The transition from complex crater to peak-ring basin on the Moon: New observations from the Lunar Orbiter Laser Altimeter (LOLA) instrument

Icarus 214 (2011) 377–393

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The transition from complex crater to peak-ring basin on the Moon: New observations from the Lunar Orbiter Laser Altimeter (LOLA) instrument David M.H. Baker a,⇑, James W. Head a, Caleb I. Fassett a, Seth J. Kadish a, Dave E. Smith b,c, Maria T. Zuber b,c, Gregory A. Neumann b a b c

Department of Geological Sciences, Brown University, Providence, RI 02912, United States Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 208771, United States Department of Earth, Atmospheric and Planetary Sciences, MIT, Cambridge, MA 02139, United States

a r t i c l e

i n f o

Article history: Received 17 November 2010 Revised 15 April 2011 Accepted 23 May 2011 Available online 2 June 2011 Keywords: Moon Mercury Cratering Impact processes

a b s t r a c t Impact craters on planetary bodies transition with increasing size from simple, to complex, to peak-ring basins and finally to multi-ring basins. Important to understanding the relationship between complex craters with central peaks and multi-ring basins is the analysis of protobasins (exhibiting a rim crest and interior ring plus a central peak) and peak-ring basins (exhibiting a rim crest and an interior ring). New data have permitted improved portrayal and classification of these transitional features on the Moon. We used new 128 pixel/degree gridded topographic data from the Lunar Orbiter Laser Altimeter (LOLA) instrument onboard the Lunar Reconnaissance Orbiter, combined with image mosaics, to conduct a survey of craters >50 km in diameter on the Moon and to update the existing catalogs of lunar peak-ring basins and protobasins. Our updated catalog includes 17 peak-ring basins (rim-crest diameters range from 207 km to 582 km, geometric mean = 343 km) and 3 protobasins (137–170 km, geometric mean = 157 km). Several basins inferred to be multi-ring basins in prior studies (Apollo, Moscoviense, Grimaldi, Freundlich–Sharonov, Coulomb–Sarton, and Korolev) are now classified as peak-ring basins due to their similarities with lunar peak-ring basin morphologies and absence of definitive topographic ring structures greater than two in number. We also include in our catalog 23 craters exhibiting small ring-like clusters of peaks (50–205 km, geometric mean = 81 km); one (Humboldt) exhibits a rim-crest diameter and an interior morphology that may be uniquely transitional to the process of forming peak rings. A power-law fit to ring diameters (Dring) and rim-crest diameters (Dr) of peak-ring basins on the Moon [Dring = 0.14 ± 0.10(Dr)1.21±0.13] reveals a trend that is very similar to a power-law fit to peak-ring basin diameters on Mercury [Dring = 0.25 ± 0.14(Drim)1.13±0.10] [Baker, D.M.H. et al. [2011]. Planet. Space Sci., in press]. Plots of ring/rim-crest ratios versus rim-crest diameters for peak-ring basins and protobasins on the Moon also reveal a continuous, nonlinear trend that is similar to trends observed for Mercury and Venus and suggest that protobasins and peak-ring basins are parts of a continuum of basin morphologies. The surface density of peak-ring basins on the Moon (4.5  107 per km2) is a factor of two less than Mercury (9.9  107 per km2), which may be a function of their widely different mean impact velocities (19.4 km/s and 42.5 km/s, respectively) and differences in peak-ring basin onset diameters. New calculations of the onset diameter for peak-ring basins on the Moon and the terrestrial planets re-affirm previous analyses that the Moon has the largest onset diameter for peak-ring basins in the inner Solar System. Comparisons of the predictions of models for the formation of peak-ring basins with the characteristics of the new basin catalog for the Moon suggest that formation and modification of an interior melt cavity and nonlinear scaling of impact melt volume with crater diameter provide important controls on the development of peak rings. In particular, a power-law model of growth of an interior melt cavity with increasing crater diameter is consistent with power-law fits to the peak-ring basin data for the Moon and Mercury. We suggest that the relationship between the depth of melting and depth of the transient cavity offers a plausible control on the onset diameter and subsequent development of peak-ring basins and also multi-ring basins, which is consistent with both planetary gravitational acceleration and mean impact velocity being important in determining the onset of basin morphological forms on the terrestrial planets. Ó 2011 Elsevier Inc. All rights reserved.

⇑ Corresponding author. Address: Department of Geological Sciences, Brown University, Box 1846, Providence, RI 02912, United States. Fax: +1 401 863 3978. E-mail address: [email protected] (D.M.H. Baker). 0019-1035/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2011.05.030

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1. Introduction Major lines of inquiry in the study of impact craters on the terrestrial planets over the past half-century have focused on the onset and formation of multi-ring basins occurring at the largest crater diameters. Many hypotheses have been developed to explain the formation of rings interior and exterior to the transient cavity of multi-ring basins, including frozen crustal tsunamis (Baldwin, 1981), differential depths of excavation to form nested craters (Hodges and Wilhelms, 1978), the formation of exterior rings by mega-terracing (Head, 1974, 1977; Head et al., 2011), and gravity-driven collapse and formation of tectonic rings due to the contrasting strengths of the lithosphere and aesthenosphere (Melosh and McKinnon, 1978; Melosh, 1982, 1989; Collins et al., 2002). Although these models have provided much insight into the formation of large impact structures on the terrestrial planets (e.g., Melosh, 1989; Spudis, 1993), there is currently no consensus on how the rings of multi-ring basins form. Important to understanding the mechanisms of multi-ring basin formation have been analyses of peak-ring basins and other transitional morphologies between complex craters with central peaks and multi-ring basins. Many crater catalogs of these basin types have been produced (Wood and Head, 1976; Wood, 1980; Wilhelms et al., 1987; Pike and Spudis, 1987; Pike, 1988; Spudis, 1993; Alexopoulos and McKinnon, 1994), which traditionally include measurements of major morphological features such as the diameter of the crater’s rim crest, ring, and central peak. Trends in the ring and rim-crest diameters of peak-ring basins have been used as evidence to support a number of peak-ring basin formation models (Pike and Spudis, 1987; Pike, 1988). However, the lack of complete population data for peak-ring basins on the terrestrial planets due to limitations in image and topographic resolution has inhibited accurate interpretations of the relationship between peak-ring basin morphologies and the mechanisms of their formation. With the addition of new and improved spacecraft data, it is important to update the existing catalogs of craters and basins, including observations of their morphological characteristics. This is especially important for the airless bodies, Mercury (Baker et al., 2011) and the Moon, where relatively low erosion and resurfacing rates throughout geologic history have preserved much of their basin populations. We use new topographic data from the Lunar Orbiter Laser Altimeter (LOLA) (Smith et al., 2010), in combination with a global Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) (Robinson et al., 2010) image mosaic at 100 m/pixel resolution to update the current catalog of peak-ring basins and other basin morphologies in the transition from complex craters to multi-ring basins on the Moon. LOLA currently provides gridded topography at better than 128 pixel/degree (235 m/pixel) resolution, a substantial improvement over previous topographic data of the Moon, including the 8–30 km/pixel resolution data from the Clementine Light Imaging Detection and Ranging (LiDAR) instrument (Smith et al., 1997) and the 15 pixel/ degree resolution data from the Kaguya Laser Altimeter (Araki et al., 2009). Our catalog of the lunar peak-ring basin and protobasin populations, including measurements of basin rim-crest, ring, and central-peak diameters, is then compared with catalogs on the other terrestrial planets, including a recent, comprehensive catalog of peak-ring basins and other transitional basins on Mercury (Baker et al., 2011). We then use our lunar basin catalog to test the predictions of one basin formation model, which seeks to explain the formation of peak rings by modification of the crater interior from a growing impact melt cavity.

2. The size-morphology progression Transitional morphologies in the size progression from complex craters to multi-ring basins have traditionally included at least two

classes of basins: peak-ring basins (or double-ring or two-ring basins) and protobasins (or central-peak basins) (Pike, 1988; Baker et al., 2011). Peak-ring basins are the most numerous transitional forms and their interior morphologies are characterized by a single, continuous or semi-continuous interior ring of peaks with no central peak. The lunar basin, Schrödinger, (rim-crest diameter, as measured in this study = 326 km) best exemplifies this morphology, showing a nearly continuous ring of peaks (Fig. 1A). LOLA gridded topography shows that Schrödinger has a depth of about 4 km with a peak ring that is tens of kilometers in width and rises about 1 km above the surrounding floor materials (Figs. 1A and 2A). Protobasins posses both a central peak and an interior ring of peaks, but these features are commonly smaller in diameter and have less topographic relief than either central peaks in complex craters and peak rings in peak-ring basins (Pike, 1988). Antoniadi (rim-crest diameter, as measured in this study = 137 km) is a type example of a protobasin on the Moon (Fig. 1B). Its peak ring has less relief (200– 300 m) than the peak ring of Schrödinger, and it has a small, but prominent central peak that rises above the surrounding peak ring (Fig. 2B). However, the smoothness of Antoniadi’s interior suggests that substantial infilling has occurred, which has certainly affected the relative topography of its central peak and peak ring. A third class of basins, called ringed peak-cluster basins, has also been identified from analysis of recent flyby data of Mercury (Baker et al., 2011). Like peak-ring basins, ringed peak-cluster basins have a single interior ring of peaks without a central peak (Fig. 1C) and overlap in rim-crest diameter with protobasins; however, the relatively small diameter of their peak rings relative to their rim-crest diameter precludes these basins from classification as traditional peak-ring basins. The type example of a ringed peak-cluster basin on Mercury is the 125-km diameter crater, Eminescu, which exhibits a very well-defined interior ring (Schon et al., 2011). On the Moon, many craters with small interior rings of central peak material are identified; however, only one of these craters, Humboldt (rim-crest diameter, as measured in this study = 205 km) overlaps in rim-crest diameter with protobasins and is thus classified as a potential ringed peakcluster basin. Humboldt has a disaggregated ring-like array of central peak elements (Fig. 1C) that is nearly 1 km in relief (Fig. 2C). A central depression in the middle of the array of peaks slopes steeply to about 100 m below the fractured fill material that occupies the floor of Humboldt (Fig. 2C).

3. Methods There have been several comprehensive catalogs of basins on the Moon (Wood and Head, 1976; Pike and Spudis, 1987; Wilhelms et al., 1987; Spudis, 1993), which were based primarily on Apolloera data, including image data from the Lunar Orbiter and Apollo Terrain Mapping Camera. While there are many similarities between these catalogs, there are some disagreements, particularly with identification of multiple exterior and interior rings and central peak plus ring structures. We have elucidated the identification of protobasins and peak-ring basins by analyzing new Lunar Orbiter Laser Altimeter (LOLA) (Smith et al., 2010) global gridded topography and hillshade data at 128 pixel/degree (235 m/pixel) resolution in combination with a Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) (Robinson et al., 2010) global image mosaic at 100 m/pixel resolution. We also used detrended LOLA gridded topography data to remove the effects of long-wavelength topographic variations and to help emphasize local variations in topography such as peak rings. All craters on the Moon greater than 50 km in diameter were analyzed in ArcGIS (ESRI, www.esri.com) using a recent catalog of lunar craters (Head et al., 2010) to ensure complete surveying of basin types. Particular scrutiny was given to basins already cataloged, including many

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Fig. 1. Examples of a peak-ring basin (A), protobasin (B), and ringed peak-cluster basin (C) on the Moon. Top panels show outlines of circle fits to the basin rim crest and interior ring (dashed lines) on LOLA hillshade gridded topography. Bottom panels show LOLA colored gridded topography at 128 pixel/degree on LOLA hillshade gridded topography. (A) Schrödinger (326 km; 133.53°E, 74.90°S), a peak-ring basin, exhibits a nearly continuous interior ring of peaks with no central peak. (B) Antoniadi (137 km; 187.04°E, 69.35°S), a protobasin, has a less prominent peak ring surrounding a small central peak. (C) Humboldt (205 km; 81.06°E, 27.12°S) is a ringed peak-cluster basin with an incomplete, diminutive ring of central peak elements.

multi-ring basins where some ring designations were most uncertain (Pike and Spudis, 1987). The diameters of basin features, including rim crests, rings, and central peaks, were measured (where present) by visually fitting circles to the features using the CraterTools extension in ArcGIS (Kneissl et al., 2010). Circle-fits were carefully selected to best approximate the mean diameter value for the features (Baker et al., 2011) (Fig. 1). For example, peak rings were fit by a circle intermediate between circles that inscribe and circumscribe the peak ring. Fits to rim crests were defined by the most prominent topographic divides along the crater rim crest. Central peaks were the most difficult to measure due to their irregular outlines. For those irregular central peaks, we chose circular fits that approximated a diameter that is intermediate between the maximum and minimum areal dimensions of the feature (Baker et al., 2011) (Fig. 1). As in previous catalogs, our confidence in the identification and measurement of peak rings is presented as a scale from 1 (lowest) to 3 (highest) (Tables A1–A3). Most basins are cataloged with the highest confidence, however, three peak-ring basins remain more speculative due to incomplete preservation of interior morphologies or possible mis-interpretation of interior features as primary basin structure. The continuity of observable peak rings are also designated as being greater than or less than 180° of arc (Tables A1–A3). 4. The basin catalog Our catalog is a refinement of earlier catalogs of peak-ring basins and protobasins on the Moon. We have excluded some

ambiguous basins and have re-classified several other basins, particularly those near the transition diameters between peak-ring basins and protobasins and peak-ring basins and multi-ring basins. These re-classifications largely reflect our improved ability to recognize genuine basin ring and central peak structures from new LOLA topographic and image data. Our refined catalog includes 17 peak-ring basins (Table A1), 3 protobasins (Table A2), and 1 ringed peak-cluster basin (Table A3). LOLA gridded topography images of each basin in Tables A1–A3 are also included as online supplementary material. Twenty-two craters exhibiting ring-like arrangements of central peak elements are also cataloged (Table A3), but are not classified as ringed peak-cluster basins due to their small (<114 km) rim-crest diameters that fall below the transitional rim-crest diameter range between complex craters and peak-ring basins (see discussion in Section 6.1). All of the peak-ring basins and protobasins cataloged in this study have appeared in earlier catalogs, but have been variously classified as one or multiple basin types based on the available data at the time the catalogs were generated. Our peak-ring basin catalog includes five basins that have been previously classified as multi-ring basins by Pike and Spudis (1987): Apollo, Moscoviense, Grimaldi, Coulomb–Sarton, and Korolev. Our catalog also includes Freundlich–Sharonov, which was recognized as a candidate multi-ring basin but with only one 600-km diameter ring identified (Wilhelms et al., 1987; Spudis, 1993). Upon careful examination of LOLA topographic data (Fig. 3), we find that all of these basins are fit best by no more than two topographic rings. For example, a possible ring exterior to Apollo (Fig. 3A) appears to be associated with the rim structure of South

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Fig. 2. Radially averaged LOLA topographic profiles of Schrödinger (A), Antoniadi (B), and Humboldt (C) (see Fig. 1 for locations). After Head et al. (2011), the profiles were calculated by averaging 360 great circle transects radiating from the basins’ centers and separated by 1° of azimuth. The topography along each of the 360 transects was calculated using a bilinear interpolation with the number of data points set to equal the 16 pixel/degree resolution of the LOLA data used for the profiles.

Pole Aitken basin and is not concentric to Apollo’s main topographic rings. Moscoviense (Fig. 3B) has been traditionally interpreted to be a multi-ring basin (e.g., Pike and Spudis, 1987) due to the presence of three concentric but off-centered ring structures. The offset characteristic of the three rings of Moscoviense to the southwest has suggested that Moscoviense may have formed from an oblique impact (see discussion in Thaisen et al. (2011)). However, a survey of offset peak rings in basins on Venus, for which impact direction could be inferred from ejecta patterns, determined that there was no correlation between ring offset and direction of impactor approach (McDonald et al., 2008). It was suggested that other parameters, such as target rock heterogeneities likely contributed to the offset ring characteristics of these peak rings on Venus. Furthermore, the effects of oblique impacts on basin morphology, especially on the scale of multi-ring basins are still poorly understood (Pierazzo and Melosh, 2000). Alternatively, we

favor a scenario whereby the inner two rings of Moscoviense represent a peak-ring basin superposed on a larger, older impact basin (e.g., Ishihara et al., 2011; Thaisen et al., 2011). Several geophysical and morphological characteristics of Moscoviense support a superposed impact scenario. First, the anomalously thin crust and high gravity of Moscoviense is more easily explained by double impacts than a single oblique impact (Ishihara et al., 2011). Second, the prominence and regular outline of the intermediate ring appears much more analogous to a basin rim-crest compared to the more plateau-like, irregular topography of the intermediate rings in multi-ring basins such as Orientale (Head et al., 2011). Finally, the innermost ring of Moscoviense is very prominent and sharp, sharing many similarities with other peak-ring basins on the Moon (Figs. 1A and 2A). Several of the basins (e.g., Grimaldi, Fig. 3C, and Freundlich–Sharonov, Fig. 3D) exhibit central depressions that have been classified as potential ring structures (Pike and Spudis, 1987). While these depressions may be related to the basin formation process, they are also interior to and are morphologically distinct from peak rings, which have more circular planform shapes and a distinct topographic signature that is raised above the surrounding basin floor material (Fig. 2A). We therefore do not include the rims of these depressions as separate rings in our catalog. Due to its highly degraded nature, our classification of Coulomb–Sarton (Fig. 3E) is the most uncertain of the large basins. However, we find that the observed impact structure can be best fit by two rings that are consistent with the rim-crest and ring diameters of other peakring basins on the Moon. The most uncertain basins in our catalog should be a focus during re-examinations using even higher resolution data or improved techniques. Lastly, in contrast to Pike and Spudis (1987), we do not include Amundsen–Ganswindt in our peak-ring basin catalog, as the irregular interior topography of the basin does not resemble a ring and is likely to be modified ejecta material. Our catalog includes three protobasins, two of which, Antoniadi and Compton, are unambiguous examples of basins exhibiting a central peak surrounded by an interior ring of peaks. We also include the crater, Hausen, in our catalog. While the interior ring of Hausen is not as well defined as those of Antoniadi and Compton, an incipient ring is observed. The subtlety of Hausen’s ring topography may be related to the size of the central peak, as there appears to be a correlation between size of the central peak and prominence of the interior ring (Pike, 1988). Hausen exhibits the largest central peak and least pronounced ring and Antoniadi exhibits the smallest central peak and the most topographically prominent ring (although the center of Antoniadi has been flooded by mare deposits (Fig. 1B), likely reducing the relief of its central peak and peak ring). Although the lunar protobasin population is very small, this correlation between central peak size and ring prominence and size is consistent with observations of the more numerous protobasin population on Mercury (Pike, 1988). Pike and Spudis (1987) include three other craters, Campbell, Fermi, Hipparchus, and Mendeleev in their protobasin catalog. With the exception of Mendeleev, we do not observe topographic rings in all of these craters in the new LOLA topography. For Mendeleev, we observe an interior ring but do not observe a central peak structure; Mendeleev is therefore classified as a peak-ring basin in our catalog. Pike and Spudis (1987) also include craters exhibiting relatively small ring/rim-crest ratios as potential protobasins (although central peak structures were not directly observed in these craters, possibly due to the effects of resurfacing or erosion). However, ring/rim-crest ratios alone cannot be used to recognize protobasins because the trends of ring and rim-crest diameters of protobasins appear statistically indistinguishable from peak-ring basins (Baker et al., 2011). Of the potential protobasins cataloged by Pike and Spudis (1987), we include Bailly, Milne, and Schwarzschild in our peak-ring basin catalog due to the presence of a

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Fig. 3. Large peak-ring basins on the Moon previously inferred to be multi-ring basins (Wilhelms et al., 1987; Pike and Spudis, 1987; Spudis, 1993). Left panels show dashed outlines of the observed basin rim crest and ring on a Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) image mosaic. Middle panels show LOLA colored gridded topography at 128 pixel/degree on LOLA hillshade gridded topography. Right panels show detrended LOLA topography maps. (A) Apollo (492 km; 208.28°E, 36.07°S). (B) Moscoviense (421 km; 147.36°E, 26.34°N). (C) Grimaldi (460 km; 291.31°E, 5.01°S). (D) Freundlich–Sharonov (582 km; 175.00°E, 18.35°N). (E) Coulomb–Sarton (316 km; 237.47°E, 51.35°N). (F) Korolev (417 km; 202.53°E, 4.44°S). See text (Section 4) for a discussion of the ring designations of the basins.

prominent interior ring and no observable central peak. While it is still possible that small central peaks within these structures have been erased by resurfacing processes, the absence of a central peak precludes them from being classified as a protobasin in our catalog. We do not observe interior rings or central peaks for the remaining possible protobasins classified by Pike and Spudis (1987). Ringed peak-cluster basins have not been included in previous basin catalogs of the Moon. From analyses of recent flyby images of Mercury, Schon et al. (2011) and Baker et al. (2011) interpret at least some ringed peak-cluster craters to be transitional types between complex craters possessing central peaks and peak-ring basins. Support for such a transitional morphology included overlap between the rim-crest diameters of ringed peak-cluster basins with rim-crest diameters of protobasins and small peak-ring basins, the clear ring-like morphology of the peak elements (ringed

peak clusters), and similar trends between the diameters of ringed peak clusters and central peak diameters in complex craters. These trends, as well as geological mapping, led the authors to suggest that ringed peak clusters are the product of early development of a melt cavity that directly modifies the centers of central uplift structures. While at least 23 craters >50 km in diameter on the Moon exhibit interior morphologies with ring-like central peaks (Table A3), the diameter range for these craters is large (50– 205 km, with all but one between 50 and 114 km) and only one, Humboldt, has a rim-crest diameter (205 km) that overlaps with the rim-crest diameters of protobasins. It is therefore likely that most ring-like central peak structures do not represent unique transitional types in the size-morphology progression from complex craters to peak-ring basins. The association of ring-like central peaks with floor-fractured craters has led to the interpretation that

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Fig. 3 (continued)

some ring-like central peaks result from collapse of the innermost portions of the central peak structure during magmatic intrusion (Schultz, 1976). Regardless of their origin, the small (<114 km) rim-crest diameters over which most craters with ring-like central peaks occur on the Moon suggest that their development is not related to the peak-ring basin forming process. Humboldt, classified here as the only ringed peak-cluster basin on the Moon, is more likely to be a unique transitional basin type; however, the fractured fill that occupies Humboldt’s floor suggests similarities with floor-fractured craters at smaller rim-crest diameters.

5. New basin statistics Based on our new rim-crest measurements, we have revised the general statistics for peak-ring basins and protobasins on the Moon (Table 1). The rim-crest diameters of peak-ring basins range from 207 to 582 km, with a geometric mean diameter of 343 km. Our

peak-ring basin data have a much larger rim-crest diameter range than the 320–365 km range from Pike and Spudis (1987) and has a smaller geometric mean rim-crest diameter compared to the mean rim-crest diameter of 335 km from Pike and Spudis (1987). The three protobasins in our catalog give a range from 137 to 170 km with a geometric mean of 157 km, compared to the larger range of values (135–365 km) and larger geometric mean rim-crest diameter (204 km) for protobasins in the catalog of Pike and Spudis (1987). Using our new basin catalog, we also calculate the onset diameter for peak-ring basins on the Moon. The term ‘‘onset diameter’’ has been defined loosely in previous studies; examples of such usage include the minimum diameter of a population or the diameter at which one crater morphology outnumbers another (see discussions in Pike (1983, 1988) and Baker et al. (2011)). In an analysis of basins on Mercury, Baker et al. (2011) chose to calculate the onset diameter for peak-ring basins based on the rim-crest diameter range where multiple crater morphologies overlap. In

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Table 1 Statistics of planetary parameters and of peak-ring basins, protobasins, and ringed peak-cluster basins on the Moon (this study, Tables A1–A3), Mercury (Baker et al., 2011), Mars (Pike and Spudis, 1987), and Venus (Alexopoulos and McKinnon, 1994). This table is reproduced from Table 1 of Baker et al. (2011), and is updated using our new lunar basin catalog (Tables A1–A3). Moona

Mercuryb

Marsc

Venusd

Gravitational acceleration (m/s ) Surface area (km2) Mean impact velocitye (km/s)

1.62 3.8  107 19.4

3.70 7.5  107 42.5

3.69 1.4  108 10.6

8.87 4.6  108 25.2

Peak-ring basins (Npr) Npr/km2 Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km) Onset diameter, method 1f (km) Onset diameter, method 2g (km)

17 4.5  107 343 207 582 206 227

74 9.9  107 180 84 320 126 + 33/26 116

15 1.0  107 140 52 442 80 + 29/21 56

66 1.4  107 57 31 109 42 + 10/8 33

Protobasins (Nproto) Nproto/km2 Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km)

3 7.9  108 157 137 170

32 4.3  107 102 75 172

7 4.9  108 118 64 153

6 1.3  108 62 53 70

Ringed peak-cluster (Nrpc) Nrpc/km2 Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km)

1 2.6  108 – – –

9 1.2  107 96 73 133

– – – – –

– – – – –

2

a

Basin data from this study (Tables A1–A3). Basin data from Baker et al. (2011). c Basin data from Pike and Spudis (1987). d Basin data from Alexopoulos and McKinnon (1994). Calculations exclude the suspected multi-ring basins Klenova, Meitner, Mead, and Isabella. e Mean impact velocity from Le Feuvre and Wieczorek (2008). f After Baker et al. (2011). Peak-ring basin onset diameters determined by first identifying the range of diameters over which examples of two or more crater morphological forms can both be found, and then the onset diameter is defined as the geometric mean of the rim-crest diameters of all craters or basins within this range (see text for a discussion on calculating onset diameter). Uncertainties are one standard deviation about the geometric mean, calculated by multiplying and dividing the geometric mean by the geometric, or multiplicative, standard deviation. Peak-ring basin and protobasin data used for the calculations are from this study (Moon), Baker et al. (2011) (Mercury), Pike and Spudis (1987) (Mars), and Alexopoulos and McKinnon (1994) (Venus). Complex crater rim-crest diameters used for the calculations are from the catalogs compiled by Pike (1988) (Mercury), Barlow (2006) (Mars), and Schaber and Strom (1999) (Venus); diameters of complex craters and peak-ring basin diameters on the Moon do not overlap. g Peak-ring basin onset diameters calculated by taking the 5th percentile of the peak-ring basin population data. See text for the details of this calculation. b

this method (‘‘onset diameter, method 1’’, Table 1), the range of diameters is first identified over which examples of two or more crater morphological forms can both be found, and then the onset diameter is defined as the geometric mean of the rim-crest diameters of all craters or basins within this range (Baker et al., 2011). For Mercury, Venus, and Mars, rim-crest diameters for peak-ring basins overlap the rim-crest diameters of both protobasins and complex craters (Baker et al., 2011). However, on the Moon no overlap exists between peak-ring basins and other morphological classes of basins. We therefore take the onset diameter for peakring basins on the Moon to be the geometric mean of the minimum diameter of the lunar peak-ring basin population and the maximum diameter of the next morphologically distinct population with smaller rim-crest diameters. We use the minimum peak-ring basin rim-crest diameter of 207 km (Schwarzschild) and the maximum rim-crest diameter of 205 km for the ringed peak-cluster basin, Humboldt, to obtain an onset diameter of 206 km for peak-ring basins on the Moon. Onset diameters calculated using the overlap method for basins on the other terrestrial planets (Mercury, Mars, and Venus) are presented in Table 1. The overlap method for calculating the onset diameter for peakring basins has the advantage of defining onset diameter of peakring basins by the spectrum of basin morphologies in the transition between complex craters and peak-ring basins and is therefore related to the physical processes resulting in the onset of interior basin rings. A second advantage is that the uncertainty in the estimated onset diameter is also derivable from the calculation. However, there are situations, such as in the Moon, where distinct crater morphological forms (e.g., peak-ring basins and protobasins) share little or no overlap in rim-crest diameter. Also, the robust-

ness and reproducibility of this method is affected by where the worker defines the overlap diameter range, which is usually defined from the use of multiple catalogs from more than one worker. As such, while its use is directly tied to the observed morphological transition, the overlap method’s applicability and reproducibility is limited, as it cannot be easily applied to planets with little or no overlap, and it is not able to be reliably reproduced by other workers because of its dependence on multiple crater populations that may not have been compiled using the same survey techniques. Satisfying these criteria is crucial for use in interplanetary comparisons and in understanding how the physical properties of the planets are modulating the basin-forming process. A more reproducible and applicable method for calculating onset diameter is to select a given percentile of the population. We calculate the 5th percentile of the peak-ring basin populations (‘‘onset diameter, method 2’’, Table 1) to obtain alternative onset diameters for peak-ring basins on the terrestrial planets: 227 km (Moon), 116 km (Mercury), 56 km (Mars), 33 km (Venus). Peakring basin diameter data used in the calculations are from this study (Moon), Baker et al. (2011) (Mercury), Alexopoulos and McKinnon (1994) (Venus), and Pike and Spudis (1987) (Mars). The 5th percentile is chosen as it is an easily reproducible, descriptive statistic that is based on an historical standard of significance in statistical analysis. The method is robust against outliers, as it is defined by the tail of the distribution itself, not a single data point defining the minimum value of the population. The method is applicable to all planets and is independent, as it relies only on a single basin population and is independent of the interplanetary variations encountered in the population distributions of other transitional crater morphologies. In addition, since basin

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Fig. 4. Log–log plots of ring diameter (Dring) versus rim-crest diameter (Dr) for peak-ring basins (red circles), protobasins (blue squares), and ringed peak-cluster basins (green diamonds) on the Moon (A, Tables A1–A3) and Mercury (B, from Baker et al., 2011). Also plotted for the Moon are the ring and rim-crest diameters for craters exhibiting ringlike central peaks (Table A3). Peak-ring basins follow a power law trend of Dring = 0.14 ± 0.10(Dr)1.21±0.13 (R2 = 0.96) on the Moon, which is very similar to the power law trend for peak-ring basins on Mercury [Dring = 0.25 ± 0.14(Dr)1.13±0.10, R2 = 0.87, Baker et al., 2011) (Table 2). Protobasins occur at smaller diameters, but appear to follow the tail-end of the peak-ring basin trend for the Moon and Mercury. Also shown are the trends for the diameters of central peaks (Dcp) in complex craters on the Moon (Dcp = 0.259Dr  2.57, Hale and Head, 1979a, and Dcp = 0.107(Dr)1.095, Hale and Grieve, 1982) and Mercury (Dcp = 0.44(Dr)0.82, Pike, 1988). The ringed peak-cluster basin, Humboldt, and craters with ring-like central peaks plot at intermediate values between the two complex crater trends for the Moon. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

populations can now be cataloged based on complete, or nearly complete, data coverage of the planetary surface, we can be confident that we are using populations rather than samples of particular crater and basin morphologies when calculating onset diameters. While the use of the 5th percentile to define peak-ring basin onset diameter does not rely on more than a single basin population and is not directly derived from the observed morphological transition between complex crater and peak-ring basin, peak-ring basin onset diameters calculated by this method consistently fall within the uncertainties of onset diameters calculated using a method based on the diameters of overlapping morphologies, as described above (Table 1).

6. Analysis and interplanetary comparisons Our refined catalog of transitional lunar basin types between complex craters and multi-ring basins permits us to better compare and evaluate several key characteristics of basin populations on the Moon and the terrestrial planets. These characteristics include: (1) ring and rim-crest diameter systematics, (2) surface density of peak-ring basins, and (3) peak-ring basin onset diameter. The airless body, Mercury, has the largest population of preserved peak-ring basins and protobasins in the inner Solar System (Baker et al., 2011), and thus provides an important dataset for comparison with the population of peak-ring basins and protobasins on the Moon. The basin catalogs for Venus and Mars should also be considered in interplanetary comparisons; however, resurfacing, erosion, and the effects of volatiles have influenced the present populations and morphologies of basins on these planets, rendering them less useful in comparison studies. Since the impact record on Earth is largely incomplete and highly modified by erosion, interior structures cannot be accurately identified and therefore present large uncertainties when used in interplanetary comparisons.

As such, impact structures on Earth are not used in this study. In the following sections, we analyze our new catalog of basins on the Moon and identify key similarities and differences with the other planetary bodies, especially Mercury. In the next section, these comparisons are then placed in context of the predictions of a model of peak-ring basin formation that explains their morphological characteristics as resulting from the nonlinear scaling of impact melt. 6.1. Ring versus rim-crest diameter trends Following the methods of Pike (1988) and Baker et al. (2011), we plot the ring diameter versus the rim-crest diameter in log– log space for lunar peak-ring basins, protobasins, and craters with ring-like central peaks and the ringed peak-cluster basin, Humboldt. Several trends are observed. First, peak-ring basins form a straight-line in log–log space at large rim-crest diameters in Fig. 4, and can be fit by a power law trend of the form

Dring ¼ ADpr

ð1Þ

where Dring is the diameter of the interior ring, Dr is the basin rimcrest diameter, and p is the slope of the best-fitting line on a log–log plot. Power-law fits were calculated in KaleidaGraph (Synergy Software, www.synergy.com), which uses the Levenberg–Marquardt non-linear curve-fitting algorithm (Press et al., 1992) to iteratively minimize the sum of the squared errors in the ordinate. The use of this criterion for minimization implies that fractional errors in the estimates of interior ring diameters are regarded as larger than those for estimates of the rim-crest diameter. We calculate a power law fit of Dring = 0.14 ± 0.10(Dr)1.21±0.13 2 (R = 0.96, where R is the correlation coefficient for the given dataset on a log–log plot) for lunar peak-ring basins (Table 2). This fit is very similar to a power law fit to peak-ring basins on Mercury

D.M.H. Baker et al. / Icarus 214 (2011) 377–393 Table 2 Comparison of the values for the coefficients (A and p) of power-law fits to peak-ring basins on the Moon (this study) and Mercury (Baker et al., 2011). Power laws are of the form given in Eq. (1) in the text. Coefficients of power-law fits to protobasins and ringed-peak cluster basins on Mercury from Baker et al. (2011) are also given, but none are given for the Moon due to the statistically small populations. Coefficients from the power law model of an expanding melt cavity (Eq. (2), Section 7) on the Moon (this study) and Mercury (Baker et al., 2011) are given for calculations using the Croft (1985) and Holsapple (1993) scaling relationships. Power-law coefficientsa A

p

R2

0.14 ± 0.10 0.25 ± 0.14

1.21 ± 0.13 1.13 ± 0.10

0.96 0.87

Protobasins (P90 km) Moon – Mercury 0.26 ± 0.36

– 1.09 ± 0.29

– 0.69

Ringed peak-cluster basins Moon – Mercury 0.18 ± 0.34

– 1.02 ± 0.41

– 0.78

Model (Croft, 1985) Moon 0.14 + 0.03/0.02 Mercury 0.14 + 0.03/0.02

1.09 ± 0.05 1.09 + 0.05/0.06

– –

Model (Holsapple, 1993) Moon 0.11 Mercury 0.11  0.12

1.18 1.18

– –

Peak-ring basins Moonb Mercuryc

a Power laws are of the form Dring = A(Dr)p, where Dring is the ring diameter and Dr is the final (observed) rim-crest diameter. Uncertainties for power-law fits to peakring basins, protobasins and ringed peak-cluster basins are at 95% confidence. b Coefficients to fits and models for the Moon are from this study. No fits were made to the protobasin and ringed peak-cluster data for the Moon because of the statistically small populations. c Coefficients to fits and models for Mercury are from Baker et al. (2011).

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surements were of the maximum diameter of central peaks, the trend of Hale and Head (1979a) is taken to represent an upper limit to central peak diameters on the Moon. The second trend is a power law [Dcp = 0.107(Dr)1.095] determined using the planform areas enclosed by the irregular perimeters of central peaks calculated by Hale and Grieve (1982). We then assume a circular geometry for this area, from which a central peak diameter is derived. These central peak diameters are taken to represent an average value, and should produce results that are comparable to our method for measuring the average diameters of basin features on the Moon. Craters with ring-like central peaks appear to fall on a scattered trend that is intermediate between the Hale and Head (1979a) linear regression and the Hale and Grieve (1982) power law (Fig. 4A), indicating that these ring-like central peaks do not depart substantially from the trend in central-peak diameter observed from complex craters. Humboldt falls near the Hale and Grieve (1982) trend, suggesting a similarity with complex craters with central peaks. However, the clear ring-like arrangement of its interior peaks, its large rim-crest diameter compared to other craters with ring-like central peaks, and its overlap with the rimcrest diameters of protobasins, suggest that Humboldt represents a unique transitional type in the size-morphology progression from complex craters to peak-ring basins. The fact that there is only one ringed peak-cluster basin on the Moon (5% of the total basin population cataloged in this study) is expected as it is likely to be related to the overall smaller numbers of protobasins and peakring basins on the Moon. For comparison, ringed peak-cluster basins account for only 8% of the total cataloged basin population on Mercury (Baker et al., 2011), and also fall along the trend for complex craters on Mercury (Fig. 4B). 6.2. Ring/rim-crest ratios

(Dring = 0.25 ± 0.14(Dr)1.13±0.10, Fig. 4B and Table 2), and both fits are consistent with analyses of previous peak-ring basin catalogs (Pike, 1988). Since the population of protobasins on the Moon is statistically small (N = 3), fits to the protobasin data were not conducted. However, protobasins occur at smaller diameters than all peakring basins but overlap in rim-crest diameter with the largest complex craters on the Moon (Fig. 4A). The trend in ring diameter and rim-crest diameter for protobasins is aligned with the tail-end of the peak-ring basin trend (Fig. 4A). This supports the view that peak-ring basins and protobasins are parts of a continuum of basin morphologies. A similar observation is identified between protobasins and peak-ring basins on Mercury (Fig. 4B), where the power law fits to protobasins and peak-ring basins are found to be statistically indistinguishable (Table 2) (Baker et al., 2011). However, protobasins on Mercury are more numerous, and protobasins <90 km have anomalously smaller ring diameters than what is predicted by extrapolation of a power law fit to protobasins P90 km. The one lunar ringed peak-cluster basin, Humboldt, occurs at smaller rim-crest and ring diameters than peak-ring basins but is larger in rim-crest diameter than all three protobasins (Fig. 4A). Humboldt has an atypically small interior ring diameter relative to its rim-crest diameter and thus plots on a trend that is more aligned with the trend for central peak diameters in complex craters than the interior rings of peak-ring basins (Fig. 4A). Other craters with ring-like central peaks also plot near the trend for central peak diameters in lunar complex craters. Fig. 4A shows two trends for central peak diameters in lunar complex craters. The first is the least squares, linear regression of Hale and Head (1979a) (Dcp = 0.259Dr  2.57, where Dcp is the diameter of the central peak and Dr is the diameter of the crater’s rim crest), which was based on measurements of circular fits to the maximum diameter of central peaks in fresh complex craters on the Moon. Because the mea-

Rim-crest/ring ratio (or the inverse, ring/rim-crest ratio) plots (Fig. 5) have been used to suggest that protobasins and peak-ring basins represent a continuum of morphologies (Alexopoulos and McKinnon, 1994), in contrast to the view of Pike (1988), who favored a statistical distinction between peak-ring basins and protobasins. Alexopoulos and McKinnon (1994) identified a general trend of continuous, non-linearly decreasing rim-crest/ring ratios with increasing rim-crest diameter for protobasins and peak-ring basins on Venus. The basin catalogs of Wood and Head (1976), Hale and Head (1979b), Wood (1980), Hale and Grieve (1982), and Pike (1988) were also used to suggest similar trends for basins on Mercury, the Moon, and Mars, although the Moon and Mars data appeared with greater scatter (Alexopoulos and McKinnon, 1994). A recent comprehensive survey of 74 peak-ring basins and 32 protobasins on Mercury (Baker et al., 2011) further emphasized these observations by examining the inverse, ring/rim-crest ratios, and noted that peak-ring basins flatten to an equilibrium ring/rim-crest ratio value of around 0.5–0.6. As in Baker et al. (2011), we also calculate ring/rim-crest ratios (in contrast to the convention of using rim-crest/ring ratios from Alexopoulos and McKinnon (1994)), for consistency with earlier studies (Wood and Head, 1976; Pike, 1988) and to avoid magnifying the effects of errors in small denominators. Ring/rim-crest ratios from our refined lunar basin catalog (Fig. 5A) have less scatter than the catalogs used in Alexopoulos and McKinnon (1994), and reveal a trend that is very similar to that observed for Mercury (Fig. 5B) (Baker et al., 2011) and Venus (Fig. 5C) (Alexopoulos and McKinnon, 1994), although at larger rim-crest diameters. The ring/rim-crest ratios for peak-ring basins on the Moon range from 0.35 to 0.56 (arithmetic mean = 0.48), with smaller rim-crest diameters generally having smaller ratios than larger rim-crest diameters (Fig. 5A). The ring/rim-crest ratios on the Moon also flatten to a value of around 0.5 for the largest peak-ring basins. Protobasins have smaller ratios, ranging from

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et al., 2011), which appear distinct from the general continuum of ring/rim-crest ratios between protobasins and peak-ring basins. The ring/rim-crest ratios for craters with ring-like central peaks are also at very low values (range = 0.12–0.24 and arithmetic mean = 0.17) and are similar to the ratio of Humboldt, although they occur at much smaller rim-crest diameters.

6.3. Onset diameter of peak-ring basins

Fig. 5. Ring/rim-crest diameter ratios for peak-ring basins (red circles), protobasins (blue squares), and ringed peak-cluster basins (green diamonds) on the Moon (A), Mercury (B), and Venus (C). Basin data are from this study (the Moon, Tables A1– A3), Baker et al. (2011) (Mercury), and Alexopoulos and McKinnon (1994) (Venus). The 0.5 ratio line is drawn in each panel for reference. Also note the change in scale of the x-axis between the Moon (A) and Mercury (B) plots. Nonlinear, curved trends are observed for protobasins and peak-ring basins for each of the planets. The trend is steeper at smaller rim-crest diameters and then flattens to values of 0.5–0.6 for the Moon and Mercury (A and B) and to 0.7 for Venus (C). The continuity between the ring/rim-crest ratios of protobasins and peak-ring basins suggest that they form a continuum of basin morphologies that is a direct result of the process of peak-ring basin formation. Ringed peak-cluster basins appear to diverge from the continuous trend shared by protobasins and peak-ring basins. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

0.33 to 0.44, with an arithmetic mean of 0.39. Since there are very few protobasins on the Moon, the lower rim-crest diameter end of the trend is not as well-defined as Mercury (Fig. 5B) and on Venus (Fig. 5C). The ring/rim-crest ratio (0.16) of the lunar ringed peakcluster basin, Humboldt, is much smaller than protobasins and peak-ring basins of similar rim-crest diameter (Fig. 5A). This is consistent with similarly small (arithmetic mean = 0.20) ring/rimcrest ratios for ringed peak-cluster basins on Mercury (Baker

Comparisons of the onset diameter for peak-ring basins on the terrestrial planets have been complicated due to the lack of a standard method for calculating this metric. Some authors have compared only transitional diameter ranges, noting that the transitional diameters decrease from the Moon to Mercury and Mars (Wood and Head, 1976; Pike, 1988). Others have used the minimum diameter of the peak-ring basin populations on the terrestrial planets to define onset diameter, yielding a similar decreasing onset diameter ordering from the Moon (140 km) to Mercury (75 km), Mars (45 km), and Venus (40 km) (Pike, 1983; Alexopoulos and McKinnon, 1994). Our calculations for the onset diameter of peak-ring basins (Table 1) do not change this general ordering, but provide new values that are based on the most recent and complete basin catalogs of the terrestrial planets and that are statistical more robust compared with previous values. While the onset diameters for the Moon and Mercury are the most reliable due to relatively complete preservation of their crater populations, the onset diameters for Mars and Venus are more speculative due to the prevalence of erosional and resurfacing processes and effects of differing target properties (e.g., volatiles and temperature) on these planets. Mars’ smaller onset diameter for peak-ring basins compared with Mercury, which has a similar gravitational acceleration, has traditionally been attributed to the effect of different target materials, including volatiles (e.g., Pike, 1988; Melosh, 1989; Alexopoulos and McKinnon, 1992). Mars is also anomalous in its large range of peak-ring basin diameters (52–442 km), suggesting that additional parameters other than gravity and impact velocity alone are influencing Mars’ population of peak-ring basins. The surface of Venus has also been globally resurfaced either in a catastrophic manner or at a rate equal to the crater production rate, and thus preserves only a 0.5 Ga crater retention age (Schaber et al., 1992). For these reasons, we exercise caution when interpreting the peak-ring basin and protobasin populations of Mars and Venus in context of the basin populations on the other planets. We also do not calculate an onset diameter for the Earth due to the obvious incompleteness of its impact basin record and the large uncertainties associated with interpreting highly eroded basin structures. It has long been recognized that there is an inverse relationship between the onset diameter of peak-ring basins and the surface gravitational acceleration (g) of the planetary body (Pike, 1983, 1988; Melosh, 1989; Alexopoulos and McKinnon, 1992). This relationship has been used to suggest that the formation of peak rings is largely the result of a gravity-driven process. Gravity-induced collapse of the transient cavity has thus served as the foundation for many current models of peak-ring basin formation, including hydrodynamic collapse of an over-heightened central peak (Melosh, 1982, 1989; Collins et al., 2002). The dependence of peak-ring basin onset diameter on planetary impactor velocity has been more uncertain. Pike (1988) demonstrated that the geometric mean diameters of peak-ring basins do not correlate with the approach velocity of asteroids and short period comets (V1) on the terrestrial planets. An improved correlation was found when approach velocity was combined with g (i.e., g/V1), although g alone still provided the best correlation with the geometric mean diameter of peak-ring basins.

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Fig. 6. Plots of the 5th percentile onset diameters for peak-ring basins on the Moon, Mercury, Mars, and Venus (Table 1, ‘‘onset diameter, method 2’’) versus surface p gravitational acceleration (g) (A), mean impact velocity (Vmean) (B), the ratio of g/Vmean (C), and the ratio of g/ Vmean (D) (Table 1). Solid lines are power law fits formed by minimizing the sum of the squared errors in the ordinate. The fits are displayed to emphasize general trends in the data and are not meant to be statistically rigorous representations. We did not include a fit for mean impact velocity due to lack of a clear trend. A correlation between onset diameter and gravity (A) is the strongest, with little correlation existing with mean impact velocity alone (B). The correlations of onset diameter with a combination of gravity and mean impact velocity (C and D) are more comparable or stronger than with gravity alone, suggesting that both gravity and mean impact velocity are important in influencing the onset of peak-ring basins.

We plot our onset diameters (5th percentiles, Table 1) for peakring basins as a function of the planet’s surface gravitational acceleration (g) and the planet’s mean impact velocity (Vmean) in log–log space (Fig. 6). The mean impact velocities are taken from recent modeling of the distribution of planetary impactors (Le Feuvre and Wieczorek, 2008). We also include power-law fits to the data by minimizing the sum of the squared errors in the ordinate. Given the uncertainties in the plotted data (especially for Mars and Venus) these fits are not meant to be statistically rigorous representations and should only be viewed as illustrating the general trends in the plotted data, As in previous studies, the strongest correlation with peak-ring basin onset diameter is the planet’s gravitational acceleration (Fig. 6A). No correlation is observed between onset diameter and velocity alone (Fig. 6B), although a stronger correlation is observed when the mean impact velocity is combined with gravity (i.e., g/Vmean) (Fig. 6C). Although it may have no physical significance, there is a very strong correlation (in log–log space) between onset diameter and gravitational accelerap tion over the square root of the velocity (g Vmean) (Fig. 6D). To first-order, these comparisons suggest that gravity is likely to be important in the process of forming peak rings. While there is no correlation between peak-ring basin onset diameter and impact velocity alone, a fairly strong correlation is found when impact velocity is combined with gravity. Like gravity, this correlation is not perfect, and the details of its physical meaning are not certain without a more detailed examination of the parameter space of impact events. Based on these observations, we suggest that both

gravity and velocity are likely to be important in the formation of peak rings. 6.4. Surface density of peak-ring basins The Moon has about a factor of two fewer peak-ring basins per unit area (4.5  107 per km2) than Mercury (9.9  107 per km2, Baker et al., 2011) and a factor of two to five greater number of peak-ring basins per unit area than Mars or Venus (Table 1). While the crater size distributions for impact craters between 100 km and 500 km in diameter are nearly the same on the Moon and Mercury (e.g., Strom et al., 2005) the mean and onset diameters for peak-ring basins on the Moon are much higher than on Mercury. The lower onset diameter for peak-ring basins on Mercury (Table 1) may account for the factor of two larger number of peak-ring basins per area on Mercury than on the Moon. The large number of peak-ring basins on Mercury has also been attributed to the high mean impact velocities of its impactors and increased impact melt production (Head, 2010; Baker et al., 2011). This could facilitate the onset of peak-ring basins at smaller impactor sizes, which are more numerous than larger-sized impactors. The surface density of craters between 100 km and 500 km in diameter is much lower on Mars than on Mercury and the Moon due to extensive erosion and resurfacing (Strom et al., 2005), which could partially explain the relatively small number of peak-ring basins on Mars. Venus has also undergone much resurfacing, which certainly has affected the number of peak-ring basins preserved on its surface.

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obliteration processes is uncertain. A much improved correlation is found when gravitational acceleration is combined with velocity (Fig. 7C).

7. Peak-ring basin formation models

Fig. 7. Plots of the surface density of peak-ring basins on the Moon, Mercury, Mars, and Venus (Table 1) versus surface gravitational acceleration (g) (A), mean impact velocity (Vmean) (B) and the ratio of g/Vmean (C). As in Fig. 6, solid lines are power law fits formed by minimizing the sum of the squared errors in the ordinate. The fits are displayed to emphasize general trends in the data and are not meant to be statistically rigorous representations. We did not include a fit for gravity due to lack of a clear trend. No correlation with gravity is observed (A), while there is a slight correlation with velocity (B). A stronger correlation is found when gravity and velocity are combined (C). The basin records on Venus and Mars are likely incomplete (see discussion in Section 6.3), which complicates full understanding of these first-order correlations.

The number of peak-ring basin per unit area is plotted versus the planet’s mean impact velocity and gravitational acceleration in Fig. 7. Again, power law fits to the data are given to illustrate the general trends in the plotted data. There appears to be no correlation between the number of peak-ring basins and the planet’s gravitational acceleration (Fig. 7A), while there is a weak correlation with mean impact velocity (Fig. 7B). Increasing the densities of peak-ring basins on Venus and Mars, which have certainly been affected to some degree by resurfacing events, would act to strengthen this correlation with mean impact velocity; however, to what degree the densities of basins have been modified by crater

While there have been numerous models attempting to explain the transition from complex craters to multi-ring basins, a consensus on the process of ring formation in peak-ring basins and multiring basins has not been reached. Two major models for the formation of peak-ring basins have been proposed: (1) hydrodynamic collapse of an over-heightened central peak (Melosh, 1982, 1989; Collins et al., 2002) and (2) modification and collapse of a nested melt cavity (Grieve and Cintala, 1992; Cintala and Grieve, 1998; Head, 2010). As discussed by Baker et al. (2011), while much progress has been made in advancing hydrocode models simulating the hydrodynamic collapse process (Melosh, 1989; Collins et al., 2002, 2008; Ivanov, 2005), the model currently makes no explicit predictions on the ring and rim-crest diameter systematics of peak-ring basins on the terrestrial planets. This is largely due to poor constraints on the parameters governing the timescales of fluidization of the target material and subsequent freezing of this material to produce peak-ring structures (e.g., Wünnemann et al., 2005). While it is possible that future models will offer more explicit predictions of ring and rim-crest spacing, the current uncertainty in the models make it difficult to test against the morphologic trends observed from our basin catalogs. Given these uncertainties with the hydrodynamic collapse model, we now use our observations of the new lunar catalog to test another model of peak-ring basin formation, the ‘‘nested melt-cavity’’ model, which explains ring formation as the result of nonlinear scaling between impact melt and crater dimensions. The nested melt-cavity model is based on a suite of papers by Cintala and Grieve (Grieve and Cintala, 1992, 1997; Cintala and Grieve, 1994, 1998) who invoked a combination of terrestrial field studies and impact and thermodynamic theory to show that for given impactor and target materials, impact-melt volume will increase at a rate that is greater than growth of the crater volume with increasing energy of the impact event (Grieve and Cintala, 1992). The maximum depth of melting was also shown to increase relative to the depth of the transient cavity with increasing transient cavity diameter (Cintala and Grieve, 1998), approaching depths of around 15–20 km for impact events near the onset diameters (100–200 km) of peak-ring basins (Cintala and Grieve, 1998; Baker et al., 2011). For further descriptions of the quantitative aspects of this model, the reader is referred to the work by Cintala and Grieve (1998) and references therein. This nonlinear scaling of impact melt has been shown to be important during the modification process in the formation of peak-ring basins on the terrestrial planets, including Earth, the Moon, and Venus (Grieve and Cintala, 1992, 1997; Cintala and Grieve, 1994, 1998). Further development of this model and its extension to multi-ring basins by Head (2010) has suggested that a melt cavity nested within the displaced zone of the growing transient crater (the ‘‘nested melt cavity’’) exerts a major influence on the formation of peak rings and development of exterior rings during crater modification. The volume and depth of impact melting in complex craters is generally not sufficient to modify the uplifted morphology of the crater interior. However, with increasing size of the impact event and thus increasing volume of melt and depth of melting, a melt cavity is fully formed within the displaced zone and is sufficiently deep to retard the development of an ordinarysized central peak (Cintala and Grieve, 1998). During rebound and collapse of the transient crater, the entire impact melt cavity is translated upward and inward. Unlike rebound in complex craters,

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however, the uplifted periphery of the melt cavity remains as the only topographically prominent feature, resulting in the formation of a peak ring (Head, 2010). At smaller crater sizes, and hence shallower depths of melting, it is still possible for a small central peak to rise through the melt cavity, accounting for the central-peak and peak-ring combinations that are observed in protobasins (Cintala and Grieve, 1998; Baker et al., 2011). One of the benefits of the nested melt-cavity model is that it makes specific predictions that may be compared with the ring and rim-crest diameter systematics of basin catalogs. Analysis of a recently updated basin catalog for Mercury (Baker et al., 2011) showed many first-order consistencies with the predictions of the nested melt-cavity model, particularly in the observations of (1) the surface density of peak-ring basins on the terrestrial planets, (2) the continuum of basin morphologies between protobasins and peak-ring basins, and (3) the power-law trend of peak-ring basins. Our analysis of the new lunar catalog confirms many of these consistencies with the nested melt-cavity model, providing additional support to the importance of impact melting in forming peak rings. It is important to note that the geometries of impact melting and the transient cavity derived from theoretical calculations are only static representations of a very dynamic process. In reality, at no time during the impact event are these geometries fully achieved, and the dynamics of crater formation certainly affects how the melted portions of the displaced zone evolve and are distributed within the target material with time. However, these details of the cratering process are still poorly understood and modeled. More certain has been various analytical and numerical estimates of the volume and depths of melting (Grieve and Cintala, 1992; Pierazzo et al., 1997; Barr and Citron, 2011), which appear generally consistent with each other and with estimates of melt volumes obtained from field observations of terrestrial impact structures. Considering the geometrical assumptions and uncertainties involved with a static model for the generation of impact melt, our presentation of the nested melt-cavity model should be viewed as a first-order attempt in understanding the effects of impact melting on the morphology and development of peak-ring basins. While we find many consistencies between the model and our analysis of the basin catalogs for the Moon and Mercury, more complex and dynamic melt-zone geometries are probably more realistic, and future refinements to this model will be necessary, especially in improving dynamical simulations of impact melting during large impact events. As stated above, Mercury has the largest number of peak-ring basins per unit area of the terrestrial planets, with the Moon having a factor a two fewer peak-ring basins based on our new lunar basin catalog (Table 1). Under the nested melt-cavity model, the difference in the surface density of peak-ring basins between Mercury and the Moon may be explained by differences in mean impactor velocities on the two bodies. Because of the higher mean impact velocities on Mercury (40 km/s compared with 20 km/s on the Moon), impactors of a given size will produce approximately twice as much melt on Mercury as on the Moon (Grieve and Cintala, 1992). As a result, peak-ring basin formation will be more effective on Mercury for smaller impactors, which are more numerous than larger impactors (Head, 2010). If similar impactor size-frequency fluxes for the inner planets are assumed (Strom et al., 2005), the number of protobasins and peak-ring basins per area should increase with the mean impact velocity at the planet. From the new basin catalogs (Table 1), there appears to be a slight correlation between the number of peak-ring basins per unit area and the planet’s mean impact velocity (Fig. 7B) and an even stronger correlation with gravitational acceleration and mean impact velocity combined (Fig. 7C). These correlations are consistent with the predictions of the nested melt-cavity model and the correla-

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tions in onset diameter (Fig. 6), which suggest that both gravity and velocity are likely important in determining the onset diameter and also surface density of peak-rings on the terrestrial planets (see discussion on onset diameter, below). The low density values for Mars and Venus are likely to be due to planetary resurfacing events; if the complete basin records for Mars and Venus were available, the correlation between the number of peak-ring basins and mean impact velocity might further be strengthened. The nested melt-cavity model also predicts that there will be a continuous progression of impact basin morphologies in the transition from complex craters to peak-ring basins. Under that model, the influence of increasing melt volume and depth of impact melting becomes more important with increasing basin size. In the transition from protobasins to peak-ring basins, uplifted central peak material is suppressed by increasing depth of impact melting, and the uplifted periphery of the melt cavity emerges as the dominant interior morphology (Cintala and Grieve, 1998). This results in a continuum of basin morphologies between protobasins and peak-ring basins, which is very apparent from our new measurements of ring and rim-crest diameters on the Moon (Figs. 4 and 5). The continuous, non-linear trends observed from plots of ring/rim-crest ratios are very consistent between the Moon, Mercury, and Venus (Fig. 5). Ring/rim-crest ratios flatten to a near equilibrium value of around 0.5 for peak-ring basins on the Moon (Fig. 5A), slightly larger ratios of 0.5–0.6 for Mercury (Fig. 5B), and much larger ratios (0.7) for Venus (Fig. 5C). These differences in shapes of the ring/rim-crest ratios may be controlled by the differences in the physical characteristics of the planet. Under the nested melt-cavity model, these characteristics would include those controlling the production of impact melt, such as impact velocity and target properties such as composition, temperature, and volatiles (Grieve and Cintala, 1997). Ringed peak-cluster basins diverge most from this curved trend for the Moon and Mercury, which can be explained by their similarities with complex craters. Baker et al. (2011) and Schon et al. (2011) suggest that the interior ring in ringed peak-cluster basins may be the result of direct modification of the central portions of the uplift structure. At the relatively small rim-crest diameters of ringed peak-cluster basins, the depth of melting has only begun to penetrate the uplift structure and a melt cavity has not been developed. Rebound of the transient cavity floor therefore results in a disaggregated ring-like array of central peak elements instead of a single central uplift structure or a large peak ring. In this fashion, ringed peak-cluster basins represent unique transitional forms in the process of forming peak rings. The predictions of a growing melt cavity with increasing basin size may also be compared to the power law trends between ring and rim-crest diameter for peak-ring basins (Fig. 4). Since the solids making up the periphery of the melt cavity eventually translate inward and upward to form the peak ring, relationships between the expected melt volume at a given basin diameter and an estimate of the melt cavity geometry can give a first-order model of how peak-ring diameters should expand with increasing rim-crest diameter. Assuming a hemispherical melt cavity and using the power law relationship between melt volume and diameter of the transient cavity from Grieve and Cintala (1992) in combination with crater modification scaling relationships (Croft, 1985; Holsapple, 1993), Baker et al. (2011) derived a power law expression relating the diameter of the peak ring (Dring) to the diameter of the final crater rim-crest diameter (Dr):

Dring ¼ ADpr

ð2Þ


1=3 d 1=3 where A ¼ 12 ða Þ and p ¼ bd . 3 p c The constants c and d are from the melt volume relation given by Grieve and Cintala (1992), where c depends on target and

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impactor properties and impact velocity and d is a power law constant equal to 3.85. For the Moon, we take c = 1.42  104 and d = 3.85, which are appropriate to an anorthositic target composition, a chondritic impactor, and an impact velocity of 20 km/s (Cintala and Grieve, 1998). These values, however, do not account for the vaporized portion of the melt cavity, which, when factored into the calculations, can increase the total volume of the melt cavity by 20–30% from a melt only calculation (M.J. Cintala, personal communication, 2010). However, this should only produce about a 5–10% difference in modeled peak ring diameters, which is on the order of the uncertainty in our peak-ring diameter measurements and should not significantly affect our results. The values for the constants a and b are dependent on the crater modification scaling relationships used to convert transient cavity diameters to final crater diameters. We use the constants of Croft (1985) [a = (Dsc)0.15±0.04 and b = 0.85 ± 0.04] and Holsapple (1993) [a = 0.980(Dsc)0.079 and b = 0.921], which were derived largely from lunar and terrestrial data. Both of the scaling relationships for transient crater modification include a transition diameter from simple to complex craters (Dsc) appropriate to the Moon (19 km, Pike, 1988), which tailors the relationship to planetary-specific variables such as gravity and target strength. Holsapple (1993) also includes two relationships that account for the transient rim-crest diameter and the transient excavation diameter. We use the transient rimcrest diameter relationship for consistency with the melt volume power law of Grieve and Cintala (1992). The power-law fit to lunar peak-ring basins (Fig. 4A and Table 2) follows the same form as Eq. (2), and the values for the constants A and p determined from this fit may be directly compared with the predicted values from the melt-cavity model (Table 2) (Baker et al., 2011). The power law fit to lunar peak-ring basins is very consistent with the model predictions. The modeled value for the constant A in Eq. (4) ranges from 0.12 to 0.17 (mean = 0.14) using the Croft (1985) scaling and is 0.11 using the Holsapple (1993) scaling. These values fall within the uncertainty in A values determined from the power-law fit to peak-ring basin data on the Moon (0.04–0.24) (Table 2). Modeled values for the slope of the power law trend, p, range from 1.04 to 1.14 using the Croft (1985) scaling and 1.18 using the Holsapple (1993) scaling, which nearly completely fall within the uncertainty of the p values determined from

lunar peak-ring basins (1.08–1.34) (Table 2). The consistency between the model predictions of a growing melt cavity and the power law fits to peak-ring basins on the Moon and also comparisons on Mercury (Fig. 4A) (Baker et al., 2011) (Table 2) support the first-order predictions of the nested melt-cavity model and suggest that impact melting and melt cavity formation exhibit important controls on the formation of impact basin rings. Finally, while the apparent gravity dependence of the onset diameter for peak-ring basins (Fig. 6A) has generally favored a gravity-driven phenomenon for basin formation (e.g., Melosh, 1989), the nested melt-cavity model predicts that impact velocity should also be important in determining the onset of peak-ring basin morphologies. The onset diameters of peak-ring basins on the terrestrial planets do not appear to depend on mean impact velocity by itself (Fig. 6B), although a combination of gravitational acceleration and mean impact velocity provides an improved correlation with peak-ring basin onset diameter on the terrestrial planets (Fig. 6C and D). Thus, onset diameter is likely to be dependent on both gravitational acceleration and impact velocity. Under the nested melt-cavity model, gravity primarily determines the dimensions of the transient cavity and the final crater diameter, while kinetic energy and thus impact velocity largely determines the volume of melt that is produced during the impact event. Cintala and Grieve (Grieve and Cintala, 1992, 1997; Cintala and Grieve, 1994, 1998) have examined a variety of trends between crater dimensions and impact melting, suggesting that the ratio of the maximum depth of melting (dm) to the depth of the transient cavity (dtc) may be important in determining the onset of peak rings in basins. Cintala and Grieve (1998, their Fig. 7) observed that the depth of melting approaches the depth of the transient cavity with dm/dtc ratios of 0.8–0.9 at the onset diameters for peak-ring basins on the Earth, Moon, and Venus. While the predicted depths of melting at these onset diameters do not meet or exceed the depths of the transient cavity (dm/dtc P 1.0), as emphasized in the general discussion of the onset of peak-ring basins in Grieve and Cintala (1997) and Cintala and Grieve (1998), sufficient depths of melting appear necessary for peak-ring basin formation. We used our calculated onset diameters (Table 1) and the plot of dm/dtc ratio versus transient cavity diameter (Cintala and Grieve, 1998, their Fig. 10) to determine the dm/dtc ratio predicted for the onset diameter of

Table A1 Catalog of peak-ring basins on the Moon. Peak-ring basins are characterized by a single interior topographic ring or a discontinuous ring of peaks with no central peak. Number

Namea

Longitudeb

Latitude

Rim crest (km)

Ring (km)

Ring/rim-crest ratio

Peak-ring arc (deg)

Confidencec

Pike and Spudis (1987)d

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Schwarzschild d’Alembert Milne Bailly Poincaré Coulomb–Sarton Planck Schrödinger Mendeleev Birkhoff Lorentz Schiller–Zucchius Korolev Moscoviense Grimaldi Apollo Freundlich– Sharonov

120.09 164.84 112.77 291.20 163.15 237.47 135.09 133.53 141.14 213.42 263.00 314.82 202.53 147.36 291.31 208.28 175.00

70.36 51.05 31.25 67.18 57.32 51.35 57.39 74.90 5.44 58.88 34.30 55.72 4.44 26.34 5.01 36.07 18.35

207 232 264 299 312 316 321 326 331 334 351 361 417 421 460 492 582

71 106 114 130 175 159 160 150 144 163 173 179 206 192 234 247 318

0.35 0.46 0.43 0.43 0.56 0.50 0.50 0.46 0.44 0.49 0.49 0.50 0.49 0.46 0.51 0.50 0.55

<180 <180 >180 <180 >180 >180 <180 >180 <180 <180 <180 >180 <180 >180 >180 >180 >180

1 1 3 3 3 2 1 3 2 2 2 3 3 3 3 3 2

Protobasin Protobasin Protobasin Protobasin Peak-ring basin Multi-ring basin Peak-ring basin Peak-ring basin Protobasin Peak-ring basin Peak-ring basin Peak-ring basin Multi-ring basin Multi-ring basin Multi-ring basin Multi-ring basin Not classified

a Names shown for basins are those approved by the IAU as of this writing (http://planetarynames.wr.usgs.gov). Names not approved by the IAU, but used by Pike and Spudis (1987) and Wilhelms et al. (1987), are denoted by an asterisk (*). b Longitudes are positive eastward. c Confidence levels are given for ring measurements (3 = highest and 1 = lowest). d Basin classification of Pike and Spudis (1987).

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a b c d

Number

Namea

Longitudeb

Latitude

Rim-crest (km)

Ring (km)

Ring/rim-crest ratio

Central peak (km)

Peak-ring arc (deg)

Confidencec

Pike and Spudis (1987)d

1 2 3

Antoniadi Compton Hausen

187.04 103.96 271.24

69.35 55.92 65.34

137 166 170

56 73 55

0.41 0.44 0.33

6 15 31

>180 >180 <180

3 3 2

Protobasin Protobasin Not classified

Names shown for basins are those approved by the IAU as of this writing (http://planetarynames.wr.usgs.gov). Longitudes are positive eastward. Confidence levels are given for ring measurements (3 = highest and 1 = lowest). Basin classification of Pike and Spudis (1987).

Table A3 Catalog of craters with ring-like central peaks on the Moon. Also included is the ringed peak-cluster basin, Humboldt. Ringed peak-cluster basins are characterized by a ring of central peak elements with a ring diameter that is anomalously small compared to protobasins or peak-ring basins of the same rim-crest diameter. Number

Namea

Ringed peak-cluster basins 1 Humboldt Craters with ring-like central peaks 1 Lindenau 2 Eistein 3 Eijkman 4 Carpenter 5 Zucchius 6 Eudoxus 7 Philolaus 8 Fabricius 9 Cantor 10 King 11 Olcott 12 Hayn 13 Unnamed 14 Colombo 15 Metius 16 Berkner 17 Atlas 18 Lobachevskiy 19 Posidonius 20 Vestine 21 Gassendi 22 Wiener a b c

Longitudeb

Latitude

Rim-crest (km)

Ring (km)

Ring/rim-crest ratio

Ring arc (deg)

Confidencec

81.06

27.12

205

32

0.16

>180

3

24.85 271.80 217.42 308.78 309.48 16.33 327.29 41.79 118.65 120.48 117.84 84.07 170.29 46.10 43.37 254.72 44.33 113.07 30.00 93.71 320.00 146.63

32.33 16.70 63.23 69.52 61.38 44.25 72.24 42.80 38.02 4.92 20.61 64.47 57.24 15.17 40.42 25.14 46.71 9.76 31.86 33.86 17.49 41.02

50 51 57 61 64 66 70 76 76 77 80 82 83 83 84 86 87 87 99 99 112 114

9 8 8 12 11 10 15 18 13 15 15 14 13 16 15 15 15 15 15 13 17 14

0.18 0.16 0.15 0.19 0.17 0.16 0.22 0.24 0.17 0.19 0.19 0.17 0.16 0.19 0.18 0.17 0.17 0.17 0.15 0.13 0.15 0.12

>180 >180 >180 >180 >180 >180 >180 <180 <180 >180 >180 >180 >180 <180 <180 >180 <180 <180 <180 <180 <180 >180

1 1 2 1 3 2 1 3 1 3 2 2 2 1 2 2 2 1 1 2 2 1

Names shown for basins are those approved by the IAU as of this writing (http://planetarynames.wr.usgs.gov). Longitudes are positive eastward. Confidence levels are given for ring measurements (3 = highest and 1 = lowest).

peak-ring basins on the Moon. For comparison, we also determined the dm/dtc ratio at the onset diameter of peak-ring basins on Mercury by using the maximum depth of melting calculations for Mercury derived from impedance matching of the Grieve and Cintala (1992) model (Ernst et al., 2010, their Fig. 5). In calculating the dm/dtc ratio for Mercury, we assumed that the depth of the transient cavity is approximately one-third of its rim-crest diameter (Cintala and Grieve, 1998). The crater modification scaling relationship of Croft (1985) was also used to convert the measured rim-crest diameters on the Moon and Mercury to transient cavity diameters. We find a dm/dtc ratio of about 0.7 (dm  35 km) for the onset diameter of peak-ring basins on the Moon (227 km) and a dm/dtc ratio of about 0.8 (dm  20 km) for the onset diameter of peak-ring basins on Mercury (116 km). The similar ratios for both Mercury and the Moon suggest that sufficient depth of melting relative to the depth of the transient cavity must be achieved before peak rings are fully developed. This is consistent with a growing melt cavity within the displaced zone that suppresses the formation of central peak elements to form a peak ring through weakening of the central uplifted portions of the crater interior (Cintala and Grieve, 1998; Head, 2010). Once the depth of melting reaches a value close to roughly three-fourths the depth of the

transient cavity depth, complete suppression of the central peak is achieved, and the peak ring is the only topographic feature that remains. For multi-ring basins on the Moon, the depth of melting generally meets or exceeds the depth of the transient cavity diameter. For example, if we take the Outer Rook ring of Orientale basin to be the diameter of the transient cavity (620 km) (Head et al., 2011), the dm/dtc ratio is slightly greater than 1.0 (Cintala and Grieve, 1998). This is consistent with a hybrid mega-terrace and nested melt-cavity model for the onset of multi-ring basins (Head, 2010), in which deep penetration of the melt cavity past the displaced zone creates a strength discontinuity that allows mega-terraces to form through translation of crustal blocks laterally in toward the melt cavity. Based on the above observations, critical thresholds in the ratio between depth of melting and the dimensions of the transient cavity appear to offer plausible explanations for the onset of basin morphologies on the terrestrial planets, including interior peak rings and the exterior rings of multi-ring basins. The scaling of these two parameters depends on both gravity and velocity, and is therefore consistent with the first-order correlations shown in Fig. 6. We suggest that while gravity is important in determining the dimensions of the transient cavity

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and final crater diameter, it is not the dominant process in forming peak rings. Instead, our observations from the catalogs of basins on the terrestrial planets suggest that velocity, and therefore kinetic energy and subsequent melting of target material during impact is likely to exhibit the strongest control on peak-ring basin formation.

between our analyses of basin catalogs and the nested melt-cavity model are promising, much work is needed to corroborate these observations, including advanced impact simulations that are able to model accurately impact melt production and its effects during crater modification. Acknowledgments

8. Conclusions We have updated the current catalogs of protobasins and peakring basins on the Moon using new 128 pixel/degree (235 m/pixel) resolution gridded topography from the Lunar Orbiter Laser Altimeter (LOLA). Our refined catalog includes 17 peak-ring basins, 3 protobasins, and 1 ringed peak-cluster basins. Several basins previously inferred to be multi-ring basins (Apollo, Moscoviense, Grimaldi, Freundlich–Sharonov, Coulomb–Sarton, and Korolev) are now re-classified as peak-ring basins due to the absence of more than two prominent topographic rings observed in the LOLA data or overall consistency with a peak-ring basin origin. Interplanetary comparisons of basin catalogs emphasize some previous observations and provide new constraints on the dominant mechanisms of peak-ring basin formation. Key observations include: (1) Onset diameter calculations for peak-ring basins suggest correlations with a combination of both gravity and mean impact velocity (Fig. 6). The Moon has the largest onset diameter of the terrestrial planets (227 km), followed by Mercury (116 km), Mars (56 km), and Venus (33 km) (Table 1). (2) The Moon has a surface density of peak-ring basins (4.5  107 per km2) that is intermediate between Mercury (9.9  107 per km2) and Mars (1.0  107 per km2) and Venus (1.4  107 per km2) (Table 1). The differences in the number of peak-ring basins between the Moon and Mercury may be due to their different mean impact velocities and onset diameters of peak-ring basins. (3) Ring/rim-crest ratios (Fig. 5) indicate continuous, nonlinear trends that are similar on the Moon, Mercury, and Venus and suggest that protobasins and peak-ring basins are parts of a continuum of basin morphologies. Ring/rim-crest ratios flatten to values of around 0.5 for the Moon, slightly higher values of 0.5–0.6 for Mercury, and a much higher ratio of 0.7 on Venus. (4) Power-law fits to plots of the ring and rim-crest diameters of peak-ring basins on the Moon and Mercury are very similar (Fig. 4 and Table 2) and are both consistent with a power law model of a growing melt cavity with increasing basin size (Eq. (2)). Our analysis of the morphological characteristics of peak-ring basins and protobasins on the Moon and the terrestrial planets shows many consistencies with the predictions of the nested melt-cavity model for basin formation. Under this model, basin rings are formed from the nonlinear scaling of impact melt and development of an expanding melt cavity within the displaced zone, which acts to suppress central uplift structures with increasing depth of melting. At a depth of melting approximately threefourths the depth of transient cavity, the depth of melting is sufficient to completely retard the formation of a central uplift structure and a peak ring emerges as the dominant interior morphology. Multi-ring basins are likely to form as the melt cavity expands to depths equal to or greater than the depth of the transient cavity, which acts to substantially weaken the basin interior and initiates mega-terracing and formation of a topographic ring exterior to transient cavity rim. While the first-order consistencies

We thank Ian Garrick-Bethell for use of the code to calculate the averaged LOLA topography profiles and Sam Schon for productive discussions on the populations of impact basins on Mercury. We also thank Mark Cintala for helpful discussions on the scaling of impact melting and the LOLA and LROC teams for their efforts in acquiring and processing the data. Reviews by Gordon Osinski and an anonymous reviewer helped to improve the quality of the manuscript. Thanks are extended to the NASA Lunar Reconnaissance Obiter Mission, Lunar Orbiter Laser Altimeter (LOLA) instrument for financial assistance (NNX09AM54G). Appendix A Catalogs of all peak-ring basins, protobasins, and ringed peakcluster basins on the Moon as compiled in the present study are presented in Tables A1–A3, respectively. LOLA gridded topography images of each basin are also found as online supplementary material. Appendix B. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.icarus.2011.05.030. References Alexopoulos, J.S., McKinnon, W.B., 1992. Multiringed impact craters on Venus – An overview from Arecibo and Venera images and initial Magellan data. Icarus 100 (2), 347–363. Alexopoulos, J.S., McKinnon, W.B., 1994. Large impact craters and basins on Venus, with implications for ring mechanics on the terrestrial planets. In: Dressler, B.O., Grieve, R.A.F., Sharpton, V.L. (Eds.), Large Meteorite Impacts and Planetary Evolution. Special Paper 293. Geological Society of America, Boulder, Colo, pp. 29–50. Araki, H. et al., 2009. Lunar global shape and polar topography derived from Kaguya-LALT Laser Altimetry. Science 323 (5916), 897–900. Baker, D.M.H. et al., 2011. The transition from complex crater to peak-ring basin on Mercury: New observations from MESSENGER flyby data and constraints on basin-formation models. Planet. Space Sci. in press. doi:10.1016/j.pss.2011. 05.010. Baldwin, R.B., 1981. On the tsunami theory of the origin of multi-ring basins. Multiring basins: Formation and evolution. In: Schultz, P.H., Merrill, R.B. (Eds.), Multiring basins: Formation and evolution. Proc. Lunar Planet. Sci. 12A, 275–288. Barlow, N.G., 2006. Status report on the ‘‘Catalog of Large Martian Impact Craters’’, version 2.0. Lunar Planet. Sci. 37 (abstract 1337). Barr, A.C., Citron, R.I., 2011. Scaling of melt production in hypervelocity impacts from high-resolution numerical simulations. Icarus 211 (1), 913–916. Cintala, M.J., Grieve, R.A.F., 1994. The effects of differential scaling of impact melt and crater dimensions on lunar and terrestrial craters: Some brief examples. In: Dressler, B.O., Grieve, R.A.F., Sharpton, V.L. (Eds.), Large Meteorite Impacts and Planetary Evolution. Special Paper 293. Geological Society of America, Boulder, Colo, pp. 51–59. Cintala, M.J., Grieve, R.A.F., 1998. Scaling impact-melt and crater dimensions: Implications for the lunar cratering record. Meteorit. Planet. Sci. 33, 889–912. Collins, G.S., Melosh, H.J., Morgan, J.V., Warner, M.R., 2002. Hydrocode simulations of Chicxulub crater collapse and peak-ring formation. Icarus 157, 24–33. doi:10.1006/icar.2002.6822. Collins, G.S., Morgan, J.M., Barton, P., Christeson, G.L., Gulick, S., Urrutia, J., Warner, M., Wünnemann, K., 2008. Dynamic modeling suggests terrace zone asymmetry in the Chicxulub crater is caused by target heterogeneity. Earth Planet. Sci. Lett. 270, 221–230. Croft, S.K., 1985. The scaling of complex craters. J. Geophys. Res. 90 (Suppl.), C828– C842. Ernst, C.M., Murchie, S.L., Barnouin, O.S., Robinson, M.S., Denevi, B.W., Blewett, D.T., Head, J.W., Izenberg, N.R., Solomon, S.C., Robertson, J.H., 2010. Exposure of spectrally distinct material by impact craters on Mercury: Implications for global stratigraphy. Icarus 209, 210–233.

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