Planetary and Space Science

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1 Planetary and Space Science 59 (2011) Contents lists available at ScienceDirect Planetary and Space Science journal homepage: The transition from complex crater to peak-ring basin on Mercury: New observations from MESSENGER flyby data and constraints on basin formation models David M. H. Baker a,n, James W. Head a, Samuel C. Schon a, Carolyn M. Ernst b, Louise M. Prockter b, Scott L. Murchie b, Brett W. Denevi b, Sean C. Solomon c, Robert G. Strom d a Department of Geological Sciences, Brown University, Box 1846, Providence, RI 02912, USA b Johns Hopkins University Applied Physics Laboratory, Johns Hopkins Road, Laurel, MD 20723, USA c Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, DC 20015, USA d Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA article info Article history: Received 15 September 2010 Received in revised form 20 April 2011 Accepted 10 May 2011 Available online 12 June 2011 Keywords: Mercury Peak ring Impact process Crater Basin MESSENGER abstract The study of peak-ring basins and other impact crater morphologies transitional between complex craters and multi-ring basins is important to our understanding of the mechanisms for basin formation on the terrestrial planets. Mercury has the largest population, and the largest population per area, of peak-ring basins and protobasins in the inner solar system and thus provides important data for examining questions surrounding peak-ring basin formation. New flyby images from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft have more than doubled the area of Mercury viewed at close range, providing nearly complete global coverage of the planet s surface when combined with flyby data from Mariner 10. We use this new near-global dataset to compile a catalog of peak-ring basins and protobasins on Mercury, including measurements of the diameters of the basin rim crest, interior ring, and central peak (if present). Our catalog increases the population of peak-ring basins by 150% and protobasins by 100% over previous catalogs, including 44 newly identified peak-ring basins (total¼74) and 17 newly identified protobasins (total¼32). A newly defined transitional basin type, the ringed peak-cluster basin (total¼9), is also described. The new basin catalog confirms that Mercury has the largest population of peak-ring basins of the terrestrial planets and also places the onset rim-crest diameter for peak-ring basins at 126 þ km, which is intermediate between the onset diameter for peak-ring basins on the Moon and those for the other terrestrial planets. The ratios of ring diameter to rim-crest diameter further emphasize that protobasins and peak-ring basins are parts of a continuum of basin morphologies relating to their processes of formation, in contrast to previous views that these forms are distinct. Comparisons of the predictions of peak-ring basin-formation models with the characteristics of the basin catalog for Mercury suggest that formation and modification of an interior melt cavity and nonlinear scaling of impact melt volume with crater diameter provide important controls on the development of peak rings. The relationship between impact-melt production and peak-ring formation is strengthened further by agreement between power laws fit to ratios of ring diameter to rim-crest diameter for peak-ring basins and protobasins and the power-law relation between the dimension of a melt cavity and the crater diameter. More detailed examination of Mercury s peak-ring basins awaits the planned insertion of the MESSENGER spacecraft into orbit about Mercury in & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Although there has been much progress in understanding the transition in impact crater forms with increasing crater diameter n Corresponding author. Tel.: þ ; fax: þ address: david_baker@brown.edu (D.M.H. Baker). from complex craters to multi-ring basins (e.g., Wood and Head, 1976; Pike, 1988; Melosh, 1989; Spudis, 1993), there are many outstanding questions that remain to be resolved with improved modeling and analysis of current and future planetary remotesensing data. These questions include the mechanisms responsible for the onset of transitional morphologies, such as peak-ring basins, with increasing crater diameter; the mode of formation of basin rings and their relation to the transient crater rim; and /$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi: /j.pss

2 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) whether there are variations in the mechanism or style of ring emplacement across the inner solar system. Analysis of the characteristics of peak-ring basins is critical to understanding these questions, as they constitute key transitional forms (Fig. 1). Although these basin types are present on all of the terrestrial planets (e.g., Spudis, 1993), Mercury has long been recognized as having the highest number and density of peak-ring basins (Wood and Head, 1976), and the innermost planet thus provides an important laboratory for analyzing these questions surrounding the peak-ring basin formation process. Previous catalogs of peak-ring basins and other basin populations on Mercury (Wood and Head, 1976; Schaber et al., 1977; Frey and Lowry, 1979; Pike and Spudis, 1987; Pike, 1988) were based on Mariner 10 flyby images, which cover only 45% of the planetary surface (Murray et al., 1974). Since then, images from the three Mercury flybys of the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft have more than doubled the fraction of Mercury s surface viewed at close range and, when combined with Mariner 10 images, provide nearly complete global coverage of the surface (Becker et al., 2009). Many peak-ring and otherwise transitional basins, such as Eminescu (Schon et al., this issue), Raditladi (Prockter et al., 2009), and Rachmaninoff (Prockter et al., 2010), have been recognized in the new images and can now be studied and mapped in detail. These near-global image data provide an opportunity to evaluate the population of peak-ring basins and models of peak-ring basin formation and evolution with increasing basin size. Observations of post-emplacement modification of basins are also important for recognizing how a variety of geological processes have operated on Mercury through space and time (e.g., Head et al., 2008). In this analysis, we survey the most recent controlled mosaic of MESSENGER and Mariner 10 images of Mercury (Becker et al., 2009) to compile a database of peak-ring basins and protobasins. Diameters of the basin rim crest, inner ring, and central peak (where present) were measured to evaluate consistency with current peak-ring basin formation models and to constrain the controlling processes leading to peak-ring formation. In particular, we examine the role of impact melt volume (e.g., Cintala and Grieve, 1998) in the development of the observed ring and rim-crest relationships and assess whether such a parameter should be considered as an important component in peak-ring basin-formation models. 2. Methods The spectrum of crater forms from simple craters, to complex craters, peak-ring basins, and multi-ring basins was first recognized on the Moon and has been extended to the terrestrial planets (e.g., Howard, 1974; Wood and Head, 1976). Differences in schemes for classifying these crater types, especially for transitional morphologies, have introduced much ambiguity in crater nomenclature. For example, peak-ring basins have been called two-ring or double-ring basins (Wood, 1980; Pike, 1988), and protobasins and central-peak basins have been used to describe morphologies that appear transitional between large complex craters and peak-ring basins (Wood and Head, 1976; Pike, 1988). Defining the distinguishing characteristics between craters and basins has also been an outstanding point of contention (Wood and Head, 1976; Pike, 1988; Alexopoulos and McKinnon, 1994). For consistency with previous analysis of craters on Mercury, we use the classification scheme presented by Pike (1988), which demarcates seven classes of crater and basin types on Mercury (Fig. 1): (1) simple craters, (2) modified simple craters, (3) immature complex craters, (4) mature complex craters, (5) protobasins, (6) two-ring (peak-ring) basins, and (7) multi-ring basins. In the current analysis, we focus on the distinguishing morphological characteristics of protobasins, two-ring basins, and multi-ring basins, but we choose to use the term peak-ring basin instead of two-ring basin for reasons discussed below. Protobasins are defined morphologically by the presence of both a central peak and a partial or complete ring of peaks (Fig. 1). This basin type closely resembles mature complex craters except in Fig. 1. Schematic diagram of the progression of crater morphologies with increasing crater diameter, as described by Pike (1988). Simple craters exhibit smooth, featureless interiors (simple) to minor wall slumping (modified simple). Complex craters exhibit large slump deposits and rudimentary terracing with small central peaks (immature complex) to strong terracing and single central peaks to clusters of central peak elements (mature complex). The onset of basin morphologies occurs with a ringed arrangement of peak elements (ringed peak-cluster) or the presence of both a small central peak and peak ring (protobasin). Peak-ring basins have large, prominent peak rings with no central peaks. Multi-ring basins (not pictured here) exhibit three or more rings and commonly an inner depression, as best exemplified by Orientale basin on the Moon (e.g., Head, 1974).

3 1934 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) its central uplift structure. The presence of an interior ring suggests that protobasins share similarities with larger peak-ring basins and thus represent a transitional form between complex craters and peak-ring basins (Pike, 1988). Peak-ring basins are defined as having a single interior topographic ring or a discontinuous ring of peaks or massifs with no central peak. We prefer to use the name peak-ring basin instead of Pike s (1988) two-ring basin, as the name more completely captures the morphological basis by which the basins are recognized. The term two-ring is a more ambiguous term that can be applied to any basin (peak-ring or large multi-ring basin with missing ring structures) possessing two rings, regardless of overall morphology. Multi-ring basins consist of three or more recognizable topographic rings, but many of these rings are incomplete and their recognition is often ambiguous, especially at the largest diameters and in the absence of global topographic data, as is the case for Mercury (Pike and Spudis, 1987). Craters and basins with diameters Z20 km have been identified and cataloged on Mercury (Fassett et al., 2011) from the most recent controlled image mosaic of Mercury (Becker et al., 2009), which combines flyby images from Mariner 10 and MESSENGER to cover nearly 98% of the planet at 500 m/pixel resolution. Using these new near-global image data together with the geographic information system (GIS) software, ArcGIS (Environmental Systems Resource Institute; peak-ring basins and protobasins were identified and cataloged through a survey of all craters and basins greater than 70 km in diameter (980 total). Peak-ring basins and protobasins were identified on the basis of their distinguishing morphological characteristics (Figs. 1 and 2) as discussed above. It is important to note that whereas the image mosaic used in this study covers nearly 98% of Mercury, the low incidence angles (measured from the surface normal) of many of the MESSENGER and Mariner 10 images obscure the recognition of some large basins with subtle topography. This situation cannot be avoided in locations where only one dataset is available; because of differences in illumination geometries between the MESSENGER and Mariner 10 images, both datasets were used in locations where they overlap to avoid omissions in our catalog. We also used stretched Mariner 10 radiance mosaics for complete examination of the limb regions where the Mariner 10 albedo mosaic is truncated (Becker et al., 2009). Once the basins were identified, we measured the diameters of the rim crest, inner ring, and central peak (where present) by visually fitting circles to these features (Fig. 2) using the Crater- Tools extension for ArcGIS (Kneissl et al., 2011) to avoid inaccuracies due to map projection distortions. Circular fits were made to estimate the mean diameter of each feature, and approximate circular fits were made for the few non-circular features observed (e.g., the bases of central peaks) (Fig. 2). Fits to rim crests followed the most prominent topographic divides along the crater rim. Because the massifs that form peak rings are typically a few kilometers in width, we visually fit circles with diameters that are intermediate between those that inscribe and those that circumscribe the ring (Fig. 2C). Central peaks were the most difficult to measure because of their irregular outlines. For irregular central peaks, we chose circular fits having a diameter intermediate between the maximum and minimum horizontal extent of the feature. As a check, we compared our new measurements with those of peak-ring basins and protobasins by Pike (1988); most differences between the diameter measurements were small (o2%) and were not systematically smaller or larger. Those differences that were larger for some rim-crest, ring, and central-peak diameters are the result of differences in interpretation of feature occurrence and dimensions in situations where MESSENGER data overlap Mariner 10 images and provide improved portrayal of features. Multi-ring basins included by Pike (1988) were not re-evaluated in this survey, but MESSENGER data are providing important new insight into multi-ring basin formation (e.g., Head, 2010) and modification (e.g., Prockter et al., 2010) processes. For multi-ring basins, uncertainties regarding many ring assignments await topographic data (e.g., Zuber et al., 2008) and higher-resolution, low-sun images from the upcoming orbital mission phase for more rigorous analyses. Fig. 2. Examples of (A) a ringed peak-cluster basin (Eminescu, centered at N, E; basin number 8 in Appendix A, Table A3), (B) a protobasin (van Gogh, centered at S, E; basin number 16 in Appendix A, Table A2), and (C) a peak-ring basin (Raditladi, centered at N, E; basin number 69 in Appendix A, Table A1) (data are from the MESSENGER and Mariner 10 controlled mosaic of Mercury; Becker et al., 2009). Circles (black and white lines) in the bottom row illustrate how measurements were made for diameters of basin rim-crests and interior peak rings and central peaks. Images are transverse Mercator projections centered on the basin, and north is toward the top in each image.

4 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) Results 3.1. General basin statistics We have identified 74 peak-ring basins and 32 protobasins on Mercury, including 44 newly discovered peak-ring basins and 17 newly discovered protobasins (Table 1 and Appendix A, Tables A1 and A2). We have also identified an additional nine basins that resemble peak-ring basins but have uncharacteristically small rimcrest and peak-ring diameters (Table 1 and Appendix A, Table A3); these are termed ringed peak-cluster basins (Fig. 1) here and are discussed in more detailed below. Pike (1988) originally identified 31 peak-ring basins and 20 protobasins from Mariner 10 data. Through re-evaluation of the basins of Pike (1988) with a combination of MESSENGER and Mariner 10 data for a given basin, we excluded three peak-ring basins listed by Pike (1988) from our catalog (Mendes-Pinto, Pushkin, and South of Moliere). These reclassifications were made because obvious interior peak rings were absent in both MESSENGER and Mariner 10 images, which provide different illuminations of basin features and thus an improved ability to interpret basin features that may have been ambiguous in prior analyses. We also excluded three protobasins (Ts ai Wen Chi and two unnamed basins), for similar reasons. We reclassified two protobasins of Pike (1988) (Boethius and Scarlatti) as peak-ring basins because of the absence of an observable central peak in MESSENGER images. Although we are confident in these reclassifications on the basis of current datasets, they should be corroborated with observations to be obtained by MESSENGER during the mission orbital phase. A listing of all peak-ring basin, protobasin, and ringed peakcluster basin locations and their measured rim-crest, ring, and central peak diameters is presented in Appendix A in Tables A1 A3, respectively. An image of each basin is included as online supplementary material. The new data show that peak-ring basins range in diameter from 84 to 320 km, with a geometric mean of 180 km (Table 1). These new statistics lower the geometric mean peak-ring basin diameter of Pike (1988) by 20 km and also place the onset diameter for peak-ring basins at 126 þ km (see Appendix B for a discussion on calculating onset diameter). The new data show that protobasins range in diameter from 75 to 172 km, with a geometric mean of 102 km (Table 1). Whereas the diameter range for protobasins is comparable to that given by Pike (1988), the geometric mean diameter is 8 km less. Ringed peak-cluster basins were not included in the classification of Pike (1988). These basin types range from 73 to 133 km in diameter and have the lowest geometric mean diameter of all basin types at 96 km (Table 1). General statistics for basins on the Moon and Mars (Pike and Spudis, 1987), Venus (Alexopoulos and McKinnon, 1994), and Mercury (using the new data) are compared in Table 1. As noted by previous workers (Wood and Head, 1976), Mercury has the largest number of peak-ring basins per unit area in the inner solar system. Whereas the crater size distributions for impact craters between 100 and 500 km in diameter are nearly the same on the Moon and Mercury (e.g., Strom et al., 2005), the mean and onset diameters for peak-ring basins on Mercury are much lower than on the Moon, as documented by others (Wood and Head, 1976; Pike, 1988). The lower onset diameter for peak-ring basins on Mercury (Table 1) may account for the factor of five larger number of peak-ring basins per area on Mercury than on the Moon. The surface density of craters between 100 and 500 km in diameter is much lower on Mars than on Mercury and the Moon as a result of extensive erosion and resurfacing (Strom et al., 2005), which could partially explain the relatively small number of peak-ring basins on Mars. The mean and onset diameters for peak-ring basins on Mercury are more comparable to those for Mars, perhaps owing to similar values of surface gravitational acceleration on the two bodies (see Section 4.3). The population of protobasins on Mercury is also the largest among the terrestrial Table 1 Comparison of planetary parameters and characteristics of peak-ring basins, protobasins, and ringed peak-cluster basins on Mercury, the Moon, Mars, and Venus. Mercury Moon a Mars a Venus b Gravitational acceleration (m/s 2 ) Surface area (km 2 ) Mean impact velocity c (km/s) Peak-ring basins (total N pr ) N pr /km Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km) Onset diameter (km) d 126 þ þ þ þ 10 8 Protobasins (total N proto ) N proto (km 2 ) Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km) Ringed peak-cluster basins (total N rpc ) N rpc (km 2 ) Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km) a Basin data from Pike and Spudis (1987). b Basin data from Alexopoulos and McKinnon (1994). Calculations exclude the suspected multi-ring basins Klenova, Meitner, Mead, and Isabella. c Mean impact velocity from Le Feuvre and Wieczorek (2008). d 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 calculating the geometric mean of the rim-crest diameters of all craters or basins within this range (see Appendix B). Uncertainties are one standard deviation about the geometric mean, calculated by multiplying and dividing the geometric mean by the geometric, or multiplicative, standard deviation. Peak-ring basin and protobasin data used for the calculations are from this study (Mercury), Pike and Spudis (1987) (Moon and Mars), and Alexopoulos and McKinnon (1994) (Venus). Complex crater rim-crest diameters used for the calculations are from the catalogs compiled by Pike (1988) (Mercury), Barlow (2006) (Mars), and Schaber and Strom (1999) (Venus); diameters of complex craters and peak-ring basin diameters on the Moon do not overlap.

5 1936 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) planets, with a smaller mean diameter than for such features on the Moon and Mars (Table 1) Morphological variations Although there are several relatively fresh basins on Mercury (e.g., Raditladi, Prockter et al., 2009; Eminescu, Schon et al., this issue), most basins are highly degraded and have undergone extensive modification by a number of processes, including deformation, volcanic infilling, emplacement of ejecta from nearby craters, and superposed impact craters (e.g., Watters et al., 2009a; Prockter et al., 2010). As a result, interior rings are often incomplete and may exhibit substantial azimuthal variation in their morphology. We recognize three major ring morphologies among peak-ring basins: common peak rings, scarp rings, and wrinkle-ridge rings (Fig. 3). The first ring type, common peak rings, occurs most frequently (total number N¼60, or 81% of the total population) among peak-ring basins and consists of a circular arrangement of prominent topographic peaks (Fig. 3A). These massifs may be contiguous to form a single ring or may be discontinuous, forming a partial arc or individual peak elements separated by crater floor material. Approximately two-thirds of all common peak rings preserve rings spanning at least 1801 of arc (Appendix A, Table A1). The second major ring type, scarp rings (N¼8, 11%), is defined by a scarp face that separates a higher exterior topographic bench from an interior topographic low (Fig. 3B). Relative topography is inferred from images on the basis of illumination direction and shadowing, and scarps are distinguished from peaks by their lack of shadowing at points opposite from the illuminated scarp face. Peak-ring basins with scarp rings usually lack peak elements and tend to be substantially infilled by smooth interior floor material (Fig. 3B). Similar scarp-ring morphologies have been observed on Venus (Alexopoulos and McKinnon, 1994) and have been interpreted to result from partial infilling of the crater interior by volcanic material. Alternatively, the similarities in position and spacing between scarp rings and peak rings suggest that some scarp rings may be primary features, perhaps related to incomplete development of peak-ring structures during crater collapse. Departures from the topographic prominence of common peak rings and formation of a scarp could conceivably result from variations in target properties or impactor characteristics (e.g., impact velocity and angle). Although an association between scarp rings and smooth fill material supports a model of partial volcanic infilling, the details of scarp ring formation await more detailed topographic data to be obtained by the Mercury Laser Altimeter (Zuber et al., 2008) on MESSENGER during the orbital phase of the mission. The third major ring type, wrinkle-ridge rings (N¼6, 8%), is defined by a single circular wrinkle ridge within a basin that has been nearly completely infilled by smooth plains material (Fig. 3C). Circular wrinkle ridges are not uncommon on Mercury (Head et al., 2008, 2009a) or the other terrestrial planets (e.g., Watters, 1988) and are usually interpreted to be due to localization of thrust faults by subsurface ring relief in volcanically buried impact craters (Watters, 1988). Wrinkle-ridge rings in the interiors of basins on Mercury are similarly interpreted to result from the localization of faults where volcanic fill has completely covered peak rings (Head et al., 2008). Hybrid ring morphologies consisting mostly of peak elements but with associated wrinkle ridges or scarps are also observed; we include these types in the common peak-ring class. Their occurrence further emphasizes the role of post-emplacement processes in modifying otherwise typical peak rings. Other notable morphological features within peak-ring basins include large arcuate pits that occasionally form adjacent to peak rings in highly filled basins. These pits have been inferred to result from endogenic processes, such as caldera-like collapse from an evacuated magma chamber (Gillis-Davis et al., 2009). On the basis of images obtained to date, circumferential fractures (graben) are observed only in Raditladi and Rachmaninoff basins (Watters et al., 2009b; Prockter et al., 2009, 2010) and are likely to be due to post-impact uplift of the basin floors (Watters et al., 2009b; Head et al., 2009a,b). The rings of protobasins are generally less complete and more subdued than those of peak-ring basins, although some topographically prominent protobasin rings are observed. Central peak morphologies within protobasins also vary from subdued single peaks, which are common, to less frequent prominent single peaks or complex peak clusters. Many of the central peaks appear off-center relative to the peak ring and the basin rim; peak rings may also appear off-center relative to the basin rim. Whereas morphologic variability exists among protobasins, general morphological classes of protobasins comparable to those seen in peak-ring basins are difficult to establish. Some wrinkle-ridge-like ring segments occur but do not dominate the basin-ring morphology. Large floor pits and circumferential fractures are not observed within protobasins at the resolution of current MES- SENGER flyby and Mariner 10 images. Ringed peak-cluster basins (Fig. 2A) have a clear ring-like arrangement of peak elements similar to peak-ring basins (Fig. 2C) but occur at smaller rim-crest diameters and with much Fig. 3. Three types of peak rings observed in peak-ring basins: (A) Common peak rings occur most frequently and consist of a circular arrangement of prominent topographic peaks (unnamed basin, centered at N, E; basin number 33 in Appendix A, Table A1). (B) Scarp rings are defined by a scarp face that separates a higher exterior topographic bench from an interior topographic low. Basins with scarp rings usually lack peak elements and are often substantially infilled by smooth interior floor material (unnamed basin, centered at S, E; basin number 18 in Appendix A, Table A1). (C) Wrinkle-ridge rings consist of a single circular wrinkle ridge within a basin that has been completely infilled by smooth plains material (Copland, centered at N, E; basin number 51 in Appendix A, Table A1). Images are transverse Mercator projections centered on the basin, and north is toward the top in each image.

6 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) smaller ring diameters. Many circular arrangements of central peaks have been observed in craters from 20 to 130 km in diameter on the Moon (Schultz, 1976; Smith and Hartnell, 1978; Pike, 1983a); such features appear to be distinct from central-pit craters (Schultz, 1988) and have been interpreted to result from collapse of the central portion of an uplifted peak complex (e.g., Schultz, 1976). Our observations suggest that ringed peak-cluster basins share morphological similarities with circular central peak arrangements in craters on the Moon. However, the overlap in rim-crest diameters with protobasins and the smallest peak-ring basins suggests that ringed peakcluster basins represent a distinct transitional basin morphology (see Section 4.2) Ring-diameter trends The ring diameters of all peak-ring basins, protobasins, and ringed peak-cluster basins (Fig. 1) are shown as functions of basin rim-crest diameter on a log log plot in Fig. 4A. To help elucidate trends from the individual data points (Fig. 4A), we also binned the data in 10-km rim-crest-diameter intervals (Fig. 4B). In general, the ring diameter increases as a function of rim-crest diameter for all basin types, and trends in the new data (red circles and blue squares, Fig. 4A) agree well with those of Pike (1988) (black circles and gray squares, Fig. 4A). Following the method of Pike (1988), power laws were fit to the unbinned (Fig. 4A) and binned data (Fig. 4B) for all basin types. Power laws were of the form: D ring ¼ AD p r ð1þ where D ring is the diameter of the interior ring, D r is the basin rim-crest diameter, A is a constant, and p is the slope of the bestfitting line on a log log plot. All power-law fits were calculated in KaleidaGraph (Synergy Software, which uses the Levenberg Marquardt nonlinear curve-fitting algorithm (Press et al., 1992) to minimize iteratively the sum of the squared errors in ordinate. The use of this criterion for minimization implies that fractional errors in the estimates of interior ring diameters are regarded as larger than those for estimates of the rim-crest diameter. For the binned data, fits were obtained from the mean ring diameter in the bin, and the bins were not weighted. The calculated values for A and p in Eq. (1) for all basin types in our updated catalog, as well as those derived from the catalog of Pike (1988), are given in Table 2. Peak-ring basins appear to follow a power-law relationship best (R 2 ¼0.87 and 0.94 for unbinned and binned data, respectively, where R is the correlation coefficient for the given dataset on a log log plot) with a slope of for unbinned data, which is identical to the slope derived by Pike (1988) (Table 2). Protobasins occur at generally smaller rim-crest diameters than those of peak-ring basins. The ring diameters of protobasins follow a trend similar to that for ring diameters of peak-ring basins; however, the slope of the protobasin trend steepens for rim-crest diameters o90 km, reflecting the anomalously small ring diameters for these protobasin sizes. Our observations suggest that this steepening trend is real and is likely related to the transition from central peak structures to peak rings (see Section 4.2 for further discussion). If we exclude these transitional protobasins and fit a power law to all protobasins Z90 km in diameter, we derive a power-law slope of and an A value of (R 2 ¼0.69), which are statistically indistinguishable from the trend of peak-ring basins (Table 2). If we then combine all peak-ring basins and protobasins Z90 km in diameter, we derive a power-law fit of D ring ¼( ) (D r ) (R 2 ¼0.91), which is also statistically indistinguishable and is an improved fit with Fig. 4. Ring diameter versus rim-crest diameter. (A) All (unbinned) data for peak-ring basins (PRB, red and black circles), protobasins (Proto, gray and blue squares), and ringed peak-cluster basins (RPCB, green diamonds) on Mercury. Re-measured basins from Pike (1988) are highlighted for comparison. (B) Basin data binned in 10-km rimcrest diameter intervals. Points are plotted as arithmetic mean values at the bin centers, and error bars display 71 standard deviation about the mean; means and standard deviations were calculated from the measured ring diameters in Tables A1 A3. Data points with no error bars in (B) represent bins with only one basin. Peak-ring basins and protobasins follow power-law trends (shown as straight lines for binned data in (B) that are similar to those observed by Pike (1988)). Peak-ring basins have a slope of (R 2 ¼0.87) for unbinned data (A). ProtobasinsZ90 km in rim-crest diameter follow a similar trend to peak-ring basins with a slope of (R 2 ¼0.69) but have generally smaller rim-crest diameters. Protobasinso90 km in diameter have anomalously smaller ring diameters than what is predicted by the power law fit to protobasinsz90 km in diameter. Ringed peak-cluster basins may follow a separate trend, albeit with a statistically indistinguishable slope (slope¼ , R 2 ¼0.78), and have smaller ring diameters. The power-law trend for central peak diameters of large, mature complex craters on Mercury (Pike, 1988) is shown as a solid line in (A) for comparison. The overlap between the fields for ringed peak-cluster basins and complex craters suggests similarities in the mechanism of formation between the two crater types.

7 1938 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) Table 2 Parameters from best-fitting relationships between ring diameter and rim-crest diameter for the data in this study and the catalog of Pike (1988). Coefficients to power-law fits a This study Pike (1988) A p R 2 A p Peak-ring basins Unbinned Binned Protobasins (Z90 km) b Unbinned Binned Ringed peak-cluster basins Unbinned Binned Complex-crater central peak diameters a Power laws are of the form D ring or cp ¼AD p r (Eq. 1), where D ring is the peak-ring diameter, D cp is the diameter of the central peak, and D r is the rim-crest diameter. Uncertainties are at 95% confidence. b Pike (1988) fit a power law to all protobasin rim-crest diameters. Power-law fits in this study include only protobasins Z90 km in diameter because of the anomalously small ring diameters for protobasins o90 km. smaller uncertainties than from the trends of peak-ring basins and protobasins alone. That peak-ring basins and protobasins Z90 km in diameter have statistically indistinguishable trends justifies combining these two crater classes in statistical analyses. Smaller ringed peak-cluster basins follow what may be a separate trend, albeit with a statistically indistinguishable slope (slope¼ , R 2 ¼0.78), and have much lower ring diameters than protobasins and peak-ring basins. Qualitatively, the trend of ringed peak-cluster basins is very similar to the trend of central peak basal diameters for large mature complex craters on Mercury (Fig. 4A) (Pike, 1988). The slope for central peaks of mature complex craters ( ) also falls within the uncertainty of the slope for ringed peak-clusters (Table 2). The overlap and similarity of the morphometric trends of mature complex craters and ringed peak-cluster basins support the observation that the two forms share aspects of their genesis (Schon et al., this issue). However, the clear ring-like arrangements of their interior peak elements and their overlap in rim-crest diameter with complex craters and protobasin rim-crest diameters suggest that ringed peak-cluster basins are distinctive transitional forms between large complex craters and peak-ring basins (see Section 4.2). The major trends identified in Fig. 4 indicate that there are differences in the relationship between ring and rimcrest diameter among protobasins, peak-ring basins, and ringed peak-cluster basins. Variations in ratios at a given rim-crest diameter may be due to differences in the properties of the target or impactor, variations in angle of incidence, and/or scatter about the mean impact velocity Ring/rim-crest diameter ratios The differences in the best-fitting relationship between ring diameter and rim-crest diameter for protobasins and peak-ring basins, as shown in Fig. 4, have been used to argue against combining these two morphological classes in statistical analyses (Pike, 1988). Our new power-law fits to peak-ring basins and protobasins Z90 km in diameter (Fig. 4 and Table 2), however, indicate that the trends for peak-ring basins and protobasins are statistically indistinguishable. Furthermore, plotting individual ratios of ring diameter to rim-crest diameter versus rim-crest diameter for all protobasins and peak-ring basins (Fig. 5) reveals that protobasins and peak-ring basins should be viewed as part of a continuum of basin morphologies (see also Alexopoulos and McKinnon, 1994). A general nonlinear increase of the ring/rim-crest diameter ratio is observed as a function of increasing rim-crest diameter (Fig. 5A, B). Physically, this result indicates that the ring diameters of basins increase non-proportionally as the magnitude of the impact event increases. This non-proportional increase in ring diameter becomes less dominant at large basin diameters; relative differences in ring/rim-crest diameter ratios are greatest at smaller diameters and level out to more constant values of around at larger basin diameters (Fig. 5A). Ringed peak-cluster basins (green diamonds in Fig. 5A) have markedly lower ring/rimcrest diameter ratios and appear to be separate from the generally smooth curve formed by protobasins and peak-ring basins (Fig. 5A). This observation further supports the idea that the formation of ringed peak-cluster basins is distinct from the general continuum of morphologies between protobasins and peak-ring basins. Alexopoulos and McKinnon (1994) recognized similar relationships in measurements of ring and rim-crest diameters for craters on Venus and on the Moon, Mercury, and Mars. In contrast to their convention of using rim-crest/ring diameter ratios, we choose to use the inverse, ring/rim-crest diameter ratios, for consistency with earlier studies (e.g., Pike, 1988) and to avoid magnifying the effects of errors in small denominators. Venus data from Alexopoulos and McKinnon (1994) and data for the Moon and Mars (Pike and Spudis, 1987) are plotted in Fig. 5B and C. Although the rim-crest diameters for Venus features are much smaller than for those of Mercury and the dataset is limited as a result of comparatively recent planet-wide resurfacing, a consistent curved trend is apparent (Fig. 5B). The trend is steeper in the transition from small rim-crest diameters to larger rim-crest diameters and flattens toward larger ring/rim-crest diameter ratios compared with the pattern for Mercury. Curved trends were also observed for the Moon and Mars (Alexopoulos and McKinnon, 1994) on the basis of original data from Wood and Head (1976), Hale and Head (1979), Wood (1980), andhale and Grieve (1982). Revised rimcrest and ring diameters from Pike and Spudis (1987), however,do not show this curved trend in the ring/rim-crest diameter ratio (Fig. 5C). This difference in behavior is likely due to differences in techniques of measurement, differences in interpretations of basin features, especially near the limit of image resolution at the smallest basin diameters, and differences in classification of basins based on these interpretations. Updating the existing catalogs of peak-ring basins and protobasins on the Moon and Mars using more recent

8 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) Discussion Our analysis of the new catalog of protobasins and peak-ring basins on Mercury using both MESSENGER flyby and Mariner 10 data (Table 1 and Appendix A, Tables A1 A3), strengthens some previous findings and emphasizes the following: 1. Mercury has the largest number of peak-ring basins and protobasins per surface area in the inner solar system (Table 1). In comparison with Mars and Venus, this difference is in part due to the greater effectiveness of crater obliteration processes on those bodies. 2. The onset diameter of peak-ring basins on Mercury is lower than on the Moon and higher than on Mars and Venus (Table 1). 3. Plots of ring/rim-crest diameter ratio (Fig. 5) suggest that protobasins and peak-ring basins are part of a continuum of basin morphologies and that ringed peak-cluster basins appear to be distinct from this general continuum (Fig. 4). 4. The ratio of ring diameter to rim-crest diameter increases nonlinearly with increasing rim-crest diameter; this ratio approaches a constant value at the diameters of peak-ring basins (Fig. 5A). Any successful peak-ring basin-formation model must account for all of these observations and should be consistent with observations of basin characteristics on all of the terrestrial planets. We now address the merits of two recent models put forth to explain the onset and evolution of basins with peak rings. The first is hydrodynamic collapse of an unstable central peak structure (e.g., Melosh, 1989), and the second is modification and collapse of a nested impact melt cavity (e.g., Cintala and Grieve, 1998). The two classes of models make different predictions (Melosh, 1989; Grieve and Cintala, 1992; Cintala and Grieve, 1998; Collins et al., 2002; Grieve et al., 2008) regarding the development and evolution of peak-ring basins, predictions that should be evaluated with both orbital observations of impact basins and field observations of terrestrial impact structures Hydrodynamic collapse model The hydrodynamic collapse model explains peak ring formation as a product of gravitational collapse of a fluidized, over-heightened central peak (Fig. 6). The model was initially described qualitatively from studies of basins on the Moon, Mars, and Fig. 5. Ring/rim-crest diameter ratios for peak-ring basins, protobasins, and ringed peak-cluster basins on (A) Mercury (this study), (B) Venus (Alexopoulos and McKinnon, 1994), and (C) the Moon and Mars (Pike and Spudis, 1987). Data for Mercury (A) are grouped by peak-ring basins (filled circles), protobasins (filled squares), and ringed peak-cluster basins (open diamonds). The Mercury (A) and Venus (B) data fields show a general nonlinear increase in ring/rim-crest diameter ratio with increasing basin rim-crest diameter. The four largest basin diameters shown for Venus (B) are suspected multi-ring basins (Alexopoulos and McKinnon, 1994) but are included here to facilitate comparisons with the other terrestrial planets (e.g., Alexopoulos and McKinnon, 1994). Ringed peak-cluster basins (A) appear to be distinct from the trend for protobasins and peak-ring basins. The Pike and Spudis (1987) data for the Moon and Mars do not show a similar curved trend, although use of earlier catalogs from Wood and Head (1976), Hale and Head (1979), Hale and Grieve (1982), and Wood (1980) have shown trends in ring/rim-crest diameter ratio similar to those for Mercury and Venus (Alexopoulos and McKinnon, 1994). orbital datasets (e.g., Baker et al., 2010) should clarify these inconsistencies, a step needed before major interpretations of the continuum of ring/rim-crest diameter ratios on the Moon and Mars may be made. Fig. 6. Peak-ring formation by hydrodynamic collapse of an over-heightened central peak (from Melosh, 1989). See Section 4.1 for description.

9 1940 D.M.H. Baker et al. / Planetary and Space Science 59 (2011) Mercury (Murray, 1980) and terrestrial impact structures (Grieve, 1981). Further quantitative development of this model has been made on the basis of theory (Melosh, 1989) and hydrocode modeling combined with geologic and geophysical studies (e.g., Morgan et al., 2000; Collins et al., 2002, 2008; Ivanov, 2005). The principal stages in the model include substantial transient weakening or fluidization of target material (e.g., Melosh, 1979; Gaffney and Melosh, 1982); rebounding or inward and upward wall collapse to form an over-heightened, gravitationally unstable central uplift; downward and outward collapse of the unstable central uplift; and freezing of the collapsed fluidized central peak material to form a peak ring (Fig. 6). Field observations of large terrestrial impact structures, including Vredefort, Chicxulub, and Sudbury exhibit geological and geophysical characteristics that appear to be consistent with the hydrodynamic collapse model (e.g., Morgan and Warner, 1999; Morgan et al., 2000; Grieve et al., 2008). Specifically, the observed convergence of inward-dipping faults and down-slumped blocks of crater rim material with outward-thrusting faults that dip inward within the interior of the basin are broadly similar to the kinematics predicted from hydrodynamic collapse of an over-heightened central uplift structure (Collins et al., 2002; Grieve et al., 2008). It is important to note, however, that many of the structural features observed in terrestrial impact craters have a non-unique origin (Grieve et al., 2008) and should not be interpreted under the presumption of a single basin-formation model. Furthermore, although much progress has been made in improving the current hydrocode models for peak-ring basin formation, these models currently make no explicit predictions about the relationships between ring and rim-crest diameter observed in large impact structures. This is largely due to uncertainties in the mechanism for freezing the collapsing central peak, although an increase in cohesion from a decaying acoustic energy field or dampening of oscillatory motion has been suggested (Melosh, 1989; Collins et al., 2002; Ivanov, 2005). The final ring diameter and morphology are therefore largely dependent on assumed parameters in hydrocode models (Collins et al., 2002; Ivanov, 2005; Bray et al., 2008). For example, modeling of the Ries impact crater (Wünnemann et al., 2005) has shown that the interior morphology of the final modeled crater depends on acoustic fluidization parameters, with differing sets of viscosity and decay-time values producing central peaks or ring-like topography of variable diameter. Until more explicit predictions are made, it is difficult to use our measurements of ring and rimcrest diameters to evaluate the hydrodynamic collapse model for peak-ring basin formation Nested melt-cavity model Given the uncertainties with the hydrodynamic collapse model, we now examine another model for the formation of peak-ring basins, by which peak rings are formed as the result of modification of a nested melt cavity and a nonlinear relation between impact melt volume and crater volume. In the context of the basin catalog and morphological observations of this paper, we suggest that this nested melt-cavity model offers an explanation for peak-ring formation and that impact-melt volume should be considered as an important parameter in peak-ring basin-formation models. A suite of papers by Cintala and Grieve (Grieve and Cintala, 1992, 1997; Cintala and Grieve, 1994, 1998) synthesized terrestrial field studies and impact and thermodynamic theory to show that impact-melt production and retention is disproportionally larger during large (basin-forming) impact events than smaller (simple to complex crater-forming) impact events. This nonlinear scaling between impact-melt generation and crater size results from differences in the role that kinetic energy and gravity (Table 1) play in each process. Other than affecting mean impactor velocity, gravity does not have a direct influence on melt production, whereas the dimensions of the final crater are largely controlled by gravity (Grieve and Cintala, 1997). As a result, for given impactor and target materials, impact-melt volume will increase at a rate that is greater than growth of the crater volume with increasing energy of the impact event (Grieve and Cintala, 1992). The total volume of impact melt (V m ) that is produced under specific impact velocities and impactor and target materials is related to the diameter of the transient cavity (D tc ) by a power law (Grieve and Cintala, 1992): V m ¼ cd d tc ð2þ where c is a constant that depends on target and impactor properties and impact velocity in the model, and d is a constant equal to 3.85 (Grieve and Cintala, 1992). Estimates of melt volumes in impact structures on Earth appear to follow this power-law relationship quite well (Grieve and Cintala, 1992). The maximum depth of melting was also calculated from the model, showing that the ratio of the depth of melting to the depth of the transient crater increases with increasing transient crater diameter (Cintala and Grieve, 1994, 1998). For example, at final crater diameters near the onset of peak-ring basins on Mercury (126 km, Table 1), maximum depths of melting approach 0.8 the depth of the transient cavity, or about 25 km depth (Cintala and Grieve, 1998; Ernst et al., 2010). Because of the large volumes of melt and depths of melting predicted for large impact events, nonlinear scaling between impact melting and crater growth has been suggested to be important during the modification process in the formation of peak-ring basins (Cintala and Grieve, 1998). Head (2010) extended these inferences to include multi-ring basins and proposed a conceptual scenario by which the interior melt cavity exerts a major influence on the formation of peak rings and rings exterior to the transient cavity. Under this nested melt-cavity model (Cintala and Grieve, 1998; Head, 2010), the transition from complex craters to peak-ring basins is the result of non-proportional growth in impact melt volume with increasing basin size and an increase in depth of melting relative to the depth of the transient crater, which acts to weaken the central uplifted portions of the crater interior during large impact events. Complex craters are viewed as forming in an uplift-dominated regime, in which rebound of a focused region of solids experiencing the largest shock stresses within the center of the displaced zone results in the formation of a central-uplift structure. Except for large complex craters (see discussion on ringed peak-cluster basins, below), the depth of melting is generally not sufficient in this regime to modify the uplifted morphology of the crater interior. In contrast, rings in protobasins and peak-ring basins form in an impact-melt-cavity-dominated regime due to the nonproportional increase in depth of impact melting. In this regime, the region of peak shock stress in the solid target expands to outline a broad central cavity of impact melt nested within the transient crater. During rebound and collapse of the transient crater, the entire impact melt cavity is translated upward and inward. Unlike rebound in complex craters, however, the melt cavity is sufficiently deep to retard the development of an ordinary-sized central peak (Cintala and Grieve, 1998). Rather, the uplifted periphery of the melt cavity remains as the only topographically prominent feature, resulting in the formation of a peak ring. At smaller crater sizes, and hence shallower depths of melting, it is still possible for a diminutive central peak to rise through the melt cavity, accounting for the occurrences of small central peak and peak-ring combinations that are commonly seen in protobasins. For a more detailed, quantitative description of the