Planetary and Space Science 59 (2011) 1932–1948
Contents lists available at ScienceDirect
Planetary and Space Science
journal homepage: www.elsevier.com/locate/pss
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
Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA
Department of Terrestrial Magnetism, Carnegie Institution of Washington, Washington, DC 20015, USA
d
Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 15 September 2010
Received in revised form
20 April 2011
Accepted 10 May 2011
Available online 12 June 2011
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 (total ¼ 74) and 17 newly identified protobasins (total ¼32).
A newly defined transitional basin type, the ringed peak-cluster basin (total¼ 9), is also described. The
new basin catalog confirms that Mercury has the largest population of peak-ring basins of the
þ 33
km,
terrestrial planets and also places the onset rim-crest diameter for peak-ring basins at 12626
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.
& 2011 Elsevier Ltd. All rights reserved.
Keywords:
Mercury
Peak ring
Impact process
Crater
Basin
MESSENGER
1. Introduction
Although there has been much progress in understanding the
transition in impact crater forms with increasing crater diameter
n
Corresponding author. Tel.: þ1 401 863 3485; fax: þ1 401 863 3978.
E-mail address: [email protected] (D.M.H. Baker).
0032-0633/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.pss.2011.05.010
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
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
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
1933
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).
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D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
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; www.esri.com), 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 CraterTools 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 10.681N, 114.091E; basin number 8 in Appendix A, Table A3), (B) a protobasin (van Gogh, centered
at 76.801S, 221.811E; basin number 16 in Appendix A, Table A2), and (C) a peak-ring basin (Raditladi, centered at 27.051N, 119.051E; 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.
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
3. 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
1935
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
þ 33
diameter for peak-ring basins at 12626
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
Moona
Marsa
Venusb
Gravitational acceleration (m/s2)
Surface area (km2)
Mean impact velocityc (km/s)
3.70
7.5 107
42.5
1.62
3.8 107
19.4
3.67
1.4 108
10.6
8.87
4.6 108
25.2
Peak-ring basins (total Npr)
Npr/km2
Geometric mean diameter (km)
Minimum diameter (km)
Maximum diameter (km)
Onset diameter (km)d
74
9.9 10 7
180
84
320
7
1.8 10 7
335
320
365
15
1.0 10 7
140
52
442
66
1.4 10 7
57
31
109
þ 33
12626
þ 18
33917
þ 29
8021
þ 10
428
Protobasins (total Nproto)
Nproto (km2)
Geometric mean diameter (km)
Minimum diameter (km)
Maximum diameter (km)
32
4.3 10 7
102
75
172
6
1.6 10 7
204
135
365
7
4.9 10 8
118
64
153
6
1.3 10 8
62
53
70
Ringed peak-cluster basins (total Nrpc)
Nrpc (km2)
Geometric mean diameter (km)
Minimum diameter (km)
Maximum diameter (km)
9
1.2 10 7
96
73
133
-
-
-
a
Basin data from Pike and Spudis (1987).
Basin data from Alexopoulos and McKinnon (1994). Calculations exclude the suspected multi-ring basins Klenova, Meitner, Mead, and Isabella.
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.
b
c
1936
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
planets, with a smaller mean diameter than for such features on
the Moon and Mars (Table 1).
3.2. 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 N ¼60, 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 (N ¼8, 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 (N ¼6, 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 MESSENGER 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 34.821N, 280.841E; 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 14.561S, 55.691E; 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 37.481N, 73.561E; 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.
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
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).
3.3. 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:
Dring ¼ ADpr
ð1Þ
where Dring is the diameter of the interior ring, Dr is the basin
rim-crest diameter, A is a constant, and p is the slope of the best-
1937
fitting line on a log–log plot. All power-law fits were calculated in
KaleidaGraph (Synergy Software, www.synergy.com), 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 (R2 ¼ 0.87 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 1.1370.10 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 1.09 70.29 and an
A value of 0.2670.36 (R2 ¼ 0.69), 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 Dring ¼(0.1670.07) (Dr)1.217 0.08 (R2 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 1.13 7 0.10 (R2 ¼ 0.87) for unbinned data (A). Protobasins Z90 km in rim-crest diameter follow a similar trend to peak-ring basins with a slope of 1.09 7 0.29
(R2 ¼ 0.69) but have generally smaller rim-crest diameters. Protobasins o90 km in diameter have anomalously smaller ring diameters than what is predicted by the power
law fit to protobasins Z 90 km in diameter. Ringed peak-cluster basins may follow a separate trend, albeit with a statistically indistinguishable slope (slope ¼ 1.027 0.41,
R2 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.
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D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
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 fitsa
This study
Pike (1988)
A
p
R2
A
p
Peak-ring basins
Unbinned
Binned
0.257 0.14
0.257 0.21
1.13 7 0.10
1.13 7 0.15
0.87
0.94
0.25
1.13 70.10
Protobasins (Z90 km)b
Unbinned
Binned
0.267 0.36
0.467 0.58
1.09 7 0.29
0.97 7 0.26
0.69
0.93
0.32
1.047 0.38
Ringed peak-cluster basins
Unbinned
Binned
0.187 0.34
0.187 0.43
1.02 7 0.41
1.02 7 0.52
0.78
0.76
–
–
–
–
Complex-crater central peak diameters
–
–
–
0.44
0.827 0.08
a
Power laws are of the form Dring or cp ¼ ADpr (Eq. 1), where Dring is the peak-ring diameter, Dcp is the diameter of the central peak, and Dr 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 Z 90 km in diameter because of the
anomalously small ring diameters for protobasins o 90 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
(slope¼1.0270.41, R2 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 (0.82 70.08) 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.
3.4. 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
0.5–0.6 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), and Hale 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
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
1939
4. 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.
4.1. 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.
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D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
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.
4.2. 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 (Vm) that is
produced under specific impact velocities and impactor and
target materials is related to the diameter of the transient cavity
(Dtc) by a power law (Grieve and Cintala, 1992):
Vm ¼ cDdtc
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
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
basis for the nested melt-cavity model, the reader is directed to
Cintala and Grieve (1998) and references therein.
4.3. Predictions of the nested melt-cavity model and comparison
with the Mercury dataset
The nested melt-cavity model for peak-ring basin formation
makes several predictions related to the morphological characteristics and frequency of basins in the transition between complex
craters and peak-ring basins. Some of these predictions include:
(1) a greater number of peak-ring basins for planets experiencing
the highest mean impact velocities, (2) diameter-dependent
interior morphologies, resulting in a size-morphology continuum
between protobasins and peak-ring basins and an onset of
interior basin rings, and (3) increasing ring/rim-crest diameter
ratios with increasing basin diameter due to the non-proportional
growth of the dimensions of the melt cavity relative to the
dimensions of the crater.
Comparison of these predictions of the nested melt-cavity
model with the characteristics of impact basins on Mercury
(Section 3) shows many consistencies. First, Mercury has the
largest number of protobasins and peak-ring basins per area and
in total in the inner solar system, which is consistent with the
high mean velocities of its impacts (Table 1). For similar impactor
size-frequency fluxes for the inner planets (Strom et al., 2005), the
number of protobasin and peak-ring basins per area should, to
first order, increase with the mean impact velocity at the planet
because of the lower onset diameters for transitional morphologies for high-velocity impacts. Comparisons between the airless
bodies, Mercury and the Moon, affirm this prediction (Table 1).
Because of the higher mean impact velocities on Mercury,
impactors of a given size will produce approximately twice as
much melt on Mercury as on the Moon (Grieve and Cintala, 1992).
As a result, peak-ring basin formation will be more effective on
Mercury for smaller impactors, which are more numerous than
larger impactors. These differences in impact melt production are
likely to have contributed to the factor of 5 greater peak-ring basin
population per area observed on Mercury (9.9 10 7 per km2)
than on the Moon (1.8 10 7 per km2) (Table 1) (Head, 2010). Mars,
which has a surface gravitational acceleration comparable to that at
Mercury, also has a much lower mean impact velocity ( 1/4 that of
Mercury), which may contribute to its relatively small population of
peak-ring basins and protobasins. However, Mars has a smaller peakring basin onset diameter than Mercury (Table 1), whereas a larger
onset diameter would be expected due to the lower mean impact
velocity at Mars and the similar gravitational acceleration to that at
Mercury. The smaller onset diameter for peak-ring basins on Mars
than on Mercury has traditionally been attributed to the effect of
different target materials, including near-surface volatiles at Mars
(e.g., Pike, 1988; Melosh, 1989; Alexopoulos and McKinnon, 1994).
Mars is also anomalous in its large range of peak-ring basin diameters
(52–442 km), suggesting that additional parameters other than
gravity and impact velocity alone are influencing the Martian
population of peak-ring basins. We also note that erosion and
resurfacing effects, prevalent on Mars as well as on Venus, have
certainly influenced the observable populations of peak-ring basins
and protobasins on these planets. Therefore, although Mars does not
follow the predicted dependence of peak-ring basin onset diameter
versus mean impact velocity when compared to Mercury, interpretation of its peak-ring basin population in the context of the basin
populations on other planets must account for the possible effects of
differing target materials and incompleteness of its peak-ring basin
population.
Second, the continuum of interior morphologies observed
between protobasins and peak-ring basins on Mercury is consistent
with the diameter-dependent morphology progression predicted by
1941
the nested melt-cavity model. Under that model, the influence of
increasing melt volume and depth of impact melting becomes more
important with increasing basin size. This progression is observed
as smaller protobasins transition to larger peak-ring basins
(Figs. 4 and 5A). Within this transitional regime, uplifted central
peak material is suppressed by increasing depth of impact melting,
and the uplifted periphery of the melt cavity emerges as the
dominant interior morphology. Plots of ring/rim-crest diameter
ratio (Fig. 5A) also show that the transition between protobasins
and peak-ring basins is continuous and is not characterized by a
step-like change in process. Protobasin rim-crest diameters, however, overlap both the rim-crest diameters of the largest complex
craters with central peaks and rim-crest diameters of some peakring basins. This overlap is likely to be due to a number of
subsidiary factors affecting melt volumes, including target and
impactor properties and impact angle (Grieve and Cintala, 1992;
Cintala and Grieve, 1998; Pierazzo and Melosh, 2000). However,
under this model these factors act primarily to modify the more
general trend in the transition from protobasins to peak-ring basins,
which is influenced mainly by the kinetic energy of the impact
event and subsequent volume of melt produced.
Ringed peak-cluster basins do not appear to be a part of the
morphological continuum formed between protobasins and peakring basins (Fig. 4). Instead, the rings of ringed peak-cluster basins
follow the general trend for central peak basal diameters in
complex craters (Fig. 4). This similarity with the scaling relation
for complex craters on Mercury (Fig. 4A) suggests that ringed peakcluster basins form in an uplift-dominated regime (Section 4.2), in
which a melt cavity has not been fully developed. However,
detailed geologic mapping of the interior units of Eminescu, a
ringed peak-cluster basin, has shown that impact melt was likely
to have been integral to the development of the basin’s interior
morphology (Schon et al., this issue). We therefore suggest that
ringed peak-cluster basins form at the diameters appropriate to
large complex craters in situations where the depth of impact
melting has begun to penetrate the central portion of the uplift
structure. Thereafter, rebound of the displaced zone produces a
disaggregated ring-like array of central peak elements instead of a
single, large central peak. These ringed peak-cluster morphologies
differ from those of protobasins and peak-ring basins in that their
rings result from direct modification of the central uplift structure.
Therefore, we expect these rings to be similar in diameter to that
inferred from the basal diameter trend for central peaks in complex
craters (Fig. 4A). We view ringed peak-cluster basins as transitional
to protobasins and peak-ring basins due to their clear ring-like
interior features and because impact melting is of sufficient
volume to modify the interior morphology of these basin types
(for a more detailed description of the geology of these crater
forms see Schon et al., this issue)
In summary, relative differences in the depth of impact
melting due to nonlinear impact-melt scaling can account for
the onset of peak-ring formation, which is marked by a transition
in crater size between an uplift-dominated regime (by which
complex craters with central peaks and ringed peak-cluster basins
form) and an impact-melt-cavity-dominated regime (resulting in
protobasins and peak-ring basins). A continuous morphological
transition within the melt-cavity-dominated regime is observed
between protobasins and peak-ring basins, a trend consistent
with the predictions of the nested melt-cavity model.
Lastly, ring/rim-crest diameter ratios of protobasins and peakring basins increase nonlinearly with increasing basin rim-crest
diameter on Mercury (Fig. 5A). This phenomenon is predicted from
nonlinear scaling of impact melt volume (Grieve and Cintala, 1997;
Cintala and Grieve, 1998); increasingly more impact melting
and non-proportional growth of the interior melt cavity with
increasing crater size results in continuous, nonlinearly increasing
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D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
ring/rim-crest ratios with increasing basin rim-crest diameters.
A critical finding from the characteristics of basins on Mercury is
that the ring/rim-crest diameter ratio flattens out to an apparent
equilibrium value of about 0.5–0.6 for peak-ring basins (Fig. 3A).
This equilibrium value among peak-ring basins is also expressed as
a power-law trend in a log–log plot of ring diameter versus rimcrest diameter (Fig. 4).
The power-law trend for ring dimensions in peak-ring basins
(Fig. 4) is similar to the power-law relationship predicted by
growth of an interior melt cavity, as described by Eq. (2) above
(Grieve and Cintala, 1992). If we represent the melt cavity by a
hemisphere, then the volume of melt in the cavity may be related
to the diameter of the melt cavity as follows:
1
Vm ¼ 12
pD3
ð3Þ
If we assume that the diameter of the hemisphere (D)
approximately equals the diameter of the peak ring (Dring), we
may equate Eqs. (3) and (2) to find an expression for Dring:
Dring ¼
12 1=3
c
ðDtc Þd=3
p
ð4Þ
We seek to relate Dring to the final basin rim-crest diameter
(Dr). The transient cavity diameter may be approximated by a
scaling relationship for transient crater modification of the form:
Dtc ffi aDbr
ð5Þ
The values for the constants a and b are dependent on
the method used to derive Eq. (5). We use the constants of
Croft (1985) [a ¼(Dsc)0.15 7 0.04 and b ¼0.8570.04] and Holsapple
(1993) [a ¼0.980(Dsc)0.079 and b ¼0.921], which were derived
largely from lunar and terrestrial data. Both of the scaling
relationships for transient crater modification include a transition
diameter from simple to complex craters (Dsc) appropriate to
Mercury (10.374 km, Pike, 1988), which tailors the relationship
to planetary-specific variables such as gravity and target strength.
Holsapple (1993) also included two relationships that account for
the transient rim-crest diameter and the transient excavation
diameter. We use the transient rim-crest diameter relationship
for consistency with Eq. (2).
Combining Eq. (5) with Eq. (4), we find a power-law expression for the ring diameter as a function of the rim-crest diameter
of the final crater:
Dring ¼ ADpr
ð6Þ
where A ¼ ð12c=pÞ1=3 ðad Þ1=3 and p ¼ ðbd=3Þ.
Eq. (6) is the power-law relationship between peak-ring
diameter and crater rim-crest diameter as predicted for hemispherical growth of an impact melt cavity. Power-law fits for
peak-ring basins and protobasins on Mercury (Fig. 4) follow the
same form (Eq. (1)), and the values for the constants A and p
determined from these fits (Table 2) may be directly compared
with the predicted values from the melt-cavity model. The values
for A in Eq. (6) are dependent on the chosen values for the
constant c in Eq. (2) and the values for a in the scaling relationships for transient crater modification (Eq. (5)). The values for c
have been determined for specific target and impactor properties
and impact velocities (Grieve and Cintala, 1992). For Mercury, we
take c¼2.00 10 4 and d ¼3.83, which are appropriate to an
anorthositic target composition, a chondritic impactor, and an
impact velocity of 40 km/s (M.J. Cintala, personal communication,
2010). These values for c and d also account for the volume of the
melt cavity that is vaporized during impact, which, when factored
into the calculations, can increase the total volume of the
melt cavity by 20–30% from a melt-only calculation of volume
(M.J. Cintala, personal communication, 2010). Under these
assumptions, the value for the constant A in Eq. (6) ranges from
0.12 to 0.17 with the Croft (1985) scaling and from 0.11 to 0.12
with the Holsapple (1993) scaling. These ranges fall within the
uncertainty in A values determined from power-law fits for the
binned and unbinned peak-ring basin and protobasin data on
Mercury (Fig. 7).
More important than the value for A is the exponent, p, in
Eq. (6), which represents the slope of the power-law trend for the
model. The power-law fit to the unbinned data for peak-ring
basins on Mercury (Fig. 4A) gives a narrow range for the values of
p (1.03–1.23), which nearly completely overlaps the predicted
values of the modeled trend with either the Croft (1985) scaling
(1.03–1.14) or the Holsapple (1993) scaling (1.18) (Fig. 7). The
power-law fit to the binned data for peak-ring basins (Fig. 4B) is
Fig. 7. Ranges in values for the coefficient A (left) and the slope p (right) in the power-law relation described by Eq. (6). Values shown for the melt-cavity model use the
scaling of transient crater modification by Croft (1985) (black triangle) or Holsapple (1993) (open diamond). Dashed vertical lines delimit the range of values determined
from the model. Ranges in values determined from power laws fit to the unbinned and binned diameter data for peak-ring basins (open and filled circles) and protobasins
(Z 90 km in rim-crest diameter) (open and filled squares) (see Table 2 for specific values) are also shown. There is substantial overlap between the modeled values and the
values derived from observed basin geometry, consistent with peak-ring formation by growth of an interior melt cavity. Protobasins have values that also overlap the
modeled values, but the larger ranges introduce greater uncertainty in interpretation.
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
comparable to that for the unbinned data, albeit with a larger
range of p values (0.98–1.28) (Fig. 7). Power-law fits to the
protobasin data ( Z90 km in rim-crest diameter) yield even larger
ranges of p values, which are the result of greater scatter in the
data and overall smaller number of protobasins (Fig. 4A). Both the
binned and unbinned protobasin data have ranges in p values that
overlap the predicted values from the model but with greater
uncertainty (Fig. 7)
To first order, the good agreement between the scaling relationships for the melt-cavity model (Eq. 6) and for peak-ring basins on
Mercury suggests that peak-ring diameters may be related to
expansion of an interior melt cavity with increasing basin size.
Although a hemispherical melt cavity was assumed, a hemispherical
shape is not required by the model. Differing melt-cavity shapes
(e.g., paraboloidal) will act to decrease or increase the values of A in
Eq. (6), with the value of p remaining constant in each case. The
greater scatter and anomalously small ring diameters for protobasins at rim-crest diameters o90 km (Fig. 4A) are likely due to
non-uniform growth in the melt cavity during the initial phases of
melt cavity development. For protobasins, the melt cavity may grow
more laterally than vertically with increasing crater diameter, as
indicated by their increasing ring/rim-crest diameter ratios (Fig. 5A).
These ring/rim-crest diameter ratios then flatten to a near-constant
value at peak-ring basin diameters, indicating a transition to more
uniform growth of the melt cavity.
In summary, the predictions of the nested melt-cavity model
are generally consistent with the morphological characteristics of
peak-ring basins and protobasins on Mercury. This, in combination with detailed geological mapping of basins transitional to
peak-ring basins (Schon et al., this issue), supports a model in
which nonlinear scaling of impact melt volume and depth of
melting and development of a nested melt cavity are controlling
factors in the formation of peak-ring basins. However, it is
important to note that these observations warrant a more
thorough analysis with advanced modeling techniques. In particular, an improved understanding of how the volume of impact
melt is expressed geometrically and affects the development of
peak rings during the impact event is needed.
Variations in the impact-cratering process (e.g., projectile composition, velocity, angle of incidence) and in the substrate (e.g., composition, coherence) may account for some of the scatter about these
basic trends for Mercury (Figs. 4 and 5) and among planets. The
general physical model as described in detail by Cintala and Grieve
(1998) is based on the assumption that impacts are vertical. Oblique
impacts are much more likely, however, and more recent modeling
has shown that oblique impacts can markedly decrease the amount
of impact melt produced (Pierazzo and Melosh, 2000). Impactor and
target properties, including density, composition, volatile content, and
surface temperature, can also affect the degree of impact melting
(Grieve and Cintala, 1997; Cintala and Grieve, 1998). These variations
may be responsible for local scatter in the general curved ring/rimcrest diameter ratio trend observed for individual planets in Fig. 5.
Despite the variations caused by these factors, they do not appear to
obscure the general morphological trends in the data for basins on
Mercury.
Interplanetary comparisons are more complicated due to
major differences in surface temperature (compare Venus and
Mars) (Grieve and Cintala, 1997) and volatile content (compare
the Moon and Mars) (Schultz, 1988) as well as general differences
in target properties. These factors, although important in determining impact melt production, are likely to be subsidiary to the
dominant role of kinetic energy and thus impact velocity (Grieve
and Cintala, 1997). Also, impact angle is likely to follow a similar
distribution for each of the terrestrial planets, so this quantity
should not affect relative differences in the peak-ring basin
populations of each planet.
1943
5. Conclusions
On the basis of nearly complete global image coverage of
Mercury from MESSENGER flyby images and Mariner 10 images,
we have expanded and updated previous catalogs of peak-ring
basins and protobasins on Mercury (Fig. 1). We have identified an
additional 44 peak-ring basins and 17 protobasins, bringing their
totals to 74 and 32, respectively, an increase of 150% and
100% from previous catalogs (Table 1 and Appendix A, Tables
A1 and A2). An additional nine ringed peak-cluster basins with
comparatively small rim-crest and peak-ring diameters were also
identified (Appendix A, Table A3).
Results from our analysis of this new catalog strengthen some
previous findings and emphasize some important new observations of peak-ring basins and other transitional basin morphologies on Mercury:
1. Mercury has the largest number of peak-ring basins and
protobasins per area of the terrestrial planets, with a number
per area a factor of 5 larger than that of the Moon (Table 1).
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). The new basin catalog places the onset diameter
þ 33
for peak-ring basins at 12626
km.
3. Plots of ring/rim-crest diameter ratios (Fig. 5A) suggest that
protobasins and peak-ring basins are part of a continuum of
basin morphologies and should be considered collectively
when evaluating ring formation models, contrary to the view
of Pike (1988).
4. The ratio of ring/rim-crest diameters for the continuum from
protobasins to peak-ring basins increases nonlinearly with
increasing basin rim-crest diameter (Fig. 5A).
5. The morphologic trends of ringed peak-cluster basins
(Figs. 4 and 5A) appear distinct from those of protobasins
and peak-ring basins but share similarities with the largest
complex craters on Mercury. That ringed peak-cluster basins
have small but well-defined interior rings and rim-crest
diameters that overlap with the rim-crest diameters of protobasins and peak-ring basins suggest that they are unique
transitional forms and should be a focus of detailed geological
studies (e.g., Schon et al., this issue).
Evaluation of the characteristics of impact basins on Mercury in
the context of peak-ring basin formation models suggests an
overall consistency with a nested melt-cavity model (Cintala and
Grieve, 1998; Head, 2010). Although hydrodynamic collapse of an
unstable central peak has been widely used to model basin and
peak-ring formation (Melosh, 1989; Collins et al., 2002; Ivanov,
2005), current hydrocodes are unable to make explicit predictions
of ring and rim-crest diameter systematics. Such predictions are
warranted so that they may be tested with the current catalogs of
large impact structures on planetary bodies. The similarity
between the scaling relationship between peak-ring and basin
diameters (Eq. 1, Fig. 7) and that between melt cavity and basin
diameters (Eq. (6)) is consistent with the hypothesis that the
formation of peak rings is closely tied to impact-melt production
and development of an interior melt cavity. The flattening of the
ratio of ring/rim-crest diameters for large basin diameters may be
due to more uniform growth of an interior melt cavity at these
basin diameters. Further understanding of the significance of
impact melting and the validity of the nested melt-cavity model
may be gained from comparisons of terrestrial impact structures,
more detailed examination of Mercury’s basin population,
and advanced dynamical models of the evolution of impact melt
and its effects on the formation of peak rings during the cratering
event.
1944
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
6. Implications for future work
More detailed analysis of surface landforms on Mercury awaits the
planned insertion of the MESSENGER spacecraft into orbit about the
innermost planet in March 2011. New observations of Mercury’s
surface, including higher-resolution, lower-Sun images and global
topography from laser altimetry data (Zuber et al., 2008) and stereoderived digital terrain models (Preusker et al., 2010) will provide
substantial improvements over the current flyby data. Particular areas
of focus during MESSENGER’s orbital phase should include: (1) validating and updating the current protobasin and peak-ring basin
catalog using low-Sun images with higher resolution than those
obtained during the flybys, (2) re-examination of ring designations for
multi-ring basins with topography and low-Sun images, and
(3) examination of the detailed topography of basin interiors, including the heights of central peaks and peak rings and the relative
elevations exterior and interior to peak rings. MESSENGER, and the
later BepiColombo mission (Benkhoff et al., 2010), should provide a
definitive characterization of both fresh and modified craters and
basins and a global dataset illustrating the relationships among crater
forms from complex craters to ringed basins.
We also note that there are currently inconsistencies in the
protobasin and peak-ring basin catalogs for the Moon and Mars,
which should be updated to facilitate interplanetary comparisons
(e.g., Baker et al., 2010). New data from the Lunar Reconnaissance
Orbiter, including global, higher-resolution topography (e.g., Smith
et al., 2010) and new images, and the current plethora of Mars
orbital data, should greatly aid in this endeavor. Although there has
been much improvement in our understanding of multi-ring and
peak-ring basin formation on terrestrial planetary bodies, many
outstanding questions remain. Many of these questions should be
resolved with improved catalogs of impact basins obtained from
new spacecraft data combined with numerical modeling and field
studies of terrestrial impact structures.
Acknowledgements
We thank Seth Kadish and Caleb Fassett for use of their crater
catalog and for helpful discussions about the crater population of
Mercury. We also thank Mark Cintala for a constructive review of
the manuscript and for providing the constants used in the model
calculations. Constructive comments and suggestions from two
anonymous reviewers are appreciated. Discussions and reviews
from the MESSENGER team aided in improving the manuscript.
The MESSENGER project is supported by the NASA Discovery
Program under contracts NASW-00002 to the Carnegie Institution
of Washington and NAS5-97271 to the Johns Hopkins University
Applied Physics Laboratory.
Appendix A
Catalogs of all peak-ring basins, protobasins, and ringed peakcluster basins on Mercury compiled in the present study are
presented in Tables A1–A3, respectively. Images of each basin are
also included as online supplementary material.
Appendix B. Calculating peak-ring basin onset diameters
The ‘‘onset diameter’’ for peak-ring basins has been defined in a
variety of ways; see the extensive discussion of this topic by Pike
Table A1
Peak-ring basins on Mercury and their rim-crest and ring diameters. Peak-ring basins are characterized by a single interior topographic ring or a discontinuous ring of
peaks with no central peak.
Number
Namea
Long.b
Lat.
Rim
crest (km)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
–
–
–
–
Polygnotus
Ahmad Baba
–
–
–
Botticelli
Sōtatsu
–
Scarlatti
Mark Twain
–
–
–
–
Handel
Wang Meng
Kipling
–
–
–
–
Al-Hamadhani
–
–
–
–
North Pole Basin*
–
173.17
251.43
115.45
286.24
290.58
231.48
1.14
118.01
251.61
248.11
341.95
77.51
258.77
221.90
306.63
293.06
120.45
55.69
325.66
255.81
72.27
60.36
274.11
45.17
253.55
268.02
70.06
190.80
168.57
13.13
182.44
321.28
16.73
42.59
34.41
1.02
0.03
58.26
46.76
56.54
18.43
63.56
48.63
66.89
40.45
11.08
18.71
32.76
73.44
14.56
3.57
8.59
19.55
66.86
12.33
17.41
26.38
38.88
14.05
48.21
45.44
56.70
83.83
70.41
84
96
102
105
121
124
133
133
137
139
145
145
145
146
148
154
154
156
158
159
159
159
160
163
163
163
165
167
167
168
169
169
Ring (km)
43
42
37
49
56
63
57
73
65
72
78
66
67
81
78
76
64
86
71
84
69
83
92
87
78
74
81
74
85
92
85
47
Ring/Rim-crest
ratio
Ring typec
Ring
completiond
Pike (1988)
basin?e
0.51
0.44
0.37
0.46
0.46
0.51
0.43
0.54
0.47
0.51
0.54
0.45
0.46
0.56
0.53
0.49
0.42
0.55
0.45
0.53
0.43
0.52
0.57
0.54
0.48
0.45
0.49
0.44
0.51
0.55
0.50
0.28
Wrinkle ridge
Scarp
Common
Common
Common
Common
Common
Common
Scarp
Common
Wrinkle ridge
Common
Scarp
Common
Scarp
Common
Common
Scarp
Common
Common
Scarp
Common
Common
Common
Common
Common
Common
Wrinkle ridge
Common
Common
Common
Common
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
n
n
n
y
n
y
n
n
n
y
y
n
y
y
n
n
n
n
y
y
n
n
n
n
n
y
n
y
n
n
y
n
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
1945
Table A1 (continued )
Number
Namea
Long.b
Lat.
Rim
crest (km)
Ring (km)
Ring/Rim-crest
ratio
Ring typec
Ring
completiond
Pike (1988)
basin?e
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
–
–
–
–
–
–
Steichen
Munkácsy
Strindberg
–
–
Dürer
Praxiteles
–
Chekhov
–
–
–
Copland
Vālmiki
Ma Chih-Yuan
Wren
Cervantes
Vivaldi
Renoir
Bach
Surikov
Shelley-Delacroix Basin*
–
Dorsum Schiaparelli Basin*
–
Rodin
Mozart
–
Michelangelo
Hitomaro Basin*
Raditladi
–
Rachmaninoff
Vyāsa
–
Homer
280.84
320.50
49.49
318.08
111.07
156.70
77.10
101.01
223.36
83.33
91.59
240.75
299.51
289.84
298.65
87.06
82.32
108.47
73.56
218.62
282.69
324.00
236.14
273.85
308.05
256.95
234.98
223.88
102.99
194.27
94.17
341.13
169.64
238.60
249.87
345.45
119.05
83.69
57.52
275.08
101.78
322.84
34.82
55.69
36.51
61.13
45.29
35.60
13.10
21.93
53.23
52.20
38.78
21.50
27.09
43.35
36.30
3.05
8.25
60.14
37.48
23.66
60.44
24.70
76.05
13.55
18.40
69.90
37.04
48.34
10.52
16.80
62.02
21.76
7.68
4.81
45.09
15.84
27.05
5.50
27.67
49.82
70.23
1.00
171
171
172
172
172
174
177
184
187
188
191
192
192
194
194
195
198
200
203
206
206
207
208
212
214
215
219
221
225
227
230
234
236
238
243
256
263
288
292
306
311
320
86
97
82
74
62
88
93
90
92
82
99
93
102
89
98
109
114
124
92
102
96
123
107
104
115
106
114
107
127
119
109
122
125
139
120
122
130
120
144
192
159
186
0.51
0.56
0.48
0.43
0.36
0.51
0.53
0.49
0.49
0.44
0.52
0.48
0.53
0.46
0.51
0.56
0.58
0.62
0.45
0.50
0.46
0.59
0.51
0.49
0.54
0.49
0.52
0.48
0.56
0.52
0.47
0.52
0.53
0.58
0.49
0.47
0.49
0.42
0.49
0.63
0.51
0.58
Common
Common
Common
Common
Scarp
Common
Common
Wrinkle ridge
Common
Common
Common
Common
Common
Common
Common
Common
Common
Common
Wrinkle ridge
Common
Common
Common
Common
Common
Common
Common
Common
Common
Common
Common
Common
common
Common
Common
Common
Common
Common
Common
Common
Common
Wrinkle ridge
Common
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
n
n
n
n
n
n
n
n
y
n
n
y
n
n
y
n
n
n
n
y
y
y
y
y
y
y
y
y
n
y
n
y
y
n
y
y
n
n
n
y
n
y
a
Names shown for basins are those approved by the IAU (http://planetarynames.wr.usgs.gov) as of this writing. Names not approved by the IAU, but used by Pike
(1988), are denoted by an asterisk (*).
b
Longitudes are positive eastward. Note that this convention is opposite from that used by Pike (1988).
c
Three ring types are observed (see also Fig. 3). Common rings are the most frequent, and are characterized by a continuous topographic ring or semi-continuous ring
of peaks. Scarp rings exhibit a scarp face that separates a higher exterior topographic bench from an interior topographic low. Wrinkle-ridge rings are defined by a single
circular wrinkle ridge within a basin that has been nearly completely infilled by smooth plains material.
d
1¼ rings with 41801 arc, 2¼ rings with o 1801 arc.
e
y¼ basin cataloged by Pike (1988), n¼basin newly cataloged in this study.
(1983b, 1988). Some workers have defined the onset diameter of a
given crater morphological form as the minimum diameter of the
population of craters with that morphology (Wood and Head,
1976; Alexopoulos and McKinnon, 1994). This definition places
the onset diameters for peak-ring basins at 84 km (Mercury),
320 km (Moon), 52 km (Mars), and 31 km (Venus). This method
does not yield a stable statistic, however, as it relies on the outliers
of a given population. One statistical basis for defining onset
diameter from a single population would be to select a given
percentile of the population; the 5th percentile, for instance, would
give values of 116 km (Mercury), 322 km (Moon), 56 km (Mars),
and 33 km (Venus) for the onset diameter of peak-ring basins.
Other researchers have defined the onset diameter as the diameter
range over which more than one morphology can be found (as in
the crater to basin transition; Pike, 1988) or the diameter above
which one morphological form outnumbers another (Schenk et al.,
2004). A benefit of these two methods for specifying onset
diameter is that the definition is directly related to the observed
morphological transition. These methods, however, would be
unworkable in situations where successive morphological forms
do not overlap in rim-crest diameter or for forms that are not
numerically dominant at any rim-crest diameter.
Here we choose a definition of onset diameter derived from the
range of diameters over which more than one basin morphological
type occurs (Table 1). In this method, the range of diameters is first
identified over which examples of two or more crater morphological
forms can both be found, and then the onset diameter is defined as
the geometric mean of the rim-crest diameters of all craters or basins
within this range (Table 1). This method is based on the presumption
that the onset diameter lies within the range of diameters over which
more than one morphology is observed on the planet for a given rimcrest diameter. A benefit of this method is that the onset diameter of
peak-ring basins is defined by the spectrum of basin morphologies in
the transition between complex craters and peak-ring basins and is
therefore related to the physical processes resulting in the onset of
interior basin rings. A second benefit is that the uncertainty in the
1946
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
Table A2
Protobasins on Mercury and their rim-crest, ring, and central peak diameters. Protobasins are characterized by the presence of both a central peak and an interior ring
of peaks.
Number
Namea
Long.b
Lat.
Rim
crest (km)
Ring (km)
Central
peak (km)
Ring/Rim-crest
ratio
Ring
completionc
Pike (1988)
basin?d
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
–
–
–
Dickens
–
Moody
–
Mansur
Aśvaghosa
–
–
Jókai
Repin
–
–
van Gogh
Equiano
Hitomaro
Atget
Lu Hsun
–
Brunelleschi
–
Abedin
Oskison
Velázquez
Hawthorne
Chŏng Chŏl
Zeami
Sinan
Verdi
Bernini
310.02
296.81
132.42
204.43
78.32
144.86
308.38
196.40
338.41
80.00
104.37
221.42
296.70
332.26
99.72
221.81
329.59
344.33
166.45
336.07
117.85
337.63
284.76
349.61
144.95
304.39
244.62
242.75
212.69
329.32
190.14
219.96
50.69
13.54
14.36
73.22
25.22
13.28
26.89
47.37
10.56
10.92
20.67
71.79
19.13
12.90
26.57
76.80
40.05
16.05
25.53
0.07
65.83
8.90
21.51
62.19
60.25
37.68
51.23
46.83
2.95
15.36
64.26
80.30
75
75
77
78
80
80
87
90
92
92
93
93
94
96
97
99
101
101
101
101
108
111
116
118
122
123
127
128
128
130
138
172
30
21
24
17
29
16
23
34
30
35
44
32
30
39
33
38
46
41
35
40
52
35
52
40
52
45
58
59
43
59
54
66
11
5
10
6
17
5
4
11
10
15
13
12
11
14
9
17
16
15
9
22
15
17
12
24
28
9
25
7
10
8
34
9
0.40
0.28
0.31
0.22
0.37
0.20
0.27
0.38
0.33
0.38
0.47
0.34
0.32
0.41
0.34
0.38
0.45
0.41
0.35
0.39
0.48
0.31
0.45
0.34
0.42
0.37
0.46
0.46
0.33
0.45
0.39
0.39
2
2
2
1
2
2
2
2
2
2
2
2
2
2
2
1
2
2
1
1
2
2
2
2
1
1
2
2
2
2
1
1
n
n
n
n
n
n
n
y
y
n
n
y
n
y
n
y
y
y
n
y
n
y
n
n
n
n
y
y
y
y
y
y
a
Names shown for basins are those approved by the IAU (http://planetarynames.wr.usgs.gov/) as of this writing.
Longitudes are positive eastward. Note that this convention is opposite from that used by Pike (1988).
1¼ rings with 41801 arc, 2¼ rings with o 1801 arc.
d
y¼basin cataloged by Pike (1988), n¼ basin newly cataloged in this study.
b
c
Table A3
Ringed peak-cluster basins on Mercury and their rim-crest and ring diameters. Ringed peak-cluster basins are characterized by a ring of central peak elements with a ring
diameter that is anomalously small compared with protobasins or peak-ring basins of the same rim-crest diameter.
Number
Namea
Long.b
Lat.
Rim crest (km)
Ring (km)
Ring/Rim-crest ratio
Ring completionc
1
2
3
4
5
6
7
8
9
~
Camoes
–
–
–
–
Amaral
–
Eminescu
–
292.07
309.17
72.53
267.66
76.29
117.70
121.41
114.09
280.38
71.30
69.07
21.23
30.10
3.92
26.64
18.95
10.68
52.16
73
81
82
84
95
101
111
123
133
16
15
19
15
21
18
22
22
30
0.22
0.19
0.23
0.18
0.22
0.17
0.20
0.18
0.23
1
2
1
1
1
1
2
1
2
a
Ringed peak-cluster basins were not included in the catalog of Pike (1988). Names shown for basins are those approved by the IAU (http://planetarynames.wr.usgs.
gov) as of this writing.
b
Longitudes are positive eastward. Note that this convention is opposite from that used by Pike (1988).
c
1¼ rings with 41801 arc, 2¼ rings with o 1801 arc.
estimated onset diameter is also derivable from the range of rim-crest
diameters over which multiple morphological forms are present. The
uncertainty in the onset diameter is given as one standard deviation
about the geometric mean, which is obtained by multiplying and
dividing the geometric mean by the geometric, or multiplicative,
standard deviation (Table 1). However, there are situations for some
bodies (e.g., the Moon) where distinct crater morphological forms
have little or no overlap in rim-crest diameter. In these cases, the
onset diameter would likely be somewhere between the maximum
diameter of the population with smaller rim-crest diameters and the
minimum diameter of the population with larger rim-crest diameters. Peak-ring basin and protobasin data used for the onset
diameter calculations are from this study (Mercury), Pike and
Spudis (1987) (Moon and Mars), and Alexopoulos and McKinnon
(1994) (Venus); complex crater rim-crest diameters 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 basins on the Moon do not overlap.
D.M.H. Baker et al. / Planetary and Space Science 59 (2011) 1932–1948
Appendix C. Supplementary material
Supplementary data associated with this article can be found
in the online version at doi:10.1016/j.pss.2011.05.010.
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