The transition from complex crater to peak-ring basin on the … · Impact craters on planetary...

Icarus 214 (2011) 377–393

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Icarus

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The transition from complex crater to peak-ring basin on the Moon: Newobservations 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 Department of Geological Sciences, Brown University, Providence, RI 02912, United Statesb Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 208771, United Statesc 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 2010Revised 15 April 2011Accepted 23 May 2011Available online 2 June 2011

Keywords:MoonMercuryCrateringImpact processes

0019-1035/$ - see front matter � 2011 Elsevier Inc. Adoi:10.1016/j.icarus.2011.05.030

⇑ Corresponding author. Address: Department ofUniversity, Box 1846, Providence, RI 02912, United St

E-mail address: [email protected] (D.M.H. B

a b s t r a c t

Impact craters on planetary bodies transition with increasing size from simple, to complex, to peak-ringbasins and finally to multi-ring basins. Important to understanding the relationship between complexcraters with central peaks and multi-ring basins is the analysis of protobasins (exhibiting a rim crestand 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 theMoon. 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 conducta survey of craters >50 km in diameter on the Moon and to update the existing catalogs of lunar peak-ringbasins and protobasins. Our updated catalog includes 17 peak-ring basins (rim-crest diameters rangefrom 207 km to 582 km, geometric mean = 343 km) and 3 protobasins (137–170 km, geometricmean = 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 basinsdue to their similarities with lunar peak-ring basin morphologies and absence of definitive topographicring structures greater than two in number. We also include in our catalog 23 craters exhibiting smallring-like clusters of peaks (50–205 km, geometric mean = 81 km); one (Humboldt) exhibits a rim-crestdiameter and an interior morphology that may be uniquely transitional to the process of forming peakrings. A power-law fit to ring diameters (Dring) and rim-crest diameters (Dr) of peak-ring basins on theMoon [Dring = 0.14 ± 0.10(Dr)1.21±0.13] reveals a trend that is very similar to a power-law fit to peak-ringbasin diameters on Mercury [Dring = 0.25 ± 0.14(Drim)1.13±0.10] [Baker, D.M.H. et al. [2011]. Planet. SpaceSci., in press]. Plots of ring/rim-crest ratios versus rim-crest diameters for peak-ring basins and protoba-sins on the Moon also reveal a continuous, nonlinear trend that is similar to trends observed for Mercuryand Venus and suggest that protobasins and peak-ring basins are parts of a continuum of basin morphol-ogies. The surface density of peak-ring basins on the Moon (4.5 � 10�7 per km2) is a factor of two lessthan Mercury (9.9 � 10�7 per km2), which may be a function of their widely different mean impact veloc-ities (19.4 km/s and 42.5 km/s, respectively) and differences in peak-ring basin onset diameters. New cal-culations of the onset diameter for peak-ring basins on the Moon and the terrestrial planets re-affirmprevious analyses that the Moon has the largest onset diameter for peak-ring basins in the inner SolarSystem. Comparisons of the predictions of models for the formation of peak-ring basins with the charac-teristics of the new basin catalog for the Moon suggest that formation and modification of an interiormelt cavity and nonlinear scaling of impact melt volume with crater diameter provide important controlson the development of peak rings. In particular, a power-law model of growth of an interior melt cavitywith increasing crater diameter is consistent with power-law fits to the peak-ring basin data for theMoon and Mercury. We suggest that the relationship between the depth of melting and depth of the tran-sient cavity offers a plausible control on the onset diameter and subsequent development of peak-ringbasins and also multi-ring basins, which is consistent with both planetary gravitational accelerationand mean impact velocity being important in determining the onset of basin morphological forms onthe terrestrial planets.

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Geological Sciences, Brownates. Fax: +1 401 863 3978.aker).

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378 D.M.H. Baker et al. / Icarus 214 (2011) 377–393

1. Introduction

Major lines of inquiry in the study of impact craters on the terres-trial planets over the past half-century have focused on the onset andformation of multi-ring basins occurring at the largest crater diame-ters. Many hypotheses have been developed to explain the formationof rings interior and exterior to the transient cavity of multi-ring ba-sins, including frozen crustal tsunamis (Baldwin, 1981), differentialdepths 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 for-mation of tectonic rings due to the contrasting strengths of the lith-osphere and aesthenosphere (Melosh and McKinnon, 1978; Melosh,1982, 1989; Collins et al., 2002). Although these models have pro-vided much insight into the formation of large impact structureson the terrestrial planets (e.g., Melosh, 1989; Spudis, 1993), thereis currently no consensus on how the rings of multi-ring basins form.

Important to understanding the mechanisms of multi-ring basinformation have been analyses of peak-ring basins and other transi-tional morphologies between complex craters with central peaksand multi-ring basins. Many crater catalogs of these basin typeshave been produced (Wood and Head, 1976; Wood, 1980; Wilhelmset al., 1987; Pike and Spudis, 1987; Pike, 1988; Spudis, 1993; Alexo-poulos and McKinnon, 1994), which traditionally include measure-ments of major morphological features such as the diameter of thecrater’s rim crest, ring, and central peak. Trends in the ring andrim-crest diameters of peak-ring basins have been used as evidenceto support a number of peak-ring basin formation models (Pike andSpudis, 1987; Pike, 1988). However, the lack of complete populationdata for peak-ring basins on the terrestrial planets due to limitationsin image and topographic resolution has inhibited accurate interpre-tations of the relationship between peak-ring basin morphologiesand the mechanisms of their formation. With the addition of newand improved spacecraft data, it is important to update the existingcatalogs of craters and basins, including observations of their mor-phological characteristics. This is especially important for the airlessbodies, Mercury (Baker et al., 2011) and the Moon, where relativelylow erosion and resurfacing rates throughout geologic history havepreserved much of their basin populations. We use new topographicdata from the Lunar Orbiter Laser Altimeter (LOLA) (Smith et al.,2010), in combination with a global Lunar Reconnaissance OrbiterCamera (LROC) Wide Angle Camera (WAC) (Robinson et al., 2010)image mosaic at 100 m/pixel resolution to update the current cata-log of peak-ring basins and other basin morphologies in the transi-tion from complex craters to multi-ring basins on the Moon. LOLAcurrently provides gridded topography at better than 128 pixel/de-gree (�235 m/pixel) resolution, a substantial improvement overprevious topographic data of the Moon, including the 8–30 km/pixelresolution data from the Clementine Light Imaging Detection andRanging (LiDAR) instrument (Smith et al., 1997) and the �15 pixel/degree resolution data from the Kaguya Laser Altimeter (Arakiet al., 2009). Our catalog of the lunar peak-ring basin and protobasinpopulations, including measurements of basin rim-crest, ring, andcentral-peak diameters, is then compared with catalogs on the otherterrestrial planets, including a recent, comprehensive catalog ofpeak-ring basins and other transitional basins on Mercury (Bakeret al., 2011). We then use our lunar basin catalog to test the predic-tions of one basin formation model, which seeks to explain the for-mation of peak rings by modification of the crater interior from agrowing impact melt cavity.

2. The size-morphology progression

Transitional morphologies in the size progression from complexcraters to multi-ring basins have traditionally included at least two

classes of basins: peak-ring basins (or double-ring or two-ring ba-sins) and protobasins (or central-peak basins) (Pike, 1988; Bakeret al., 2011). Peak-ring basins are the most numerous transitionalforms and their interior morphologies are characterized by a single,continuous or semi-continuous interior ring of peaks with no centralpeak. The lunar basin, Schrödinger, (rim-crest diameter, as mea-sured in this study = 326 km) best exemplifies this morphology,showing a nearly continuous ring of peaks (Fig. 1A). LOLA griddedtopography shows that Schrödinger has a depth of about 4 km witha peak ring that is tens of kilometers in width and rises about 1 kmabove the surrounding floor materials (Figs. 1A and 2A). Protobasinsposses both a central peak and an interior ring of peaks, but thesefeatures are commonly smaller in diameter and have less topo-graphic relief than either central peaks in complex craters and peakrings in peak-ring basins (Pike, 1988). Antoniadi (rim-crest diame-ter, as measured in this study = 137 km) is a type example of a pro-tobasin 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, butprominent central peak that rises above the surrounding peak ring(Fig. 2B). However, the smoothness of Antoniadi’s interior suggeststhat substantial infilling has occurred, which has certainly affectedthe relative topography of its central peak and peak ring. A third classof basins, called ringed peak-cluster basins, has also been identifiedfrom analysis of recent flyby data of Mercury (Baker et al., 2011). Likepeak-ring basins, ringed peak-cluster basins have a single interiorring of peaks without a central peak (Fig. 1C) and overlap in rim-crestdiameter with protobasins; however, the relatively small diameterof their peak rings relative to their rim-crest diameter precludesthese basins from classification as traditional peak-ring basins. Thetype example of a ringed peak-cluster basin on Mercury is the125-km diameter crater, Eminescu, which exhibits a very well-de-fined interior ring (Schon et al., 2011). On the Moon, many craterswith 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 diameterwith protobasins and is thus classified as a potential ringed peak-cluster basin. Humboldt has a disaggregated ring-like array of cen-tral peak elements (Fig. 1C) that is nearly 1 km in relief (Fig. 2C). Acentral depression in the middle of the array of peaks slopes steeplyto about 100 m below the fractured fill material that occupies thefloor of Humboldt (Fig. 2C).

3. Methods

There have been several comprehensive catalogs of basins onthe Moon (Wood and Head, 1976; Pike and Spudis, 1987; Wilhelmset al., 1987; Spudis, 1993), which were based primarily on Apollo-era data, including image data from the Lunar Orbiter and ApolloTerrain Mapping Camera. While there are many similarities be-tween these catalogs, there are some disagreements, particularlywith identification of multiple exterior and interior rings and cen-tral peak plus ring structures. We have elucidated the identifica-tion of protobasins and peak-ring basins by analyzing new LunarOrbiter Laser Altimeter (LOLA) (Smith et al., 2010) global griddedtopography and hillshade data at 128 pixel/degree (�235 m/pixel)resolution in combination with a Lunar Reconnaissance OrbiterCamera (LROC) Wide Angle Camera (WAC) (Robinson et al.,2010) global image mosaic at 100 m/pixel resolution. We also useddetrended LOLA gridded topography data to remove the effects oflong-wavelength topographic variations and to help emphasize lo-cal variations in topography such as peak rings. All craters on theMoon greater than 50 km in diameter were analyzed in ArcGIS(ESRI, www.esri.com) using a recent catalog of lunar craters (Headet al., 2010) to ensure complete surveying of basin types. Particularscrutiny was given to basins already cataloged, including many

http://www.esri.com

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 andinterior ring (dashed lines) on LOLA hillshade gridded topography. Bottom panels show LOLA colored gridded topography at 128 pixel/degree on LOLA hillshade griddedtopography. (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 withan incomplete, diminutive ring of central peak elements.

D.M.H. Baker et al. / Icarus 214 (2011) 377–393 379

multi-ring basins where some ring designations were most uncer-tain (Pike and Spudis, 1987).

The diameters of basin features, including rim crests, rings, andcentral peaks, were measured (where present) by visually fittingcircles to the features using the CraterTools extension in ArcGIS(Kneissl et al., 2010). Circle-fits were carefully selected to bestapproximate the mean diameter value for the features (Bakeret al., 2011) (Fig. 1). For example, peak rings were fit by a circleintermediate between circles that inscribe and circumscribe thepeak ring. Fits to rim crests were defined by the most prominenttopographic divides along the crater rim crest. Central peaks werethe most difficult to measure due to their irregular outlines. Forthose irregular central peaks, we chose circular fits that approxi-mated a diameter that is intermediate between the maximumand minimum areal dimensions of the feature (Baker et al., 2011)(Fig. 1). As in previous catalogs, our confidence in the identificationand measurement of peak rings is presented as a scale from 1 (low-est) to 3 (highest) (Tables A1–A3). Most basins are cataloged withthe highest confidence, however, three peak-ring basins remainmore speculative due to incomplete preservation of interior mor-phologies or possible mis-interpretation of interior features as pri-mary basin structure. The continuity of observable peak rings arealso designated as being greater than or less than 180� of arc (Ta-bles A1–A3).

4. The basin catalog

Our catalog is a refinement of earlier catalogs of peak-ringbasins and protobasins on the Moon. We have excluded some

ambiguous basins and have re-classified several other basins, par-ticularly those near the transition diameters between peak-ringbasins and protobasins and peak-ring basins and multi-ring basins.These re-classifications largely reflect our improved ability to rec-ognize genuine basin ring and central peak structures from newLOLA topographic and image data. Our refined catalog includes17 peak-ring basins (Table A1), 3 protobasins (Table A2), and 1ringed peak-cluster basin (Table A3). LOLA gridded topographyimages of each basin in Tables A1–A3 are also included as onlinesupplementary material. Twenty-two craters exhibiting ring-likearrangements of central peak elements are also cataloged(Table A3), but are not classified as ringed peak-cluster basinsdue to their small (<114 km) rim-crest diameters that fall belowthe transitional rim-crest diameter range between complex cratersand peak-ring basins (see discussion in Section 6.1). All of thepeak-ring basins and protobasins cataloged in this study have ap-peared in earlier catalogs, but have been variously classified as oneor multiple basin types based on the available data at the time thecatalogs were generated.

Our peak-ring basin catalog includes five basins that have beenpreviously classified as multi-ring basins by Pike and Spudis(1987): Apollo, Moscoviense, Grimaldi, Coulomb–Sarton, and Koro-lev. Our catalog also includes Freundlich–Sharonov, which was rec-ognized as a candidate multi-ring basin but with only one 600-kmdiameter ring identified (Wilhelms et al., 1987; Spudis, 1993).Upon careful examination of LOLA topographic data (Fig. 3), wefind that all of these basins are fit best by no more than two topo-graphic rings. For example, a possible ring exterior to Apollo(Fig. 3A) appears to be associated with the rim structure of South

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 profileswere calculated by averaging 360 great circle transects radiating from the basins’centers and separated by 1� of azimuth. The topography along each of the 360transects was calculated using a bilinear interpolation with the number of datapoints set to equal the 16 pixel/degree resolution of the LOLA data used for theprofiles.


Pole Aitken basin and is not concentric to Apollo’s main topo-graphic rings. Moscoviense (Fig. 3B) has been traditionally inter-preted to be a multi-ring basin (e.g., Pike and Spudis, 1987) dueto the presence of three concentric but off-centered ring structures.The offset characteristic of the three rings of Moscoviense to thesouthwest has suggested that Moscoviense may have formed froman oblique impact (see discussion in Thaisen et al. (2011)). How-ever, a survey of offset peak rings in basins on Venus, for which im-pact direction could be inferred from ejecta patterns, determinedthat there was no correlation between ring offset and directionof impactor approach (McDonald et al., 2008). It was suggestedthat other parameters, such as target rock heterogeneities likelycontributed to the offset ring characteristics of these peak ringson Venus. Furthermore, the effects of oblique impacts on basinmorphology, especially on the scale of multi-ring basins are stillpoorly understood (Pierazzo and Melosh, 2000). Alternatively, we

favor a scenario whereby the inner two rings of Moscoviense rep-resent a peak-ring basin superposed on a larger, older impact basin(e.g., Ishihara et al., 2011; Thaisen et al., 2011). Several geophysicaland morphological characteristics of Moscoviense support a super-posed impact scenario. First, the anomalously thin crust and highgravity of Moscoviense is more easily explained by double impactsthan a single oblique impact (Ishihara et al., 2011). Second, theprominence and regular outline of the intermediate ring appearsmuch more analogous to a basin rim-crest compared to the moreplateau-like, irregular topography of the intermediate rings in mul-ti-ring basins such as Orientale (Head et al., 2011). Finally, theinnermost ring of Moscoviense is very prominent and sharp, shar-ing 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 thathave been classified as potential ring structures (Pike and Spudis,1987). While these depressions may be related to the basin forma-tion process, they are also interior to and are morphologically dis-tinct from peak rings, which have more circular planform shapesand a distinct topographic signature that is raised above the sur-rounding basin floor material (Fig. 2A). We therefore do not includethe rims of these depressions as separate rings in our catalog. Dueto its highly degraded nature, our classification of Coulomb–Sarton(Fig. 3E) is the most uncertain of the large basins. However, we findthat the observed impact structure can be best fit by two rings thatare consistent with the rim-crest and ring diameters of other peak-ring basins on the Moon. The most uncertain basins in our catalogshould be a focus during re-examinations using even higher reso-lution data or improved techniques. Lastly, in contrast to Pikeand Spudis (1987), we do not include Amundsen–Ganswindt inour peak-ring basin catalog, as the irregular interior topographyof the basin does not resemble a ring and is likely to be modifiedejecta material.

Our catalog includes three protobasins, two of which, Antoniadiand Compton, are unambiguous examples of basins exhibiting acentral peak surrounded by an interior ring of peaks. We also in-clude the crater, Hausen, in our catalog. While the interior ring ofHausen is not as well defined as those of Antoniadi and Compton,an incipient ring is observed. The subtlety of Hausen’s ring topog-raphy may be related to the size of the central peak, as there ap-pears to be a correlation between size of the central peak andprominence of the interior ring (Pike, 1988). Hausen exhibits thelargest central peak and least pronounced ring and Antoniadiexhibits the smallest central peak and the most topographicallyprominent ring (although the center of Antoniadi has been floodedby mare deposits (Fig. 1B), likely reducing the relief of its centralpeak and peak ring). Although the lunar protobasin population isvery small, this correlation between central peak size and ringprominence and size is consistent with observations of the morenumerous protobasin population on Mercury (Pike, 1988). Pikeand Spudis (1987) include three other craters, Campbell, Fermi,Hipparchus, and Mendeleev in their protobasin catalog. With theexception of Mendeleev, we do not observe topographic rings inall of these craters in the new LOLA topography. For Mendeleev,we observe an interior ring but do not observe a central peak struc-ture; Mendeleev is therefore classified as a peak-ring basin in ourcatalog. Pike and Spudis (1987) also include craters exhibiting rel-atively small ring/rim-crest ratios as potential protobasins(although central peak structures were not directly observed inthese craters, possibly due to the effects of resurfacing or erosion).However, ring/rim-crest ratios alone cannot be used to recognizeprotobasins because the trends of ring and rim-crest diameters ofprotobasins appear statistically indistinguishable from peak-ringbasins (Baker et al., 2011). Of the potential protobasins catalogedby Pike and Spudis (1987), we include Bailly, Milne, and Schwarzs-child in our peak-ring basin catalog due to the presence of a

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 dashedoutlines of the observed basin rim crest and ring on a Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) image mosaic. Middle panels show LOLAcolored 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 isstill possible that small central peaks within these structures havebeen erased by resurfacing processes, the absence of a central peakprecludes them from being classified as a protobasin in our catalog.We do not observe interior rings or central peaks for the remainingpossible protobasins classified by Pike and Spudis (1987).

Ringed peak-cluster basins have not been included in previousbasin catalogs of the Moon. From analyses of recent flyby imagesof Mercury, Schon et al. (2011) and Baker et al. (2011) interpretat least some ringed peak-cluster craters to be transitional typesbetween complex craters possessing central peaks and peak-ringbasins. Support for such a transitional morphology included over-lap between the rim-crest diameters of ringed peak-cluster basinswith rim-crest diameters of protobasins and small peak-ring ba-sins, the clear ring-like morphology of the peak elements (ringed

peak clusters), and similar trends between the diameters of ringedpeak clusters and central peak diameters in complex craters. Thesetrends, as well as geological mapping, led the authors to suggestthat ringed peak clusters are the product of early development ofa melt cavity that directly modifies the centers of central upliftstructures. While at least 23 craters >50 km in diameter on theMoon 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 withthe rim-crest diameters of protobasins. It is therefore likely thatmost ring-like central peak structures do not represent uniquetransitional types in the size-morphology progression from com-plex craters to peak-ring basins. The association of ring-like centralpeaks with floor-fractured craters has led to the interpretation that

Fig. 3 (continued)


some ring-like central peaks result from collapse of the innermostportions 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 centralpeaks occur on the Moon suggest that their development is not re-lated to the peak-ring basin forming process. Humboldt, classifiedhere as the only ringed peak-cluster basin on the Moon, is morelikely to be a unique transitional basin type; however, the frac-tured fill that occupies Humboldt’s floor suggests similarities withfloor-fractured craters at smaller rim-crest diameters.

5. New basin statistics

Based on our new rim-crest measurements, we have revised thegeneral statistics for peak-ring basins and protobasins on the Moon(Table 1). The rim-crest diameters of peak-ring basins range from207 to 582 km, with a geometric mean diameter of 343 km. Our

peak-ring basin data have a much larger rim-crest diameter rangethan the 320–365 km range from Pike and Spudis (1987) and has asmaller geometric mean rim-crest diameter compared to the meanrim-crest diameter of 335 km from Pike and Spudis (1987). Thethree protobasins in our catalog give a range from 137 to 170 kmwith a geometric mean of 157 km, compared to the larger rangeof values (135–365 km) and larger geometric mean rim-crestdiameter (204 km) for protobasins in the catalog of Pike and Spudis(1987).

Using our new basin catalog, we also calculate the onset diam-eter for peak-ring basins on the Moon. The term ‘‘onset diameter’’has been defined loosely in previous studies; examples of suchusage include the minimum diameter of a population or the diam-eter at which one crater morphology outnumbers another (see dis-cussions in Pike (1983, 1988) and Baker et al. (2011)). In ananalysis of basins on Mercury, Baker et al. (2011) chose to calculatethe onset diameter for peak-ring basins based on the rim-crestdiameter range where multiple crater morphologies overlap. In

Table 1Statistics 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 basincatalog (Tables A1–A3).

Moona Mercuryb Marsc Venusd

Gravitational acceleration (m/s2) 1.62 3.70 3.69 8.87Surface area (km2) 3.8 � 107 7.5 � 107 1.4 � 108 4.6 � 108

Mean impact velocitye (km/s) 19.4 42.5 10.6 25.2

Peak-ring basins (Npr) 17 74 15 66Npr/km2 4.5 � 10�7 9.9 � 10�7 1.0 � 10�7 1.4 � 10�7

Geometric mean diameter (km) 343 180 140 57Minimum diameter (km) 207 84 52 31Maximum diameter (km) 582 320 442 109Onset diameter, method 1f (km) 206 126 + 33/�26 80 + 29/�21 42 + 10/�8Onset diameter, method 2g (km) 227 116 56 33

Protobasins (Nproto) 3 32 7 6Nproto/km2 7.9 � 10�8 4.3 � 10�7 4.9 � 10�8 1.3 � 10�8

Geometric mean diameter (km) 157 102 118 62Minimum diameter (km) 137 75 64 53Maximum diameter (km) 170 172 153 70

Ringed peak-cluster (Nrpc) 1 9 – –Nrpc/km2 2.6 � 10�8 1.2 � 10�7 – –Geometric mean diameter (km) – 96 – –Minimum diameter (km) – 73 – –Maximum diameter (km) – 133 – –

a Basin data from this study (Tables A1–A3).b 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 adiscussion on calculating onset diameter). Uncertainties are one standard deviation about the geometric mean, calculated by multiplying and dividing the geometric mean bythe 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 compiledby 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 notoverlap.

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.


this method (‘‘onset diameter, method 1’’, Table 1), the range ofdiameters is first identified over which examples of two or morecrater morphological forms can both be found, and then the onsetdiameter is defined as the geometric mean of the rim-crest diam-eters of all craters or basins within this range (Baker et al., 2011).For Mercury, Venus, and Mars, rim-crest diameters for peak-ringbasins overlap the rim-crest diameters of both protobasins andcomplex craters (Baker et al., 2011). However, on the Moon nooverlap exists between peak-ring basins and other morphologicalclasses of basins. We therefore take the onset diameter for peak-ring basins on the Moon to be the geometric mean of the minimumdiameter of the lunar peak-ring basin population and the maxi-mum diameter of the next morphologically distinct populationwith smaller rim-crest diameters. We use the minimum peak-ringbasin rim-crest diameter of 207 km (Schwarzschild) and the max-imum rim-crest diameter of 205 km for the ringed peak-cluster ba-sin, Humboldt, to obtain an onset diameter of 206 km for peak-ringbasins on the Moon. Onset diameters calculated using the overlapmethod 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 peak-ring basins has the advantage of defining onset diameter of peak-ring basins by the spectrum of basin morphologies in the transitionbetween complex craters and peak-ring basins and is therefore re-lated to the physical processes resulting in the onset of interior ba-sin rings. A second advantage is that the uncertainty in theestimated onset diameter is also derivable from the calculation.However, there are situations, such as in the Moon, where distinctcrater 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 theworker defines the overlap diameter range, which is usually de-fined from the use of multiple catalogs from more than one worker.As such, while its use is directly tied to the observed morphologicaltransition, the overlap method’s applicability and reproducibility islimited, as it cannot be easily applied to planets with little or nooverlap, and it is not able to be reliably reproduced by other work-ers because of its dependence on multiple crater populations thatmay not have been compiled using the same survey techniques.Satisfying these criteria is crucial for use in interplanetary compar-isons and in understanding how the physical properties of theplanets are modulating the basin-forming process.

A more reproducible and applicable method for calculating on-set diameter is to select a given percentile of the population. Wecalculate the 5th percentile of the peak-ring basin populations(‘‘onset diameter, method 2’’, Table 1) to obtain alternative onsetdiameters for peak-ring basins on the terrestrial planets: 227 km(Moon), 116 km (Mercury), 56 km (Mars), 33 km (Venus). Peak-ring basin diameter data used in the calculations are from thisstudy (Moon), Baker et al. (2011) (Mercury), Alexopoulos andMcKinnon (1994) (Venus), and Pike and Spudis (1987) (Mars).The 5th percentile is chosen as it is an easily reproducible, descrip-tive statistic that is based on an historical standard of significancein statistical analysis. The method is robust against outliers, as it isdefined by the tail of the distribution itself, not a single data pointdefining the minimum value of the population. The method isapplicable to all planets and is independent, as it relies only on asingle basin population and is independent of the interplanetaryvariations encountered in the population distributions of othertransitional crater morphologies. In addition, since basin

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 (greendiamonds) 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 ring-like 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 trendfor 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-endof 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 tocolor in this figure legend, the reader is referred to the web version of this article.)


populations can now be cataloged based on complete, or nearlycomplete, data coverage of the planetary surface, we can be confi-dent that we are using populations rather than samples of partic-ular crater and basin morphologies when calculating onsetdiameters. While the use of the 5th percentile to define peak-ringbasin onset diameter does not rely on more than a single basinpopulation and is not directly derived from the observed morpho-logical transition between complex crater and peak-ring basin,peak-ring basin onset diameters calculated by this method consis-tently fall within the uncertainties of onset diameters calculatedusing a method based on the diameters of overlapping morpholo-gies, as described above (Table 1).

6. Analysis and interplanetary comparisons

Our refined catalog of transitional lunar basin types betweencomplex craters and multi-ring basins permits us to better com-pare and evaluate several key characteristics of basin populationson the Moon and the terrestrial planets. These characteristics in-clude: (1) ring and rim-crest diameter systematics, (2) surface den-sity of peak-ring basins, and (3) peak-ring basin onset diameter.The airless body, Mercury, has the largest population of preservedpeak-ring basins and protobasins in the inner Solar System (Bakeret al., 2011), and thus provides an important dataset for compari-son with the population of peak-ring basins and protobasins onthe Moon. The basin catalogs for Venus and Mars should also beconsidered in interplanetary comparisons; however, resurfacing,erosion, and the effects of volatiles have influenced the presentpopulations and morphologies of basins on these planets, render-ing them less useful in comparison studies. Since the impact recordon Earth is largely incomplete and highly modified by erosion, inte-rior structures cannot be accurately identified and therefore pres-ent large uncertainties when used in interplanetary comparisons.

As such, impact structures on Earth are not used in this study. Inthe following sections, we analyze our new catalog of basins onthe Moon and identify key similarities and differences with theother planetary bodies, especially Mercury. In the next section,these comparisons are then placed in context of the predictionsof a model of peak-ring basin formation that explains their mor-phological characteristics as resulting from the nonlinear scalingof 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 withring-like central peaks and the ringed peak-cluster basin, Hum-boldt. Several trends are observed. First, peak-ring basins form astraight-line in log–log space at large rim-crest diameters inFig. 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 rim-crest diameter, and p is the slope of the best-fitting line on a log–logplot. Power-law fits were calculated in KaleidaGraph (Synergy Soft-ware, www.synergy.com), which uses the Levenberg–Marquardtnon-linear curve-fitting algorithm (Press et al., 1992) to iterativelyminimize the sum of the squared errors in the ordinate. The useof this criterion for minimization implies that fractional errors inthe estimates of interior ring diameters are regarded as larger thanthose for estimates of the rim-crest diameter.

We calculate a power law fit of Dring = 0.14 ± 0.10(Dr)1.21±0.13

(R2 = 0.96, where R is the correlation coefficient for the given data-set on a log–log plot) for lunar peak-ring basins (Table 2). This fit isvery similar to a power law fit to peak-ring basins on Mercury

http://www.synergy.com

Table 2Comparison of the values for the coefficients (A and p) of power-law fits to peak-ringbasins on the Moon (this study) and Mercury (Baker et al., 2011). Power laws are ofthe form given in Eq. (1) in the text. Coefficients of power-law fits to protobasins andringed-peak cluster basins on Mercury from Baker et al. (2011) are also given, butnone are given for the Moon due to the statistically small populations. Coefficientsfrom the power law model of an expanding melt cavity (Eq. (2), Section 7) on theMoon (this study) and Mercury (Baker et al., 2011) are given for calculations using theCroft (1985) and Holsapple (1993) scaling relationships.

Power-law coefficientsa

A p R2

Peak-ring basinsMoonb 0.14 ± 0.10 1.21 ± 0.13 0.96Mercuryc 0.25 ± 0.14 1.13 ± 0.10 0.87

Protobasins (P90 km)Moon – – –Mercury 0.26 ± 0.36 1.09 ± 0.29 0.69

Ringed peak-cluster basinsMoon – – –Mercury 0.18 ± 0.34 1.02 ± 0.41 0.78

Model (Croft, 1985)Moon 0.14 + 0.03/�0.02 1.09 ± 0.05 –Mercury 0.14 + 0.03/�0.02 1.09 + 0.05/�0.06 –

Model (Holsapple, 1993)Moon 0.11 1.18 –Mercury 0.11 � 0.12 1.18 –

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 peak-ring 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 weremade to the protobasin and ringed peak-cluster data for the Moon because of thestatistically small populations.

c Coefficients to fits and models for Mercury are from Baker et al. (2011).


(Dring = 0.25 ± 0.14(Dr)1.13±0.10, Fig. 4B and Table 2), and both fits areconsistent with analyses of previous peak-ring basin catalogs (Pike,1988). Since the population of protobasins on the Moon is statisti-cally small (N = 3), fits to the protobasin data were not conducted.However, protobasins occur at smaller diameters than all peak-ring basins but overlap in rim-crest diameter with the largest com-plex craters on the Moon (Fig. 4A). The trend in ring diameter andrim-crest diameter for protobasins is aligned with the tail-end ofthe peak-ring basin trend (Fig. 4A). This supports the view thatpeak-ring basins and protobasins are parts of a continuum of basinmorphologies. A similar observation is identified between protoba-sins and peak-ring basins on Mercury (Fig. 4B), where the powerlaw fits to protobasins and peak-ring basins are found to be statis-tically indistinguishable (Table 2) (Baker et al., 2011). However,protobasins on Mercury are more numerous, and protoba-sins <90 km have anomalously smaller ring diameters than whatis predicted by extrapolation of a power law fit to protobasinsP90 km.

The one lunar ringed peak-cluster basin, Humboldt, occurs atsmaller rim-crest and ring diameters than peak-ring basins but islarger in rim-crest diameter than all three protobasins (Fig. 4A).Humboldt has an atypically small interior ring diameter relativeto its rim-crest diameter and thus plots on a trend that is morealigned with the trend for central peak diameters in complex cra-ters than the interior rings of peak-ring basins (Fig. 4A). Other cra-ters with ring-like central peaks also plot near the trend for centralpeak diameters in lunar complex craters. Fig. 4A shows two trendsfor central peak diameters in lunar complex craters. The first is theleast squares, linear regression of Hale and Head (1979a)(Dcp = 0.259Dr � 2.57, where Dcp is the diameter of the central peakand Dr is the diameter of the crater’s rim crest), which was basedon measurements of circular fits to the maximum diameter of cen-tral peaks in fresh complex craters on the Moon. Because the mea-

surements were of the maximum diameter of central peaks, thetrend of Hale and Head (1979a) is taken to represent an upper limitto central peak diameters on the Moon. The second trend is apower law [Dcp = 0.107(Dr)1.095] determined using the planformareas enclosed by the irregular perimeters of central peaks calcu-lated by Hale and Grieve (1982). We then assume a circular geom-etry for this area, from which a central peak diameter is derived.These central peak diameters are taken to represent an average va-lue, and should produce results that are comparable to our methodfor measuring the average diameters of basin features on theMoon. Craters with ring-like central peaks appear to fall on a scat-tered trend that is intermediate between the Hale and Head(1979a) linear regression and the Hale and Grieve (1982) powerlaw (Fig. 4A), indicating that these ring-like central peaks do notdepart substantially from the trend in central-peak diameter ob-served from complex craters. Humboldt falls near the Hale andGrieve (1982) trend, suggesting a similarity with complex craterswith central peaks. However, the clear ring-like arrangement ofits interior peaks, its large rim-crest diameter compared to othercraters with ring-like central peaks, and its overlap with the rim-crest diameters of protobasins, suggest that Humboldt representsa unique transitional type in the size-morphology progressionfrom complex craters to peak-ring basins. The fact that there isonly one ringed peak-cluster basin on the Moon (5% of the total ba-sin population cataloged in this study) is expected as it is likely tobe related to the overall smaller numbers of protobasins and peak-ring basins on the Moon. For comparison, ringed peak-cluster ba-sins account for only 8% of the total cataloged basin populationon Mercury (Baker et al., 2011), and also fall along the trend forcomplex craters on Mercury (Fig. 4B).

6.2. Ring/rim-crest ratios

Rim-crest/ring ratio (or the inverse, ring/rim-crest ratio) plots(Fig. 5) have been used to suggest that protobasins and peak-ringbasins represent a continuum of morphologies (Alexopoulos andMcKinnon, 1994), in contrast to the view of Pike (1988), who fa-vored a statistical distinction between peak-ring basins and proto-basins. Alexopoulos and McKinnon (1994) identified a generaltrend of continuous, non-linearly decreasing rim-crest/ring ratioswith increasing rim-crest diameter for protobasins and peak-ringbasins on Venus. The basin catalogs of Wood and Head (1976), Haleand Head (1979b), Wood (1980), Hale and Grieve (1982), and Pike(1988) were also used to suggest similar trends for basins on Mer-cury, the Moon, and Mars, although the Moon and Mars data ap-peared with greater scatter (Alexopoulos and McKinnon, 1994). Arecent comprehensive survey of 74 peak-ring basins and 32 proto-basins on Mercury (Baker et al., 2011) further emphasized theseobservations by examining the inverse, ring/rim-crest ratios, andnoted that peak-ring basins flatten to an equilibrium ring/rim-crestratio value of around 0.5–0.6. As in Baker et al. (2011), we also cal-culate ring/rim-crest ratios (in contrast to the convention of usingrim-crest/ring ratios from Alexopoulos and McKinnon (1994)), forconsistency with earlier studies (Wood and Head, 1976; Pike,1988) and to avoid magnifying the effects of errors in smalldenominators. Ring/rim-crest ratios from our refined lunar basincatalog (Fig. 5A) have less scatter than the catalogs used in Alexo-poulos and McKinnon (1994), and reveal a trend that is very simi-lar to that observed for Mercury (Fig. 5B) (Baker et al., 2011) andVenus (Fig. 5C) (Alexopoulos and McKinnon, 1994), although at lar-ger rim-crest diameters. The ring/rim-crest ratios for peak-ring ba-sins on the Moon range from 0.35 to 0.56 (arithmetic mean = 0.48),with smaller rim-crest diameters generally having smaller ratiosthan larger rim-crest diameters (Fig. 5A). The ring/rim-crest ratioson the Moon also flatten to a value of around 0.5 for the largestpeak-ring basins. Protobasins have smaller ratios, ranging from

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 scaleof the x-axis between the Moon (A) and Mercury (B) plots. Nonlinear, curved trendsare observed for protobasins and peak-ring basins for each of the planets. The trendis steeper at smaller rim-crest diameters and then flattens to values of 0.5–0.6 forthe Moon and Mercury (A and B) and to �0.7 for Venus (C). The continuity betweenthe ring/rim-crest ratios of protobasins and peak-ring basins suggest that they forma continuum of basin morphologies that is a direct result of the process of peak-ringbasin formation. Ringed peak-cluster basins appear to diverge from the continuoustrend shared by protobasins and peak-ring basins. (For interpretation of thereferences to color in this figure legend, the reader is referred to the web version ofthis article.)


0.33 to 0.44, with an arithmetic mean of 0.39. Since there are veryfew protobasins on the Moon, the lower rim-crest diameter end ofthe 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 peak-cluster basin, Humboldt, is much smaller than protobasins andpeak-ring basins of similar rim-crest diameter (Fig. 5A). This is con-sistent with similarly small (arithmetic mean = 0.20) ring/rim-crest ratios for ringed peak-cluster basins on Mercury (Baker

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

6.3. Onset diameter of peak-ring basins

Comparisons of the onset diameter for peak-ring basins on theterrestrial planets have been complicated due to the lack of a stan-dard method for calculating this metric. Some authors have com-pared only transitional diameter ranges, noting that thetransitional diameters decrease from the Moon to Mercury andMars (Wood and Head, 1976; Pike, 1988). Others have used theminimum diameter of the peak-ring basin populations on the ter-restrial planets to define onset diameter, yielding a similardecreasing onset diameter ordering from the Moon (140 km) toMercury (75 km), Mars (45 km), and Venus (40 km) (Pike, 1983;Alexopoulos and McKinnon, 1994). Our calculations for the onsetdiameter of peak-ring basins (Table 1) do not change this generalordering, but provide new values that are based on the most recentand complete basin catalogs of the terrestrial planets and that arestatistical more robust compared with previous values. While theonset diameters for the Moon and Mercury are the most reliabledue to relatively complete preservation of their crater populations,the onset diameters for Mars and Venus are more speculative dueto the prevalence of erosional and resurfacing processes and effectsof differing target properties (e.g., volatiles and temperature) onthese planets. Mars’ smaller onset diameter for peak-ring basinscompared with Mercury, which has a similar gravitational acceler-ation, has traditionally been attributed to the effect of different tar-get materials, including volatiles (e.g., Pike, 1988; Melosh, 1989;Alexopoulos and McKinnon, 1992). Mars is also anomalous in itslarge range of peak-ring basin diameters (52–442 km), suggestingthat additional parameters other than gravity and impact velocityalone are influencing Mars’ population of peak-ring basins. Thesurface of Venus has also been globally resurfaced either in a cat-astrophic manner or at a rate equal to the crater production rate,and thus preserves only a �0.5 Ga crater retention age (Schaberet al., 1992). For these reasons, we exercise caution when inter-preting the peak-ring basin and protobasin populations of Marsand Venus in context of the basin populations on the other planets.We also do not calculate an onset diameter for the Earth due to theobvious incompleteness of its impact basin record and the largeuncertainties associated with interpreting highly eroded basinstructures.

It has long been recognized that there is an inverse relationshipbetween the onset diameter of peak-ring basins and the surfacegravitational acceleration (g) of the planetary body (Pike, 1983,1988; Melosh, 1989; Alexopoulos and McKinnon, 1992). This rela-tionship has been used to suggest that the formation of peak ringsis largely the result of a gravity-driven process. Gravity-inducedcollapse of the transient cavity has thus served as the foundationfor many current models of peak-ring basin formation, includinghydrodynamic collapse of an over-heightened central peak (Me-losh, 1982, 1989; Collins et al., 2002). The dependence of peak-ringbasin onset diameter on planetary impactor velocity has beenmore uncertain. Pike (1988) demonstrated that the geometricmean diameters of peak-ring basins do not correlate with the ap-proach velocity of asteroids and short period comets (V1) on theterrestrial planets. An improved correlation was found when ap-proach velocity was combined with g (i.e., g/V1), although g alonestill provided the best correlation with the geometric mean diam-eter of peak-ring basins.

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 surfacegravitational acceleration (g) (A), mean impact velocity (Vmean) (B), the ratio of g/Vmean (C), and the ratio of g/

pVmean (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 rigorousrepresentations. 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 littlecorrelation 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 morecomparable 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 peak-ring basins as a function of the planet’s surface gravitational accel-eration (g) and the planet’s mean impact velocity (Vmean) in log–logspace (Fig. 6). The mean impact velocities are taken from recentmodeling of the distribution of planetary impactors (Le Feuvreand Wieczorek, 2008). We also include power-law fits to the databy minimizing the sum of the squared errors in the ordinate. Giventhe uncertainties in the plotted data (especially for Mars and Ve-nus) these fits are not meant to be statistically rigorous represen-tations and should only be viewed as illustrating the generaltrends in the plotted data, As in previous studies, the strongest cor-relation with peak-ring basin onset diameter is the planet’s gravi-tational acceleration (Fig. 6A). No correlation is observed betweenonset diameter and velocity alone (Fig. 6B), although a strongercorrelation is observed when the mean impact velocity is com-bined with gravity (i.e., g/Vmean) (Fig. 6C). Although it may haveno physical significance, there is a very strong correlation (inlog–log space) between onset diameter and gravitational accelera-tion over the square root of the velocity (g

pVmean) (Fig. 6D). To

first-order, these comparisons suggest that gravity is likely to beimportant in the process of forming peak rings. While there is nocorrelation between peak-ring basin onset diameter and impactvelocity alone, a fairly strong correlation is found when impactvelocity is combined with gravity. Like gravity, this correlation isnot perfect, and the details of its physical meaning are not certainwithout a more detailed examination of the parameter space of im-pact events. Based on these observations, we suggest that both

gravity and velocity are likely to be important in the formationof peak rings.

6.4. Surface density of peak-ring basins

The Moon has about a factor of two fewer peak-ring basins perunit area (4.5 � 10�7 per km2) than Mercury (9.9 � 10�7 per km2,Baker et al., 2011) and a factor of two to five greater number ofpeak-ring basins per unit area than Mars or Venus (Table 1). Whilethe crater size distributions for impact craters between 100 kmand 500 km in diameter are nearly the same on the Moon and Mer-cury (e.g., Strom et al., 2005) the mean and onset diameters forpeak-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 ba-sins per area on Mercury than on the Moon. The large number ofpeak-ring basins on Mercury has also been attributed to the highmean impact velocities of its impactors and increased impact meltproduction (Head, 2010; Baker et al., 2011). This could facilitate theonset of peak-ring basins at smaller impactor sizes, which are morenumerous than larger-sized impactors. The surface density of cra-ters between 100 km and 500 km in diameter is much lower onMars than on Mercury and the Moon due to extensive erosionand resurfacing (Strom et al., 2005), which could partially explainthe relatively small number of peak-ring basins on Mars. Venushas also undergone much resurfacing, which certainly has affectedthe number of peak-ring basins preserved on its surface.

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 impactvelocity (Vmean) (B) and the ratio of g/Vmean (C). As in Fig. 6, solid lines are power lawfits formed by minimizing the sum of the squared errors in the ordinate. The fits aredisplayed to emphasize general trends in the data and are not meant to bestatistically rigorous representations. We did not include a fit for gravity due to lackof a clear trend. No correlation with gravity is observed (A), while there is a slightcorrelation with velocity (B). A stronger correlation is found when gravity andvelocity are combined (C). The basin records on Venus and Mars are likelyincomplete (see discussion in Section 6.3), which complicates full understanding ofthese first-order correlations.


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

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

7. Peak-ring basin formation models

While there have been numerous models attempting to explainthe transition from complex craters to multi-ring basins, a consen-sus on the process of ring formation in peak-ring basins and multi-ring basins has not been reached. Two major models for the forma-tion of peak-ring basins have been proposed: (1) hydrodynamiccollapse of an over-heightened central peak (Melosh, 1982, 1989;Collins et al., 2002) and (2) modification and collapse of a nestedmelt cavity (Grieve and Cintala, 1992; Cintala and Grieve, 1998;Head, 2010). As discussed by Baker et al. (2011), while much pro-gress has been made in advancing hydrocode models simulatingthe hydrodynamic collapse process (Melosh, 1989; Collins et al.,2002, 2008; Ivanov, 2005), the model currently makes no explicitpredictions on the ring and rim-crest diameter systematics ofpeak-ring basins on the terrestrial planets. This is largely due topoor constraints on the parameters governing the timescales of flu-idization of the target material and subsequent freezing of thismaterial to produce peak-ring structures (e.g., Wünnemann et al.,2005). While it is possible that future models will offer more expli-cit predictions of ring and rim-crest spacing, the current uncer-tainty in the models make it difficult to test against themorphologic trends observed from our basin catalogs.

Given these uncertainties with the hydrodynamic collapsemodel, we now use our observations of the new lunar catalog totest another model of peak-ring basin formation, the ‘‘nestedmelt-cavity’’ model, which explains ring formation as the resultof nonlinear scaling between impact melt and crater dimensions.The nested melt-cavity model is based on a suite of papers by Cint-ala and Grieve (Grieve and Cintala, 1992, 1997; Cintala and Grieve,1994, 1998) who invoked a combination of terrestrial field studiesand impact and thermodynamic theory to show that for givenimpactor and target materials, impact-melt volume will increaseat a rate that is greater than growth of the crater volume withincreasing energy of the impact event (Grieve and Cintala, 1992).The maximum depth of melting was also shown to increase rela-tive to the depth of the transient cavity with increasing transientcavity diameter (Cintala and Grieve, 1998), approaching depthsof around 15–20 km for impact events near the onset diameters(100–200 km) of peak-ring basins (Cintala and Grieve, 1998; Bakeret al., 2011). For further descriptions of the quantitative aspects ofthis 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 beimportant during the modification process in the formation ofpeak-ring basins on the terrestrial planets, including Earth, theMoon, and Venus (Grieve and Cintala, 1992, 1997; Cintala andGrieve, 1994, 1998). Further development of this model and itsextension to multi-ring basins by Head (2010) has suggested thata melt cavity nested within the displaced zone of the growing tran-sient crater (the ‘‘nested melt cavity’’) exerts a major influence onthe formation of peak rings and development of exterior rings dur-ing crater modification. The volume and depth of impact melting incomplex craters is generally not sufficient to modify the upliftedmorphology of the crater interior. However, with increasing sizeof the impact event and thus increasing volume of melt and depthof melting, a melt cavity is fully formed within the displaced zoneand is sufficiently deep to retard the development of an ordinary-sized central peak (Cintala and Grieve, 1998). During rebound andcollapse of the transient crater, the entire impact melt cavity istranslated upward and inward. Unlike rebound in complex craters,


however, the uplifted periphery of the melt cavity remains as theonly topographically prominent feature, resulting in the formationof a peak ring (Head, 2010). At smaller crater sizes, and hence shal-lower depths of melting, it is still possible for a small central peakto rise through the melt cavity, accounting for the central-peak andpeak-ring combinations that are observed in protobasins (Cintalaand Grieve, 1998; Baker et al., 2011).

One of the benefits of the nested melt-cavity model is that itmakes specific predictions that may be compared with the ringand rim-crest diameter systematics of basin catalogs. Analysis ofa recently updated basin catalog for Mercury (Baker et al., 2011)showed many first-order consistencies with the predictions ofthe nested melt-cavity model, particularly in the observations of(1) the surface density of peak-ring basins on the terrestrial plan-ets, (2) the continuum of basin morphologies between protobasinsand peak-ring basins, and (3) the power-law trend of peak-ring ba-sins. Our analysis of the new lunar catalog confirms many of theseconsistencies with the nested melt-cavity model, providing addi-tional support to the importance of impact melting in forming peakrings.

It is important to note that the geometries of impact meltingand the transient cavity derived from theoretical calculations areonly static representations of a very dynamic process. In reality,at no time during the impact event are these geometries fullyachieved, and the dynamics of crater formation certainly affectshow the melted portions of the displaced zone evolve and are dis-tributed within the target material with time. However, these de-tails of the cratering process are still poorly understood andmodeled. More certain has been various analytical and numericalestimates of the volume and depths of melting (Grieve and Cintala,1992; Pierazzo et al., 1997; Barr and Citron, 2011), which appeargenerally consistent with each other and with estimates of meltvolumes obtained from field observations of terrestrial impactstructures. Considering the geometrical assumptions and uncer-tainties involved with a static model for the generation of impactmelt, our presentation of the nested melt-cavity model should beviewed as a first-order attempt in understanding the effects of im-pact melting on the morphology and development of peak-ring ba-sins. While we find many consistencies between the model and ouranalysis of the basin catalogs for the Moon and Mercury, morecomplex and dynamic melt-zone geometries are probably morerealistic, and future refinements to this model will be necessary,especially in improving dynamical simulations of impact meltingduring large impact events.

As stated above, Mercury has the largest number of peak-ringbasins per unit area of the terrestrial planets, with the Moon hav-ing a factor a two fewer peak-ring basins based on our new lunarbasin catalog (Table 1). Under the nested melt-cavity model, thedifference in the surface density of peak-ring basins between Mer-cury and the Moon may be explained by differences in meanimpactor velocities on the two bodies. Because of the higher meanimpact velocities on Mercury (�40 km/s compared with �20 km/son the Moon), impactors of a given size will produce approxi-mately twice as much melt on Mercury as on the Moon (Grieveand Cintala, 1992). As a result, peak-ring basin formation will bemore effective on Mercury for smaller impactors, which are morenumerous than larger impactors (Head, 2010). If similar impactorsize-frequency fluxes for the inner planets are assumed (Stromet al., 2005), the number of protobasins and peak-ring basins perarea should increase with the mean impact velocity at the planet.From the new basin catalogs (Table 1), there appears to be a slightcorrelation between the number of peak-ring basins per unit areaand the planet’s mean impact velocity (Fig. 7B) and an even stron-ger correlation with gravitational acceleration and mean impactvelocity combined (Fig. 7C). These correlations are consistent withthe predictions of the nested melt-cavity model and the correla-

tions in onset diameter (Fig. 6), which suggest that both gravityand velocity are likely important in determining the onset diame-ter and also surface density of peak-rings on the terrestrial planets(see discussion on onset diameter, below). The low density valuesfor Mars and Venus are likely to be due to planetary resurfacingevents; if the complete basin records for Mars and Venus wereavailable, the correlation between the number of peak-ring basinsand mean impact velocity might further be strengthened.

The nested melt-cavity model also predicts that there will be acontinuous progression of impact basin morphologies in the tran-sition from complex craters to peak-ring basins. Under that model,the influence of increasing melt volume and depth of impact melt-ing becomes more important with increasing basin size. In thetransition from protobasins to peak-ring basins, uplifted centralpeak material is suppressed by increasing depth of impact melting,and the uplifted periphery of the melt cavity emerges as the dom-inant interior morphology (Cintala and Grieve, 1998). This resultsin a continuum of basin morphologies between protobasins andpeak-ring basins, which is very apparent from our new measure-ments of ring and rim-crest diameters on the Moon (Figs. 4 and5). The continuous, non-linear trends observed from plots ofring/rim-crest ratios are very consistent between the Moon, Mer-cury, and Venus (Fig. 5). Ring/rim-crest ratios flatten to a near equi-librium 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 differencesin shapes of the ring/rim-crest ratios may be controlled by the dif-ferences in the physical characteristics of the planet. Under thenested melt-cavity model, these characteristics would includethose controlling the production of impact melt, such as impactvelocity and target properties such as composition, temperature,and volatiles (Grieve and Cintala, 1997). Ringed peak-cluster basinsdiverge 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 interiorring in ringed peak-cluster basins may be the result of direct mod-ification of the central portions of the uplift structure. At the rela-tively small rim-crest diameters of ringed peak-cluster basins, thedepth of melting has only begun to penetrate the uplift structureand a melt cavity has not been developed. Rebound of the transientcavity floor therefore results in a disaggregated ring-like array ofcentral peak elements instead of a single central uplift structureor a large peak ring. In this fashion, ringed peak-cluster basins rep-resent unique transitional forms in the process of forming peakrings.

The predictions of a growing melt cavity with increasing basinsize may also be compared to the power law trends between ringand rim-crest diameter for peak-ring basins (Fig. 4). Since the sol-ids making up the periphery of the melt cavity eventually translateinward and upward to form the peak ring, relationships betweenthe expected melt volume at a given basin diameter and an esti-mate of the melt cavity geometry can give a first-order model ofhow peak-ring diameters should expand with increasing rim-crestdiameter. Assuming a hemispherical melt cavity and using thepower law relationship between melt volume and diameter ofthe transient cavity from Grieve and Cintala (1992) in combinationwith crater modification scaling relationships (Croft, 1985; Holsap-ple, 1993), Baker et al. (2011) derived a power law expressionrelating the diameter of the peak ring (Dring) to the diameter ofthe final crater rim-crest diameter (Dr):

Dring ¼ ADpr ð2Þ

where A ¼ 12p c� �1=3ðadÞ1=3 and p ¼ bd

3 .The constants c and d are from the melt volume relation given

by Grieve and Cintala (1992), where c depends on target and


impactor properties and impact velocity and d is a power law con-stant equal to 3.85. For the Moon, we take c = 1.42 � 10�4 andd = 3.85, which are appropriate to an anorthositic target composi-tion, a chondritic impactor, and an impact velocity of 20 km/s(Cintala and Grieve, 1998). These values, however, do not accountfor the vaporized portion of the melt cavity, which, when factoredinto the calculations, can increase the total volume of the melt cav-ity by 20–30% from a melt only calculation (M.J. Cintala, personalcommunication, 2010). However, this should only produce abouta 5–10% difference in modeled peak ring diameters, which is onthe order of the uncertainty in our peak-ring diameter measure-ments and should not significantly affect our results. The valuesfor the constants a and b are dependent on the crater modificationscaling relationships used to convert transient cavity diameters tofinal 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 fromlunar and terrestrial data. Both of the scaling relationships for tran-sient crater modification include a transition diameter from simpleto complex craters (Dsc) appropriate to the Moon (19 km, Pike,1988), which tailors the relationship to planetary-specific variablessuch as gravity and target strength. Holsapple (1993) also includestwo relationships that account for the transient rim-crest diameterand the transient excavation diameter. We use the transient rim-crest diameter relationship for consistency with the melt volumepower 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 Aand p determined from this fit may be directly compared with thepredicted values from the melt-cavity model (Table 2) (Baker et al.,2011). The power law fit to lunar peak-ring basins is very consis-tent with the model predictions. The modeled value for the con-stant A in Eq. (4) ranges from 0.12 to 0.17 (mean = 0.14) usingthe Croft (1985) scaling and is 0.11 using the Holsapple (1993)scaling. These values fall within the uncertainty in A values deter-mined 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 powerlaw trend, p, range from 1.04 to 1.14 using the Croft (1985) scalingand 1.18 using the Holsapple (1993) scaling, which nearly com-pletely fall within the uncertainty of the p values determined from

Table A1Catalog of peak-ring basins on the Moon. Peak-ring basins are characterized by a single in

Number Namea Longitudeb Latitude Rim crest(km)

Ring(km)

1 Schwarzschild 120.09 70.36 207 712 d’Alembert 164.84 51.05 232 1063 Milne 112.77 �31.25 264 1144 Bailly 291.20 �67.18 299 1305 Poincaré 163.15 �57.32 312 1756 Coulomb–Sarton� 237.47 51.35 316 1597 Planck 135.09 �57.39 321 1608 Schrödinger 133.53 �74.90 326 1509 Mendeleev 141.14 5.44 331 144

10 Birkhoff 213.42 58.88 334 16311 Lorentz 263.00 34.30 351 17312 Schiller–Zucchius� 314.82 �55.72 361 17913 Korolev 202.53 �4.44 417 20614 Moscoviense 147.36 26.34 421 19215 Grimaldi 291.31 �5.01 460 23416 Apollo 208.28 �36.07 492 24717 Freundlich–

Sharonov�175.00 18.35 582 318

a Names shown for basins are those approved by the IAU as of this writing (http://plSpudis (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).

lunar peak-ring basins (1.08–1.34) (Table 2). The consistency be-tween the model predictions of a growing melt cavity and thepower law fits to peak-ring basins on the Moon and also compar-isons on Mercury (Fig. 4A) (Baker et al., 2011) (Table 2) supportthe first-order predictions of the nested melt-cavity model andsuggest that impact melting and melt cavity formation exhibitimportant controls on the formation of impact basin rings.

Finally, while the apparent gravity dependence of the onsetdiameter for peak-ring basins (Fig. 6A) has generally favored agravity-driven phenomenon for basin formation (e.g., Melosh,1989), the nested melt-cavity model predicts that impact velocityshould also be important in determining the onset of peak-ring ba-sin morphologies. The onset diameters of peak-ring basins on theterrestrial planets do not appear to depend on mean impact veloc-ity by itself (Fig. 6B), although a combination of gravitational accel-eration and mean impact velocity provides an improvedcorrelation with peak-ring basin onset diameter on the terrestrialplanets (Fig. 6C and D). Thus, onset diameter is likely to be depen-dent on both gravitational acceleration and impact velocity. Underthe nested melt-cavity model, gravity primarily determines thedimensions of the transient cavity and the final crater diameter,while kinetic energy and thus impact velocity largely determinesthe volume of melt that is produced during the impact event. Cint-ala and Grieve (Grieve and Cintala, 1992, 1997; Cintala and Grieve,1994, 1998) have examined a variety of trends between craterdimensions and impact melting, suggesting that the ratio of themaximum depth of melting (dm) to the depth of the transient cav-ity (dtc) may be important in determining the onset of peak rings inbasins. Cintala and Grieve (1998, their Fig. 7) observed that thedepth of melting approaches the depth of the transient cavity withdm/dtc ratios of 0.8–0.9 at the onset diameters for peak-ring basinson the Earth, Moon, and Venus. While the predicted depths ofmelting at these onset diameters do not meet or exceed the depthsof the transient cavity (dm/dtc P 1.0), as emphasized in the generaldiscussion of the onset of peak-ring basins in Grieve and Cintala(1997) and Cintala and Grieve (1998), sufficient depths of meltingappear necessary for peak-ring basin formation. We used our cal-culated onset diameters (Table 1) and the plot of dm/dtc ratio versustransient cavity diameter (Cintala and Grieve, 1998, their Fig. 10)to determine the dm/dtc ratio predicted for the onset diameter of

terior topographic ring or a discontinuous ring of peaks with no central peak.

Ring/rim-crestratio

Peak-ring arc(deg)

Confidencec Pike and Spudis(1987)d

0.35 <180 1 Protobasin0.46 <180 1 Protobasin0.43 >180 3 Protobasin0.43 <180 3 Protobasin0.56 >180 3 Peak-ring basin0.50 >180 2 Multi-ring basin0.50 <180 1 Peak-ring basin0.46 >180 3 Peak-ring basin0.44 <180 2 Protobasin0.49 <180 2 Peak-ring basin0.49 <180 2 Peak-ring basin0.50 >180 3 Peak-ring basin0.49 <180 3 Multi-ring basin0.46 >180 3 Multi-ring basin0.51 >180 3 Multi-ring basin0.50 >180 3 Multi-ring basin0.55 >180 2 Not classified

anetarynames.wr.usgs.gov). Names not approved by the IAU, but used by Pike and

http://www.planetarynames.wr.usgs.gov

Table A2Catalog of protobasins on the Moon. Protobasins are characterized by the presence of both a central peak and an interior ring of peaks.

Number Namea Longitudeb Latitude Rim-crest(km)

Ring(km)

Ring/rim-crestratio

Central peak(km)

Peak-ring arc(deg)

Confidencec Pike and Spudis(1987)d

1 Antoniadi 187.04 �69.35 137 56 0.41 6 >180 3 Protobasin2 Compton 103.96 55.92 166 73 0.44 15 >180 3 Protobasin3 Hausen 271.24 �65.34 170 55 0.33 31 <180 2 Not classified

a Names shown for basins are those approved by the IAU as of this writing (http://planetarynames.wr.usgs.gov).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).

Table A3Catalog 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 ofcentral 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 Longitudeb Latitude Rim-crest (km) Ring (km) Ring/rim-crest ratio Ring arc (deg) Confidencec

Ringed peak-cluster basins1 Humboldt 81.06 �27.12 205 32 0.16 >180 3

Craters with ring-like central peaks1 Lindenau 24.85 �32.33 50 9 0.18 >180 12 Eistein 271.80 16.70 51 8 0.16 >180 13 Eijkman 217.42 �63.23 57 8 0.15 >180 24 Carpenter 308.78 69.52 61 12 0.19 >180 15 Zucchius 309.48 �61.38 64 11 0.17 >180 36 Eudoxus 16.33 44.25 66 10 0.16 >180 27 Philolaus 327.29 72.24 70 15 0.22 >180 18 Fabricius 41.79 �42.80 76 18 0.24 <180 39 Cantor 118.65 38.02 76 13 0.17 <180 1

10 King 120.48 4.92 77 15 0.19 >180 311 Olcott 117.84 20.61 80 15 0.19 >180 212 Hayn 84.07 64.47 82 14 0.17 >180 213 Unnamed 170.29 57.24 83 13 0.16 >180 214 Colombo 46.10 �15.17 83 16 0.19 <180 115 Metius 43.37 �40.42 84 15 0.18 <180 216 Berkner 254.72 25.14 86 15 0.17 >180 217 Atlas 44.33 46.71 87 15 0.17 <180 218 Lobachevskiy 113.07 9.76 87 15 0.17 <180 119 Posidonius 30.00 31.86 99 15 0.15 <180 120 Vestine 93.71 33.86 99 13 0.13 <180 221 Gassendi 320.00 �17.49 112 17 0.15 <180 222 Wiener 146.63 41.02 114 14 0.12 >180 1

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


peak-ring basins on the Moon. For comparison, we also determinedthe dm/dtc ratio at the onset diameter of peak-ring basins on Mer-cury by using the maximum depth of melting calculations for Mer-cury derived from impedance matching of the Grieve and Cintala(1992) model (Ernst et al., 2010, their Fig. 5). In calculating thedm/dtc ratio for Mercury, we assumed that the depth of the tran-sient cavity is approximately one-third of its rim-crest diameter(Cintala and Grieve, 1998). The crater modification scaling rela-tionship of Croft (1985) was also used to convert the measuredrim-crest diameters on the Moon and Mercury to transient cavitydiameters. We find a dm/dtc ratio of about 0.7 (dm � 35 km) forthe 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 diameterof peak-ring basins on Mercury (116 km). The similar ratios forboth Mercury and the Moon suggest that sufficient depth of melt-ing relative to the depth of the transient cavity must be achievedbefore peak rings are fully developed. This is consistent with agrowing melt cavity within the displaced zone that suppressesthe formation of central peak elements to form a peak ring throughweakening of the central uplifted portions of the crater interior(Cintala and Grieve, 1998; Head, 2010). Once the depth of meltingreaches a value close to roughly three-fourths the depth of the

transient cavity depth, complete suppression of the central peakis achieved, and the peak ring is the only topographic feature thatremains.

For multi-ring basins on the Moon, the depth of melting gener-ally meets or exceeds the depth of the transient cavity diameter.For example, if we take the Outer Rook ring of Orientale basin tobe the diameter of the transient cavity (620 km) (Head et al.,2011), the dm/dtc ratio is slightly greater than 1.0 (Cintala andGrieve, 1998). This is consistent with a hybrid mega-terrace andnested melt-cavity model for the onset of multi-ring basins (Head,2010), in which deep penetration of the melt cavity past the dis-placed zone creates a strength discontinuity that allows mega-ter-races to form through translation of crustal blocks laterally intoward the melt cavity. Based on the above observations, criticalthresholds in the ratio between depth of melting and the dimen-sions of the transient cavity appear to offer plausible explanationsfor the onset of basin morphologies on the terrestrial planets,including interior peak rings and the exterior rings of multi-ringbasins. The scaling of these two parameters depends on both grav-ity and velocity, and is therefore consistent with the first-ordercorrelations shown in Fig. 6. We suggest that while gravity isimportant in determining the dimensions of the transient cavity




and final crater diameter, it is not the dominant process in formingpeak rings. Instead, our observations from the catalogs of basins onthe terrestrial planets suggest that velocity, and therefore kineticenergy and subsequent melting of target material during impactis likely to exhibit the strongest control on peak-ring basinformation.

8. Conclusions

We have updated the current catalogs of protobasins and peak-ring basins on the Moon using new 128 pixel/degree (�235 m/pix-el) resolution gridded topography from the Lunar Orbiter LaserAltimeter (LOLA). Our refined catalog includes 17 peak-ring basins,3 protobasins, and 1 ringed peak-cluster basins. Several basins pre-viously 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 ofmore than two prominent topographic rings observed in the LOLAdata or overall consistency with a peak-ring basin origin. Interplan-etary comparisons of basin catalogs emphasize some previousobservations and provide new constraints on the dominant mech-anisms of peak-ring basin formation. Key observations include:

(1) Onset diameter calculations for peak-ring basins suggestcorrelations with a combination of both gravity and meanimpact velocity (Fig. 6). The Moon has the largest onsetdiameter of the terrestrial planets (227 km), followed byMercury (116 km), Mars (56 km), and Venus (33 km)(Table 1).

(2) The Moon has a surface density of peak-ring basins(4.5 � 10�7 per km2) that is intermediate between Mercury(9.9 � 10�7 per km2) and Mars (1.0 � 10�7 per km2) andVenus (1.4 � 10�7 per km2) (Table 1). The differences in thenumber of peak-ring basins between the Moon and Mercurymay be due to their different mean impact velocities andonset diameters of peak-ring basins.

(3) Ring/rim-crest ratios (Fig. 5) indicate continuous, nonlineartrends that are similar on the Moon, Mercury, and Venusand suggest that protobasins and peak-ring basins are partsof a continuum of basin morphologies. Ring/rim-crest ratiosflatten to values of around 0.5 for the Moon, slightly highervalues 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 ofpeak-ring basins on the Moon and Mercury are very similar(Fig. 4 and Table 2) and are both consistent with a power lawmodel of a growing melt cavity with increasing basin size(Eq. (2)).

Our analysis of the morphological characteristics of peak-ringbasins and protobasins on the Moon and the terrestrial planetsshows many consistencies with the predictions of the nestedmelt-cavity model for basin formation. Under this model, basinrings are formed from the nonlinear scaling of impact melt anddevelopment of an expanding melt cavity within the displacedzone, which acts to suppress central uplift structures with increas-ing depth of melting. At a depth of melting approximately three-fourths the depth of transient cavity, the depth of melting is suffi-cient to completely retard the formation of a central uplift struc-ture and a peak ring emerges as the dominant interiormorphology. Multi-ring basins are likely to form as the melt cavityexpands to depths equal to or greater than the depth of the tran-sient cavity, which acts to substantially weaken the basin interiorand initiates mega-terracing and formation of a topographic ringexterior to transient cavity rim. While the first-order consistencies

between our analyses of basin catalogs and the nested melt-cavitymodel are promising, much work is needed to corroborate theseobservations, including advanced impact simulations that are ableto model accurately impact melt production and its effects duringcrater modification.

Acknowledgments

We thank Ian Garrick-Bethell for use of the code to calculate theaveraged LOLA topography profiles and Sam Schon for productivediscussions on the populations of impact basins on Mercury. Wealso thank Mark Cintala for helpful discussions on the scaling ofimpact melting and the LOLA and LROC teams for their efforts inacquiring and processing the data. Reviews by Gordon Osinskiand an anonymous reviewer helped to improve the quality of themanuscript. Thanks are extended to the NASA Lunar Reconnais-sance Obiter Mission, Lunar Orbiter Laser Altimeter (LOLA) instru-ment for financial assistance (NNX09AM54G).

Appendix A

Catalogs of all peak-ring basins, protobasins, and ringed peak-cluster basins on the Moon as compiled in the present study arepresented in Tables A1–A3, respectively. LOLA gridded topographyimages of each basin are also found as online supplementarymaterial.

Appendix B. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.icarus.2011.05.030.

References

Alexopoulos, J.S., McKinnon, W.B., 1992. Multiringed impact craters on Venus – Anoverview 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 PlanetaryEvolution. Special Paper 293. Geological Society of America, Boulder, Colo, pp.29–50.

Araki, H. et al., 2009. Lunar global shape and polar topography derived fromKaguya-LALT Laser Altimetry. Science 323 (5916), 897–900.

Baker, D.M.H. et al., 2011. The transition from complex crater to peak-ring basin onMercury: New observations from MESSENGER flyby data and constraints onbasin-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. Multi-ring basins: Formation and evolution. In: Schultz, P.H., Merrill, R.B. (Eds.), Multi-ring 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 impactsfrom high-resolution numerical simulations. Icarus 211 (1), 913–916.

Cintala, M.J., Grieve, R.A.F., 1994. The effects of differential scaling of impact meltand 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 andPlanetary 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 simulationsof 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 asymmetryin 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 ofspectrally distinct material by impact craters on Mercury: Implications forglobal stratigraphy. Icarus 209, 210–233.


http://dx.doi.org/10.1016/j.pss.2011.05.010


http://dx.doi.org/10.1006/icar.2002.6822


Grieve, R.A.F., Cintala, M.J., 1992. An analysis of differential impact melt-craterscaling and implications for the terrestrial cratering record. Meteoritics 27,526–538.

Grieve, R.A.F., Cintala, M.J., 1997. Planetary differences in impact melting. Adv.Space Res. 20, 1551–1560. doi:10.1016/S0273-1177(97)00877-6.

Hale, W.S., Grieve, R.A.F., 1982. Volumetric analysis of complex lunar craters:Implications for basin ring formation. J. Geophys. Res. 87 (Suppl.), A65–A76.

Hale, W.S., Head, J.W., 1979a. Central peaks in lunar craters: Morphology andmorphometry. Proc. Lunar Planet Sci. Conf. 10, 2623–2633.

Hale, W.S., Head, J.W., 1979b. Lunar central peak basins: morphology andmorphometry in the crater to basin transition zone. In: Reports of PlanetaryGeology Program, 1978–1979. Technical Memorandum 80339. NASA,Washington, DC, pp. 160–162.

Head, J.W., 1974. Orientale multi-ringed basin interior and implications for thepetrogenesis of lunar highland samples. Moon 11, 327–356.

Head, J.W., 1977. Origin of outer rings in lunar multi-ringed basins – Evidence frommorphology and ring spacing. In: Roddy, D.J., Pepin, R.O., Merrill, R.B. (Eds.),Impact and Explosion Cratering. Pergamon Press, New York, pp. 563–573.

Head, J.W., 2010. Transition from complex craters to multi-ringed basins onterrestrial planetary bodies: Scale-dependent role of the expanding melt cavityand progressive interaction with the displaced zone. Geophys. Res. Lett. 37,L02203. doi:10.1029/2009GL041790.

Head, J.W., Fassett, C.I., Kadish, S.J., Smith, D.E., Zuber, M.T., Neumann, G.A.,Mazarico, E., 2010. Global distribution of large lunar craters: Implications forresurfacing and impactor populations. Science 329 (5998), 1504–1507.

Head, J.W., Zuber, M.T., Smith, D.E., Neumann, G.R., 2011. Orientale multi-ringbasin: New insights into ring origin and excavation cavity geometry from LunarReconnaissance Orbiter (LRO) Lunar Orbiter Laser Altimeter (LOLA) data. inpreparation.

Hodges, C.A., Wilhelms, D.E., 1978. Formation of lunar basin rings. Icarus 34 (2),294–323.

Holsapple, K.A., 1993. The scaling of impact processes in planetary sciences. Ann.Rev. Earth Planet. Sci. 21, 333–373.

Ishihara, Y., Morota, T., Nakamura, R., Goossens, S., Sasaki, S., 2011. AnomalousMoscoviense basin: Single oblique impact or double impact origin? Geophys.Res. Lett. 38, L03201. doi:10.1029/2010GL045887.

Ivanov, B.A., 2005. Numerical modeling of the largest terrestrial meteorite craters.Solar Syst. Res. 39, 381–409.

Kneissl, T., van Gasselt, S., Neukum, G., 2010. Map-projection-independent cratersize-frequency determination in GIS environments – New software tool forArcGIS. Planet. Space Sci., in press. doi:10.1016/j.pss.2010.03.015.

Le Feuvre, M.L., Wieczorek, M.A., 2008. Nonuniform cratering of the terrestrialplanets. Icarus 197, 291–306. doi:10.1016/j.icarus.2008.04.011.

McDonald, M.A., Melosh, H.J., Gulick, S.P.S., 2008. Oblique impacts and peak ringposition: Venus and Chicxulub. Geophys. Res. Lett. 35, L07203. doi:10.1029/2008GL033346.

Melosh, H.J., 1982. A schematic model of crater modification by gravity. J. Geophys.Res. 87 (B1), 371–380.

Melosh, H.J., 1989. Impact Cratering: A Geologic Process. Oxford University Press,London, 253 pp.

Melosh, H.J., McKinnon, W.B., 1978. The mechanics of ringed basin formation.Geophys. Res. Lett. 5 (11), 985–988.

Pierazzo, E., Melosh, H.J., 2000. Understanding oblique impacts from experiments,observations, and modeling. Ann. Rev. Earth Planet. Sci. 28, 141–167.

Pierazzo, E., Vickery, A.M., Melosh, H.J., 1997. A reevaluation of impact meltproduction. Icarus 127, 408–423.

Pike, R.J., 1983. Comment on ‘A schematic model of crater modification by gravity’by HJ Melosh. J. Geophys. Res. 88, 2500–2504.

Pike, R.J., 1988. Geomorphology of impact craters on Mercury. In: Vilas, F.,Chapman, C.R., Matthews, M.S. (Eds.), Mercury. Univ. Arizona Press, Tucson,Ariz, pp. 165–273.

Pike, R.J., Spudis, P.D., 1987. Basin-ring spacing on the Moon, Mercury, and Mars.Earth Moon Planets 39, 129–194.

Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipesin C. Cambridge Univ. Press, New York, pp. 683–688.

Robinson, M.S. et al., 2010. Lunar Reconnaissance Orbiter Camera (LROC)instrument overview. Space Sci. Rev. 150, 81–124.

Schaber, G.G., Strom, R.G., 1999. The USGS/U. Arizona database of Venus impactcraters: Update for 1999. Lunar Planet. Sci. 30 (abstract 1221).

Schaber, G.G., Strom, R.G., Moore, H.J., Soderblom, L.A., Kirk, R.L., Chadwick, D.J.,Dawson, D.D., Gaddis, L.R., Boyce, J.M., Russell, J., 1992. Geology and distributionof impact craters on Venus: What are they telling us? J. Geophys. Res. 97,13257–13301.

Schon, S.C., Head, J.W., Baker, D.M.H., Prockter, L.M., Ernst, C.M., Solomon, S.C., 2011.Eminescu impact structure: Insight into the transition from complex crater topeak-ring basin on Mercury. Planet. Space Sci., in press. doi:10.1016/j.pss.2011.02.003.

Schultz, P.H., 1976. Floor-fractured lunar craters. Moon 15, 241–273.Smith, D.E., Zuber, M.T., Neumann, G.A., Lemoine, F.G., 1997. Topography of

the Moon from the Clementine LIDAR. J. Geophys. Res. 102 (E1), 1591–1611.

Smith, D.E. et al., 2010. The Lunar Orbiter Laser Altimeter investigation on the LunarReconnaissance Orbiter mission. Space Sci. Rev. 150, 209–241.

Spudis, P.D., 1993. The Geology of Multi-Ring Impact Basins. Cambridge Univ. Press,Cambridge, 177 pp.

Strom, R.G., Malhotra, R., Ito, T., Yoshida, F., Kring, D.A., 2005. The origin of planetaryimpactors in the inner Solar System. Science 309 (5742), 1847–1850.

Thaisen, K.G., Head, J.W., Taylore, L.A., Kramer, G.Y., Isaacson, P., Nettles, J., Petro, N.,Pieters, C.M., 2011. Geology of Moscoviense basin. J. Geophys. Res. 116, E00G07.doi:10.1029/2010JE003732.

Wilhelms, D.E., McCauley, J.F., Trask, N.J., 1987. The Geologic History of the Moon.US Geol. Surv. Prof. Pap. 1348, Washington, DC, 302 pp.

Wood, C.A., 1980. Martian double ring basins: New observations. Proc. Lunar Planet.Sci. Conf. 11, 2221–2241.

Wood, C.A., Head, J.W., 1976. Comparisons of impact basins on Mercury, Mars andthe Moon. Proc. Lunar Sci. Conf. 7, 3629–3651.

Wünnemann, K., Morgan, J.V., Jödicke, H., 2005. Is Ries crater typical for its size? Ananalysis based upon old and new geophysical data and numerical modeling. In:Kenkmann, T., Hörz, F., Deutsch, A. (Eds.), Large Meteorite Impacts III. SpecialPaper 384. Geological Society of America, Boulder, Colo, pp. 67–83.

http://dx.doi.org/10.1016/S0273-1177(97)00877-6

http://dx.doi.org/10.1029/2009GL041790

http://dx.doi.org/10.1029/2010GL045887



http://dx.doi.org/10.1029/2008GL033346

http://dx.doi.org/10.1029/2008GL033346



http://dx.doi.org/10.1029/2010JE003732

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