, indicating straight segments for all PICs and adjacent lobate scarps analyzed.

Figure 6 .
Figure 6.Box-and-whisker plots of PIC and CIC diameters.See Tables A1 and A2 for crater diameters and classifications, respectively.The crosses in the blue boxes represent the means, and the middle horizontal lines represent the modes.The top and bottom lines of the boxes represent the medians of the third and first quartiles, respectively.The ends of the vertical lines represent the maximum and minimum values.

Figure 7 .
Figure 7. Illustration of crater and surface thrust fault configurations.Also see TableA3.The surface thrust faults associated with the lobate scarps are shown in gray.The values indicate the percentage of particular configurations between the craters and lobate scarp surface thrust faults (center, edge, or none) with the identified crater geometry (PIC vs. CIC).The percentages for PICs and CICs each total more than 100% because some craters were associated with multiple lobate scarps.Our results indicate that, when an impact event occurs on top of a surface thrust fault, the resulting crater will be more likely to form a PIC than a CIC if the center of the impact is offset from the surface thrust fault (see red crater).In this scenario, 41% of PICs identified exhibit this configuration with at least one lobate scarp surface thrust fault.In comparison, only 10% of CICs exhibit this configuration.In Figure5, three of the four examples shown of PICs overprinting lobate scarps fall into this "edge" category (panels (a), (b), and (d)), while only one example falls into the "center" category (panel (c)).
Figure 7. Illustration of crater and surface thrust fault configurations.Also see TableA3.The surface thrust faults associated with the lobate scarps are shown in gray.The values indicate the percentage of particular configurations between the craters and lobate scarp surface thrust faults (center, edge, or none) with the identified crater geometry (PIC vs. CIC).The percentages for PICs and CICs each total more than 100% because some craters were associated with multiple lobate scarps.Our results indicate that, when an impact event occurs on top of a surface thrust fault, the resulting crater will be more likely to form a PIC than a CIC if the center of the impact is offset from the surface thrust fault (see red crater).In this scenario, 41% of PICs identified exhibit this configuration with at least one lobate scarp surface thrust fault.In comparison, only 10% of CICs exhibit this configuration.In Figure5, three of the four examples shown of PICs overprinting lobate scarps fall into this "edge" category (panels (a), (b), and (d)), while only one example falls into the "center" category (panel (c)).

Figure 8 .
Figure 8. Example of a crater with evidence for wall slumping associated with a straight crater rim segment.Here we show crater 122 (D = 34 km) in different MDIS images with differing lighting geometries.Perhaps this crater represents an example of an intermediate step of PIC straight rim segment formation during the crater modification phase, which would support model C for PIC formation (e.g., Schultz 1976; Eppler et al. 1983; see Section 2.2) for PICs associated with thrust faults.MESSENGER MDIS images (a) EN0227933432M, (b) EN0245441590M, and (c) EN0219610891M.

Figure A2 .
Figure A2.Identified PICs for craters 33-134 (seeTable A2).Cyan arrows indicate examples of straight rim segments.See Table A1 for information on PIC locations, diameters, and MDIS image coverage.See Figures A1 and A3 for additional identified PICs.

Figure A3 .
Figure A3.Identified PICs for craters 140-152 (seeTable A2).Cyan arrows indicate examples of straight rim segments.See Table A1 for information on PIC locations, diameters, and MDIS image coverage.See Figures A1 and A2 for additional identified PICs.

Figure A4 .
Figure A4.Rose diagrams showing the azimuth distributions of PIC rims and adjacent lobate scarps for craters 1-11 (TableA1).Modes are represented by blue petals, and red stars denote similar orientations between PIC straight rim segments and lobate scarps.

Figure A5 .
Figure A5.Rose diagrams showing the azimuth distributions of PIC rims and adjacent lobate scarps for craters 13-18 (TableA1).Modes are represented by blue petals, and red stars denote similar orientations between PIC straight rim segments and lobate scarps.

Figure A6 .
Figure A6.Rose diagrams showing the azimuth distributions of PIC rims and adjacent lobate scarps for craters 21-38 (TableA1).Modes are represented by blue petals, and red stars denote similar orientations between PIC straight rim segments and lobate scarps.

Figure A7 .
Figure A7.Rose diagrams showing the azimuth distributions of PIC rims and adjacent lobate scarps for craters 49-102 (TableA1).Modes are represented by blue petals, and red stars denote similar orientations between PIC straight rim segments and lobate scarps.

Figure A8 .
Figure A8.Rose diagrams showing the azimuth distributions of PIC rims and adjacent lobate scarps for craters 115-140 (TableA1).Modes are represented by blue petals, and red stars denote similar orientations between PIC straight rim segments and lobate scarps.

Table 1
Results Showing the Modes of PIC and Lobate Scarp Azimuths

Table 2
Comparison Summary of PIC and CIC Characteristics

Table A2
Craters that Exhibit Apparent Straight Rim Segments, Chi-squared Test Results, and Identified PICs

Table A4 (
Continued)Note.See TableA1for locations of each crater and adjacent lobate scarp.
Figure A1.Identified PICs for craters 1-22 (seeTable A2).Cyan arrows indicate examples of straight rim segments.See Table A1 for information on PIC locations, diameters, and MDIS image coverage.See Figures A2 and A3 for additional identified PICs.
Table A2).Cyan arrows indicate examples of straight rim segments.See Table A1 for information on PIC locations, diameters, and MDIS image coverage.See Figures A1 and A3 for additional identified PICs.
Table A2).Cyan arrows indicate examples of straight rim segments.See Table A1 for information on PIC locations, diameters, and MDIS image coverage.See Figures A1 and A2 for additional identified PICs.