Icarus 214 (2011) 377–393
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Icarus
journal homepage: www.elsevier.com/locate/icarus
The transition from complex crater to peak-ring basin on the Moon: New
observations from the Lunar Orbiter Laser Altimeter (LOLA) instrument
David M.H. Baker a,⇑, James W. Head a, Caleb I. Fassett a, Seth J. Kadish a, Dave E. Smith b,c, Maria T. Zuber b,c,
Gregory A. Neumann b
a
b
c
Department of Geological Sciences, Brown University, Providence, RI 02912, United States
Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 208771, United States
Department of Earth, Atmospheric and Planetary Sciences, MIT, Cambridge, MA 02139, United States
a r t i c l e
i n f o
Article history:
Received 17 November 2010
Revised 15 April 2011
Accepted 23 May 2011
Available online 2 June 2011
Keywords:
Moon
Mercury
Cratering
Impact processes
a b s t r a c t
Impact craters on planetary bodies transition with increasing size from simple, to complex, to peak-ring
basins and finally to multi-ring basins. Important to understanding the relationship between complex
craters with central peaks and multi-ring basins is the analysis of protobasins (exhibiting a rim crest
and interior ring plus a central peak) and peak-ring basins (exhibiting a rim crest and an interior ring).
New data have permitted improved portrayal and classification of these transitional features on the
Moon. We used new 128 pixel/degree gridded topographic data from the Lunar Orbiter Laser Altimeter
(LOLA) instrument onboard the Lunar Reconnaissance Orbiter, combined with image mosaics, to conduct
a survey of craters >50 km in diameter on the Moon and to update the existing catalogs of lunar peak-ring
basins and protobasins. Our updated catalog includes 17 peak-ring basins (rim-crest diameters range
from 207 km to 582 km, geometric mean = 343 km) and 3 protobasins (137–170 km, geometric
mean = 157 km). Several basins inferred to be multi-ring basins in prior studies (Apollo, Moscoviense,
Grimaldi, Freundlich–Sharonov, Coulomb–Sarton, and Korolev) are now classified as peak-ring basins
due to their similarities with lunar peak-ring basin morphologies and absence of definitive topographic
ring structures greater than two in number. We also include in our catalog 23 craters exhibiting small
ring-like clusters of peaks (50–205 km, geometric mean = 81 km); one (Humboldt) exhibits a rim-crest
diameter and an interior morphology that may be uniquely transitional to the process of forming peak
rings. A power-law fit to ring diameters (Dring) and rim-crest diameters (Dr) of peak-ring basins on the
Moon [Dring = 0.14 ± 0.10(Dr)1.21±0.13] reveals a trend that is very similar to a power-law fit to peak-ring
basin diameters on Mercury [Dring = 0.25 ± 0.14(Drim)1.13±0.10] [Baker, D.M.H. et al. [2011]. Planet. Space
Sci., in press]. Plots of ring/rim-crest ratios versus rim-crest diameters for peak-ring basins and protobasins on the Moon also reveal a continuous, nonlinear trend that is similar to trends observed for Mercury
and Venus and suggest that protobasins and peak-ring basins are parts of a continuum of basin morphologies. The surface density of peak-ring basins on the Moon (4.5 107 per km2) is a factor of two less
than Mercury (9.9 107 per km2), which may be a function of their widely different mean impact velocities (19.4 km/s and 42.5 km/s, respectively) and differences in peak-ring basin onset diameters. New calculations of the onset diameter for peak-ring basins on the Moon and the terrestrial planets re-affirm
previous analyses that the Moon has the largest onset diameter for peak-ring basins in the inner Solar
System. Comparisons of the predictions of models for the formation of peak-ring basins with the characteristics of the new basin catalog for the Moon suggest that formation and modification of an interior
melt cavity and nonlinear scaling of impact melt volume with crater diameter provide important controls
on the development of peak rings. In particular, a power-law model of growth of an interior melt cavity
with increasing crater diameter is consistent with power-law fits to the peak-ring basin data for the
Moon and Mercury. We suggest that the relationship between the depth of melting and depth of the transient cavity offers a plausible control on the onset diameter and subsequent development of peak-ring
basins and also multi-ring basins, which is consistent with both planetary gravitational acceleration
and mean impact velocity being important in determining the onset of basin morphological forms on
the terrestrial planets.
Ó 2011 Elsevier Inc. All rights reserved.
⇑ Corresponding author. Address: Department of Geological Sciences, Brown
University, Box 1846, Providence, RI 02912, United States. Fax: +1 401 863 3978.
E-mail address: [email protected] (D.M.H. Baker).
0019-1035/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved.
doi:10.1016/j.icarus.2011.05.030
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D.M.H. Baker et al. / Icarus 214 (2011) 377–393
1. Introduction
Major lines of inquiry in the study of impact craters on the terrestrial planets over the past half-century have focused on the onset and
formation of multi-ring basins occurring at the largest crater diameters. Many hypotheses have been developed to explain the formation
of rings interior and exterior to the transient cavity of multi-ring basins, including frozen crustal tsunamis (Baldwin, 1981), differential
depths of excavation to form nested craters (Hodges and Wilhelms,
1978), the formation of exterior rings by mega-terracing (Head,
1974, 1977; Head et al., 2011), and gravity-driven collapse and formation of tectonic rings due to the contrasting strengths of the lithosphere and aesthenosphere (Melosh and McKinnon, 1978; Melosh,
1982, 1989; Collins et al., 2002). Although these models have provided much insight into the formation of large impact structures
on the terrestrial planets (e.g., Melosh, 1989; Spudis, 1993), there
is currently no consensus on how the rings of multi-ring basins form.
Important to understanding the mechanisms of multi-ring basin
formation have been analyses of peak-ring basins and other transitional morphologies between complex craters with central peaks
and multi-ring basins. Many crater catalogs of these basin types
have been produced (Wood and Head, 1976; Wood, 1980; Wilhelms
et al., 1987; Pike and Spudis, 1987; Pike, 1988; Spudis, 1993; Alexopoulos and McKinnon, 1994), which traditionally include measurements of major morphological features such as the diameter of the
crater’s rim crest, ring, and central peak. Trends in the ring and
rim-crest diameters of peak-ring basins have been used as evidence
to support a number of peak-ring basin formation models (Pike and
Spudis, 1987; Pike, 1988). However, the lack of complete population
data for peak-ring basins on the terrestrial planets due to limitations
in image and topographic resolution has inhibited accurate interpretations of the relationship between peak-ring basin morphologies
and the mechanisms of their formation. With the addition of new
and improved spacecraft data, it is important to update the existing
catalogs of craters and basins, including observations of their morphological characteristics. This is especially important for the airless
bodies, Mercury (Baker et al., 2011) and the Moon, where relatively
low erosion and resurfacing rates throughout geologic history have
preserved much of their basin populations. We use new topographic
data from the Lunar Orbiter Laser Altimeter (LOLA) (Smith et al.,
2010), in combination with a global Lunar Reconnaissance Orbiter
Camera (LROC) Wide Angle Camera (WAC) (Robinson et al., 2010)
image mosaic at 100 m/pixel resolution to update the current catalog of peak-ring basins and other basin morphologies in the transition from complex craters to multi-ring basins on the Moon. LOLA
currently provides gridded topography at better than 128 pixel/degree (235 m/pixel) resolution, a substantial improvement over
previous topographic data of the Moon, including the 8–30 km/pixel
resolution data from the Clementine Light Imaging Detection and
Ranging (LiDAR) instrument (Smith et al., 1997) and the 15 pixel/
degree resolution data from the Kaguya Laser Altimeter (Araki
et al., 2009). Our catalog of the lunar peak-ring basin and protobasin
populations, including measurements of basin rim-crest, ring, and
central-peak diameters, is then compared with catalogs on the other
terrestrial planets, including a recent, comprehensive catalog of
peak-ring basins and other transitional basins on Mercury (Baker
et al., 2011). We then use our lunar basin catalog to test the predictions of one basin formation model, which seeks to explain the formation of peak rings by modification of the crater interior from a
growing impact melt cavity.
2. The size-morphology progression
Transitional morphologies in the size progression from complex
craters to multi-ring basins have traditionally included at least two
classes of basins: peak-ring basins (or double-ring or two-ring basins) and protobasins (or central-peak basins) (Pike, 1988; Baker
et al., 2011). Peak-ring basins are the most numerous transitional
forms and their interior morphologies are characterized by a single,
continuous or semi-continuous interior ring of peaks with no central
peak. The lunar basin, Schrödinger, (rim-crest diameter, as measured in this study = 326 km) best exemplifies this morphology,
showing a nearly continuous ring of peaks (Fig. 1A). LOLA gridded
topography shows that Schrödinger has a depth of about 4 km with
a peak ring that is tens of kilometers in width and rises about 1 km
above the surrounding floor materials (Figs. 1A and 2A). Protobasins
posses both a central peak and an interior ring of peaks, but these
features are commonly smaller in diameter and have less topographic relief than either central peaks in complex craters and peak
rings in peak-ring basins (Pike, 1988). Antoniadi (rim-crest diameter, as measured in this study = 137 km) is a type example of a protobasin on the Moon (Fig. 1B). Its peak ring has less relief (200–
300 m) than the peak ring of Schrödinger, and it has a small, but
prominent central peak that rises above the surrounding peak ring
(Fig. 2B). However, the smoothness of Antoniadi’s interior suggests
that substantial infilling has occurred, which has certainly affected
the relative topography of its central peak and peak ring. A third class
of basins, called ringed peak-cluster basins, has also been identified
from analysis of recent flyby data of Mercury (Baker et al., 2011). Like
peak-ring basins, ringed peak-cluster basins have a single interior
ring of peaks without a central peak (Fig. 1C) and overlap in rim-crest
diameter with protobasins; however, the relatively small diameter
of their peak rings relative to their rim-crest diameter precludes
these basins from classification as traditional peak-ring basins. The
type example of a ringed peak-cluster basin on Mercury is the
125-km diameter crater, Eminescu, which exhibits a very well-defined interior ring (Schon et al., 2011). On the Moon, many craters
with small interior rings of central peak material are identified;
however, only one of these craters, Humboldt (rim-crest diameter,
as measured in this study = 205 km) overlaps in rim-crest diameter
with protobasins and is thus classified as a potential ringed peakcluster basin. Humboldt has a disaggregated ring-like array of central peak elements (Fig. 1C) that is nearly 1 km in relief (Fig. 2C). A
central depression in the middle of the array of peaks slopes steeply
to about 100 m below the fractured fill material that occupies the
floor of Humboldt (Fig. 2C).
3. Methods
There have been several comprehensive catalogs of basins on
the Moon (Wood and Head, 1976; Pike and Spudis, 1987; Wilhelms
et al., 1987; Spudis, 1993), which were based primarily on Apolloera data, including image data from the Lunar Orbiter and Apollo
Terrain Mapping Camera. While there are many similarities between these catalogs, there are some disagreements, particularly
with identification of multiple exterior and interior rings and central peak plus ring structures. We have elucidated the identification of protobasins and peak-ring basins by analyzing new Lunar
Orbiter Laser Altimeter (LOLA) (Smith et al., 2010) global gridded
topography and hillshade data at 128 pixel/degree (235 m/pixel)
resolution in combination with a Lunar Reconnaissance Orbiter
Camera (LROC) Wide Angle Camera (WAC) (Robinson et al.,
2010) global image mosaic at 100 m/pixel resolution. We also used
detrended LOLA gridded topography data to remove the effects of
long-wavelength topographic variations and to help emphasize local variations in topography such as peak rings. All craters on the
Moon greater than 50 km in diameter were analyzed in ArcGIS
(ESRI, www.esri.com) using a recent catalog of lunar craters (Head
et al., 2010) to ensure complete surveying of basin types. Particular
scrutiny was given to basins already cataloged, including many
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
379
Fig. 1. Examples of a peak-ring basin (A), protobasin (B), and ringed peak-cluster basin (C) on the Moon. Top panels show outlines of circle fits to the basin rim crest and
interior ring (dashed lines) on LOLA hillshade gridded topography. Bottom panels show LOLA colored gridded topography at 128 pixel/degree on LOLA hillshade gridded
topography. (A) Schrödinger (326 km; 133.53°E, 74.90°S), a peak-ring basin, exhibits a nearly continuous interior ring of peaks with no central peak. (B) Antoniadi (137 km;
187.04°E, 69.35°S), a protobasin, has a less prominent peak ring surrounding a small central peak. (C) Humboldt (205 km; 81.06°E, 27.12°S) is a ringed peak-cluster basin with
an incomplete, diminutive ring of central peak elements.
multi-ring basins where some ring designations were most uncertain (Pike and Spudis, 1987).
The diameters of basin features, including rim crests, rings, and
central peaks, were measured (where present) by visually fitting
circles to the features using the CraterTools extension in ArcGIS
(Kneissl et al., 2010). Circle-fits were carefully selected to best
approximate the mean diameter value for the features (Baker
et al., 2011) (Fig. 1). For example, peak rings were fit by a circle
intermediate between circles that inscribe and circumscribe the
peak ring. Fits to rim crests were defined by the most prominent
topographic divides along the crater rim crest. Central peaks were
the most difficult to measure due to their irregular outlines. For
those irregular central peaks, we chose circular fits that approximated a diameter that is intermediate between the maximum
and minimum areal dimensions of the feature (Baker et al., 2011)
(Fig. 1). As in previous catalogs, our confidence in the identification
and measurement of peak rings is presented as a scale from 1 (lowest) to 3 (highest) (Tables A1–A3). Most basins are cataloged with
the highest confidence, however, three peak-ring basins remain
more speculative due to incomplete preservation of interior morphologies or possible mis-interpretation of interior features as primary basin structure. The continuity of observable peak rings are
also designated as being greater than or less than 180° of arc (Tables A1–A3).
4. The basin catalog
Our catalog is a refinement of earlier catalogs of peak-ring
basins and protobasins on the Moon. We have excluded some
ambiguous basins and have re-classified several other basins, particularly those near the transition diameters between peak-ring
basins and protobasins and peak-ring basins and multi-ring basins.
These re-classifications largely reflect our improved ability to recognize genuine basin ring and central peak structures from new
LOLA topographic and image data. Our refined catalog includes
17 peak-ring basins (Table A1), 3 protobasins (Table A2), and 1
ringed peak-cluster basin (Table A3). LOLA gridded topography
images of each basin in Tables A1–A3 are also included as online
supplementary material. Twenty-two craters exhibiting ring-like
arrangements of central peak elements are also cataloged
(Table A3), but are not classified as ringed peak-cluster basins
due to their small (<114 km) rim-crest diameters that fall below
the transitional rim-crest diameter range between complex craters
and peak-ring basins (see discussion in Section 6.1). All of the
peak-ring basins and protobasins cataloged in this study have appeared in earlier catalogs, but have been variously classified as one
or multiple basin types based on the available data at the time the
catalogs were generated.
Our peak-ring basin catalog includes five basins that have been
previously classified as multi-ring basins by Pike and Spudis
(1987): Apollo, Moscoviense, Grimaldi, Coulomb–Sarton, and Korolev. Our catalog also includes Freundlich–Sharonov, which was recognized as a candidate multi-ring basin but with only one 600-km
diameter ring identified (Wilhelms et al., 1987; Spudis, 1993).
Upon careful examination of LOLA topographic data (Fig. 3), we
find that all of these basins are fit best by no more than two topographic rings. For example, a possible ring exterior to Apollo
(Fig. 3A) appears to be associated with the rim structure of South
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D.M.H. Baker et al. / Icarus 214 (2011) 377–393
Fig. 2. Radially averaged LOLA topographic profiles of Schrödinger (A), Antoniadi
(B), and Humboldt (C) (see Fig. 1 for locations). After Head et al. (2011), the profiles
were calculated by averaging 360 great circle transects radiating from the basins’
centers and separated by 1° of azimuth. The topography along each of the 360
transects was calculated using a bilinear interpolation with the number of data
points set to equal the 16 pixel/degree resolution of the LOLA data used for the
profiles.
Pole Aitken basin and is not concentric to Apollo’s main topographic rings. Moscoviense (Fig. 3B) has been traditionally interpreted to be a multi-ring basin (e.g., Pike and Spudis, 1987) due
to the presence of three concentric but off-centered ring structures.
The offset characteristic of the three rings of Moscoviense to the
southwest has suggested that Moscoviense may have formed from
an oblique impact (see discussion in Thaisen et al. (2011)). However, a survey of offset peak rings in basins on Venus, for which impact direction could be inferred from ejecta patterns, determined
that there was no correlation between ring offset and direction
of impactor approach (McDonald et al., 2008). It was suggested
that other parameters, such as target rock heterogeneities likely
contributed to the offset ring characteristics of these peak rings
on Venus. Furthermore, the effects of oblique impacts on basin
morphology, especially on the scale of multi-ring basins are still
poorly understood (Pierazzo and Melosh, 2000). Alternatively, we
favor a scenario whereby the inner two rings of Moscoviense represent a peak-ring basin superposed on a larger, older impact basin
(e.g., Ishihara et al., 2011; Thaisen et al., 2011). Several geophysical
and morphological characteristics of Moscoviense support a superposed impact scenario. First, the anomalously thin crust and high
gravity of Moscoviense is more easily explained by double impacts
than a single oblique impact (Ishihara et al., 2011). Second, the
prominence and regular outline of the intermediate ring appears
much more analogous to a basin rim-crest compared to the more
plateau-like, irregular topography of the intermediate rings in multi-ring basins such as Orientale (Head et al., 2011). Finally, the
innermost ring of Moscoviense is very prominent and sharp, sharing many similarities with other peak-ring basins on the Moon
(Figs. 1A and 2A). Several of the basins (e.g., Grimaldi, Fig. 3C,
and Freundlich–Sharonov, Fig. 3D) exhibit central depressions that
have been classified as potential ring structures (Pike and Spudis,
1987). While these depressions may be related to the basin formation process, they are also interior to and are morphologically distinct from peak rings, which have more circular planform shapes
and a distinct topographic signature that is raised above the surrounding basin floor material (Fig. 2A). We therefore do not include
the rims of these depressions as separate rings in our catalog. Due
to its highly degraded nature, our classification of Coulomb–Sarton
(Fig. 3E) is the most uncertain of the large basins. However, we find
that the observed impact structure can be best fit by two rings that
are consistent with the rim-crest and ring diameters of other peakring basins on the Moon. The most uncertain basins in our catalog
should be a focus during re-examinations using even higher resolution data or improved techniques. Lastly, in contrast to Pike
and Spudis (1987), we do not include Amundsen–Ganswindt in
our peak-ring basin catalog, as the irregular interior topography
of the basin does not resemble a ring and is likely to be modified
ejecta material.
Our catalog includes three protobasins, two of which, Antoniadi
and Compton, are unambiguous examples of basins exhibiting a
central peak surrounded by an interior ring of peaks. We also include the crater, Hausen, in our catalog. While the interior ring of
Hausen is not as well defined as those of Antoniadi and Compton,
an incipient ring is observed. The subtlety of Hausen’s ring topography may be related to the size of the central peak, as there appears to be a correlation between size of the central peak and
prominence of the interior ring (Pike, 1988). Hausen exhibits the
largest central peak and least pronounced ring and Antoniadi
exhibits the smallest central peak and the most topographically
prominent ring (although the center of Antoniadi has been flooded
by mare deposits (Fig. 1B), likely reducing the relief of its central
peak and peak ring). Although the lunar protobasin population is
very small, this correlation between central peak size and ring
prominence and size is consistent with observations of the more
numerous protobasin population on Mercury (Pike, 1988). Pike
and Spudis (1987) include three other craters, Campbell, Fermi,
Hipparchus, and Mendeleev in their protobasin catalog. With the
exception of Mendeleev, we do not observe topographic rings in
all of these craters in the new LOLA topography. For Mendeleev,
we observe an interior ring but do not observe a central peak structure; Mendeleev is therefore classified as a peak-ring basin in our
catalog. Pike and Spudis (1987) also include craters exhibiting relatively small ring/rim-crest ratios as potential protobasins
(although central peak structures were not directly observed in
these craters, possibly due to the effects of resurfacing or erosion).
However, ring/rim-crest ratios alone cannot be used to recognize
protobasins because the trends of ring and rim-crest diameters of
protobasins appear statistically indistinguishable from peak-ring
basins (Baker et al., 2011). Of the potential protobasins cataloged
by Pike and Spudis (1987), we include Bailly, Milne, and Schwarzschild in our peak-ring basin catalog due to the presence of a
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
381
Fig. 3. Large peak-ring basins on the Moon previously inferred to be multi-ring basins (Wilhelms et al., 1987; Pike and Spudis, 1987; Spudis, 1993). Left panels show dashed
outlines of the observed basin rim crest and ring on a Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) image mosaic. Middle panels show LOLA
colored gridded topography at 128 pixel/degree on LOLA hillshade gridded topography. Right panels show detrended LOLA topography maps. (A) Apollo (492 km; 208.28°E,
36.07°S). (B) Moscoviense (421 km; 147.36°E, 26.34°N). (C) Grimaldi (460 km; 291.31°E, 5.01°S). (D) Freundlich–Sharonov (582 km; 175.00°E, 18.35°N). (E) Coulomb–Sarton
(316 km; 237.47°E, 51.35°N). (F) Korolev (417 km; 202.53°E, 4.44°S). See text (Section 4) for a discussion of the ring designations of the basins.
prominent interior ring and no observable central peak. While it is
still possible that small central peaks within these structures have
been erased by resurfacing processes, the absence of a central peak
precludes them from being classified as a protobasin in our catalog.
We do not observe interior rings or central peaks for the remaining
possible protobasins classified by Pike and Spudis (1987).
Ringed peak-cluster basins have not been included in previous
basin catalogs of the Moon. From analyses of recent flyby images
of Mercury, Schon et al. (2011) and Baker et al. (2011) interpret
at least some ringed peak-cluster craters to be transitional types
between complex craters possessing central peaks and peak-ring
basins. Support for such a transitional morphology included overlap between the rim-crest diameters of ringed peak-cluster basins
with rim-crest diameters of protobasins and small peak-ring basins, the clear ring-like morphology of the peak elements (ringed
peak clusters), and similar trends between the diameters of ringed
peak clusters and central peak diameters in complex craters. These
trends, as well as geological mapping, led the authors to suggest
that ringed peak clusters are the product of early development of
a melt cavity that directly modifies the centers of central uplift
structures. While at least 23 craters >50 km in diameter on the
Moon exhibit interior morphologies with ring-like central peaks
(Table A3), the diameter range for these craters is large (50–
205 km, with all but one between 50 and 114 km) and only one,
Humboldt, has a rim-crest diameter (205 km) that overlaps with
the rim-crest diameters of protobasins. It is therefore likely that
most ring-like central peak structures do not represent unique
transitional types in the size-morphology progression from complex craters to peak-ring basins. The association of ring-like central
peaks with floor-fractured craters has led to the interpretation that
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D.M.H. Baker et al. / Icarus 214 (2011) 377–393
Fig. 3 (continued)
some ring-like central peaks result from collapse of the innermost
portions of the central peak structure during magmatic intrusion
(Schultz, 1976). Regardless of their origin, the small (<114 km)
rim-crest diameters over which most craters with ring-like central
peaks occur on the Moon suggest that their development is not related to the peak-ring basin forming process. Humboldt, classified
here as the only ringed peak-cluster basin on the Moon, is more
likely to be a unique transitional basin type; however, the fractured fill that occupies Humboldt’s floor suggests similarities with
floor-fractured craters at smaller rim-crest diameters.
5. New basin statistics
Based on our new rim-crest measurements, we have revised the
general statistics for peak-ring basins and protobasins on the Moon
(Table 1). The rim-crest diameters of peak-ring basins range from
207 to 582 km, with a geometric mean diameter of 343 km. Our
peak-ring basin data have a much larger rim-crest diameter range
than the 320–365 km range from Pike and Spudis (1987) and has a
smaller geometric mean rim-crest diameter compared to the mean
rim-crest diameter of 335 km from Pike and Spudis (1987). The
three protobasins in our catalog give a range from 137 to 170 km
with a geometric mean of 157 km, compared to the larger range
of values (135–365 km) and larger geometric mean rim-crest
diameter (204 km) for protobasins in the catalog of Pike and Spudis
(1987).
Using our new basin catalog, we also calculate the onset diameter for peak-ring basins on the Moon. The term ‘‘onset diameter’’
has been defined loosely in previous studies; examples of such
usage include the minimum diameter of a population or the diameter at which one crater morphology outnumbers another (see discussions in Pike (1983, 1988) and Baker et al. (2011)). In an
analysis of basins on Mercury, Baker et al. (2011) chose to calculate
the onset diameter for peak-ring basins based on the rim-crest
diameter range where multiple crater morphologies overlap. In
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Table 1
Statistics of planetary parameters and of peak-ring basins, protobasins, and ringed peak-cluster basins on the Moon (this study, Tables A1–A3), Mercury (Baker et al., 2011), Mars
(Pike and Spudis, 1987), and Venus (Alexopoulos and McKinnon, 1994). This table is reproduced from Table 1 of Baker et al. (2011), and is updated using our new lunar basin
catalog (Tables A1–A3).
Moona
Mercuryb
Marsc
Venusd
Gravitational acceleration (m/s )
Surface area (km2)
Mean impact velocitye (km/s)
1.62
3.8 107
19.4
3.70
7.5 107
42.5
3.69
1.4 108
10.6
8.87
4.6 108
25.2
Peak-ring basins (Npr)
Npr/km2
Geometric mean diameter (km)
Minimum diameter (km)
Maximum diameter (km)
Onset diameter, method 1f (km)
Onset diameter, method 2g (km)
17
4.5 107
343
207
582
206
227
74
9.9 107
180
84
320
126 + 33/26
116
15
1.0 107
140
52
442
80 + 29/21
56
66
1.4 107
57
31
109
42 + 10/8
33
Protobasins (Nproto)
Nproto/km2
Geometric mean diameter (km)
Minimum diameter (km)
Maximum diameter (km)
3
7.9 108
157
137
170
32
4.3 107
102
75
172
7
4.9 108
118
64
153
6
1.3 108
62
53
70
Ringed peak-cluster (Nrpc)
Nrpc/km2
Geometric mean diameter (km)
Minimum diameter (km)
Maximum diameter (km)
1
2.6 108
–
–
–
9
1.2 107
96
73
133
–
–
–
–
–
–
–
–
–
–
2
a
Basin data from this study (Tables A1–A3).
Basin data from Baker et al. (2011).
c
Basin data from Pike and Spudis (1987).
d
Basin data from Alexopoulos and McKinnon (1994). Calculations exclude the suspected multi-ring basins Klenova, Meitner, Mead, and Isabella.
e
Mean impact velocity from Le Feuvre and Wieczorek (2008).
f
After Baker et al. (2011). Peak-ring basin onset diameters determined by first identifying the range of diameters over which examples of two or more crater morphological
forms can both be found, and then the onset diameter is defined as the geometric mean of the rim-crest diameters of all craters or basins within this range (see text for a
discussion on calculating onset diameter). Uncertainties are one standard deviation about the geometric mean, calculated by multiplying and dividing the geometric mean by
the geometric, or multiplicative, standard deviation. Peak-ring basin and protobasin data used for the calculations are from this study (Moon), Baker et al. (2011) (Mercury),
Pike and Spudis (1987) (Mars), and Alexopoulos and McKinnon (1994) (Venus). Complex crater rim-crest diameters used for the calculations are from the catalogs compiled
by Pike (1988) (Mercury), Barlow (2006) (Mars), and Schaber and Strom (1999) (Venus); diameters of complex craters and peak-ring basin diameters on the Moon do not
overlap.
g
Peak-ring basin onset diameters calculated by taking the 5th percentile of the peak-ring basin population data. See text for the details of this calculation.
b
this method (‘‘onset diameter, method 1’’, Table 1), the range of
diameters is first identified over which examples of two or more
crater morphological forms can both be found, and then the onset
diameter is defined as the geometric mean of the rim-crest diameters of all craters or basins within this range (Baker et al., 2011).
For Mercury, Venus, and Mars, rim-crest diameters for peak-ring
basins overlap the rim-crest diameters of both protobasins and
complex craters (Baker et al., 2011). However, on the Moon no
overlap exists between peak-ring basins and other morphological
classes of basins. We therefore take the onset diameter for peakring basins on the Moon to be the geometric mean of the minimum
diameter of the lunar peak-ring basin population and the maximum diameter of the next morphologically distinct population
with smaller rim-crest diameters. We use the minimum peak-ring
basin rim-crest diameter of 207 km (Schwarzschild) and the maximum rim-crest diameter of 205 km for the ringed peak-cluster basin, Humboldt, to obtain an onset diameter of 206 km for peak-ring
basins on the Moon. Onset diameters calculated using the overlap
method for basins on the other terrestrial planets (Mercury, Mars,
and Venus) are presented in Table 1.
The overlap method for calculating the onset diameter for peakring basins has the advantage of defining onset diameter of peakring basins by the spectrum of basin morphologies in the transition
between complex craters and peak-ring basins and is therefore related to the physical processes resulting in the onset of interior basin rings. A second advantage is that the uncertainty in the
estimated onset diameter is also derivable from the calculation.
However, there are situations, such as in the Moon, where distinct
crater morphological forms (e.g., peak-ring basins and protobasins)
share little or no overlap in rim-crest diameter. Also, the robust-
ness and reproducibility of this method is affected by where the
worker defines the overlap diameter range, which is usually defined from the use of multiple catalogs from more than one worker.
As such, while its use is directly tied to the observed morphological
transition, the overlap method’s applicability and reproducibility is
limited, as it cannot be easily applied to planets with little or no
overlap, and it is not able to be reliably reproduced by other workers because of its dependence on multiple crater populations that
may not have been compiled using the same survey techniques.
Satisfying these criteria is crucial for use in interplanetary comparisons and in understanding how the physical properties of the
planets are modulating the basin-forming process.
A more reproducible and applicable method for calculating onset diameter is to select a given percentile of the population. We
calculate the 5th percentile of the peak-ring basin populations
(‘‘onset diameter, method 2’’, Table 1) to obtain alternative onset
diameters for peak-ring basins on the terrestrial planets: 227 km
(Moon), 116 km (Mercury), 56 km (Mars), 33 km (Venus). Peakring basin diameter data used in the calculations are from this
study (Moon), Baker et al. (2011) (Mercury), Alexopoulos and
McKinnon (1994) (Venus), and Pike and Spudis (1987) (Mars).
The 5th percentile is chosen as it is an easily reproducible, descriptive statistic that is based on an historical standard of significance
in statistical analysis. The method is robust against outliers, as it is
defined by the tail of the distribution itself, not a single data point
defining the minimum value of the population. The method is
applicable to all planets and is independent, as it relies only on a
single basin population and is independent of the interplanetary
variations encountered in the population distributions of other
transitional crater morphologies. In addition, since basin
384
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
Fig. 4. Log–log plots of ring diameter (Dring) versus rim-crest diameter (Dr) for peak-ring basins (red circles), protobasins (blue squares), and ringed peak-cluster basins (green
diamonds) on the Moon (A, Tables A1–A3) and Mercury (B, from Baker et al., 2011). Also plotted for the Moon are the ring and rim-crest diameters for craters exhibiting ringlike central peaks (Table A3). Peak-ring basins follow a power law trend of Dring = 0.14 ± 0.10(Dr)1.21±0.13 (R2 = 0.96) on the Moon, which is very similar to the power law trend
for peak-ring basins on Mercury [Dring = 0.25 ± 0.14(Dr)1.13±0.10, R2 = 0.87, Baker et al., 2011) (Table 2). Protobasins occur at smaller diameters, but appear to follow the tail-end
of the peak-ring basin trend for the Moon and Mercury. Also shown are the trends for the diameters of central peaks (Dcp) in complex craters on the Moon
(Dcp = 0.259Dr 2.57, Hale and Head, 1979a, and Dcp = 0.107(Dr)1.095, Hale and Grieve, 1982) and Mercury (Dcp = 0.44(Dr)0.82, Pike, 1988). The ringed peak-cluster basin,
Humboldt, and craters with ring-like central peaks plot at intermediate values between the two complex crater trends for the Moon. (For interpretation of the references to
color in this figure legend, the reader is referred to the web version of this article.)
populations can now be cataloged based on complete, or nearly
complete, data coverage of the planetary surface, we can be confident that we are using populations rather than samples of particular crater and basin morphologies when calculating onset
diameters. While the use of the 5th percentile to define peak-ring
basin onset diameter does not rely on more than a single basin
population and is not directly derived from the observed morphological transition between complex crater and peak-ring basin,
peak-ring basin onset diameters calculated by this method consistently fall within the uncertainties of onset diameters calculated
using a method based on the diameters of overlapping morphologies, as described above (Table 1).
6. Analysis and interplanetary comparisons
Our refined catalog of transitional lunar basin types between
complex craters and multi-ring basins permits us to better compare and evaluate several key characteristics of basin populations
on the Moon and the terrestrial planets. These characteristics include: (1) ring and rim-crest diameter systematics, (2) surface density of peak-ring basins, and (3) peak-ring basin onset diameter.
The airless body, Mercury, has the largest population of preserved
peak-ring basins and protobasins in the inner Solar System (Baker
et al., 2011), and thus provides an important dataset for comparison with the population of peak-ring basins and protobasins on
the Moon. The basin catalogs for Venus and Mars should also be
considered in interplanetary comparisons; however, resurfacing,
erosion, and the effects of volatiles have influenced the present
populations and morphologies of basins on these planets, rendering them less useful in comparison studies. Since the impact record
on Earth is largely incomplete and highly modified by erosion, interior structures cannot be accurately identified and therefore present large uncertainties when used in interplanetary comparisons.
As such, impact structures on Earth are not used in this study. In
the following sections, we analyze our new catalog of basins on
the Moon and identify key similarities and differences with the
other planetary bodies, especially Mercury. In the next section,
these comparisons are then placed in context of the predictions
of a model of peak-ring basin formation that explains their morphological characteristics as resulting from the nonlinear scaling
of impact melt.
6.1. Ring versus rim-crest diameter trends
Following the methods of Pike (1988) and Baker et al. (2011),
we plot the ring diameter versus the rim-crest diameter in log–
log space for lunar peak-ring basins, protobasins, and craters with
ring-like central peaks and the ringed peak-cluster basin, Humboldt. Several trends are observed. First, peak-ring basins form a
straight-line in log–log space at large rim-crest diameters in
Fig. 4, and can be fit by a power law trend of the form
Dring ¼ ADpr
ð1Þ
where Dring is the diameter of the interior ring, Dr is the basin rimcrest diameter, and p is the slope of the best-fitting line on a log–log
plot. Power-law fits were calculated in KaleidaGraph (Synergy Software, www.synergy.com), which uses the Levenberg–Marquardt
non-linear curve-fitting algorithm (Press et al., 1992) to iteratively
minimize the sum of the squared errors in the ordinate. The use
of this criterion for minimization implies that fractional errors in
the estimates of interior ring diameters are regarded as larger than
those for estimates of the rim-crest diameter.
We calculate a power law fit of Dring = 0.14 ± 0.10(Dr)1.21±0.13
2
(R = 0.96, where R is the correlation coefficient for the given dataset on a log–log plot) for lunar peak-ring basins (Table 2). This fit is
very similar to a power law fit to peak-ring basins on Mercury
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
Table 2
Comparison of the values for the coefficients (A and p) of power-law fits to peak-ring
basins on the Moon (this study) and Mercury (Baker et al., 2011). Power laws are of
the form given in Eq. (1) in the text. Coefficients of power-law fits to protobasins and
ringed-peak cluster basins on Mercury from Baker et al. (2011) are also given, but
none are given for the Moon due to the statistically small populations. Coefficients
from the power law model of an expanding melt cavity (Eq. (2), Section 7) on the
Moon (this study) and Mercury (Baker et al., 2011) are given for calculations using the
Croft (1985) and Holsapple (1993) scaling relationships.
Power-law coefficientsa
A
p
R2
0.14 ± 0.10
0.25 ± 0.14
1.21 ± 0.13
1.13 ± 0.10
0.96
0.87
Protobasins (P90 km)
Moon
–
Mercury
0.26 ± 0.36
–
1.09 ± 0.29
–
0.69
Ringed peak-cluster basins
Moon
–
Mercury
0.18 ± 0.34
–
1.02 ± 0.41
–
0.78
Model (Croft, 1985)
Moon
0.14 + 0.03/0.02
Mercury
0.14 + 0.03/0.02
1.09 ± 0.05
1.09 + 0.05/0.06
–
–
Model (Holsapple, 1993)
Moon
0.11
Mercury
0.11 0.12
1.18
1.18
–
–
Peak-ring basins
Moonb
Mercuryc
a
Power laws are of the form Dring = A(Dr)p, where Dring is the ring diameter and Dr
is the final (observed) rim-crest diameter. Uncertainties for power-law fits to peakring basins, protobasins and ringed peak-cluster basins are at 95% confidence.
b
Coefficients to fits and models for the Moon are from this study. No fits were
made to the protobasin and ringed peak-cluster data for the Moon because of the
statistically small populations.
c
Coefficients to fits and models for Mercury are from Baker et al. (2011).
385
surements were of the maximum diameter of central peaks, the
trend of Hale and Head (1979a) is taken to represent an upper limit
to central peak diameters on the Moon. The second trend is a
power law [Dcp = 0.107(Dr)1.095] determined using the planform
areas enclosed by the irregular perimeters of central peaks calculated by Hale and Grieve (1982). We then assume a circular geometry for this area, from which a central peak diameter is derived.
These central peak diameters are taken to represent an average value, and should produce results that are comparable to our method
for measuring the average diameters of basin features on the
Moon. Craters with ring-like central peaks appear to fall on a scattered trend that is intermediate between the Hale and Head
(1979a) linear regression and the Hale and Grieve (1982) power
law (Fig. 4A), indicating that these ring-like central peaks do not
depart substantially from the trend in central-peak diameter observed from complex craters. Humboldt falls near the Hale and
Grieve (1982) trend, suggesting a similarity with complex craters
with central peaks. However, the clear ring-like arrangement of
its interior peaks, its large rim-crest diameter compared to other
craters with ring-like central peaks, and its overlap with the rimcrest diameters of protobasins, suggest that Humboldt represents
a unique transitional type in the size-morphology progression
from complex craters to peak-ring basins. The fact that there is
only one ringed peak-cluster basin on the Moon (5% of the total basin population cataloged in this study) is expected as it is likely to
be related to the overall smaller numbers of protobasins and peakring basins on the Moon. For comparison, ringed peak-cluster basins account for only 8% of the total cataloged basin population
on Mercury (Baker et al., 2011), and also fall along the trend for
complex craters on Mercury (Fig. 4B).
6.2. Ring/rim-crest ratios
(Dring = 0.25 ± 0.14(Dr)1.13±0.10, Fig. 4B and Table 2), and both fits are
consistent with analyses of previous peak-ring basin catalogs (Pike,
1988). Since the population of protobasins on the Moon is statistically small (N = 3), fits to the protobasin data were not conducted.
However, protobasins occur at smaller diameters than all peakring basins but overlap in rim-crest diameter with the largest complex craters on the Moon (Fig. 4A). The trend in ring diameter and
rim-crest diameter for protobasins is aligned with the tail-end of
the peak-ring basin trend (Fig. 4A). This supports the view that
peak-ring basins and protobasins are parts of a continuum of basin
morphologies. A similar observation is identified between protobasins and peak-ring basins on Mercury (Fig. 4B), where the power
law fits to protobasins and peak-ring basins are found to be statistically indistinguishable (Table 2) (Baker et al., 2011). However,
protobasins on Mercury are more numerous, and protobasins <90 km have anomalously smaller ring diameters than what
is predicted by extrapolation of a power law fit to protobasins
P90 km.
The one lunar ringed peak-cluster basin, Humboldt, occurs at
smaller rim-crest and ring diameters than peak-ring basins but is
larger in rim-crest diameter than all three protobasins (Fig. 4A).
Humboldt has an atypically small interior ring diameter relative
to its rim-crest diameter and thus plots on a trend that is more
aligned with the trend for central peak diameters in complex craters than the interior rings of peak-ring basins (Fig. 4A). Other craters with ring-like central peaks also plot near the trend for central
peak diameters in lunar complex craters. Fig. 4A shows two trends
for central peak diameters in lunar complex craters. The first is the
least squares, linear regression of Hale and Head (1979a)
(Dcp = 0.259Dr 2.57, where Dcp is the diameter of the central peak
and Dr is the diameter of the crater’s rim crest), which was based
on measurements of circular fits to the maximum diameter of central peaks in fresh complex craters on the Moon. Because the mea-
Rim-crest/ring ratio (or the inverse, ring/rim-crest ratio) plots
(Fig. 5) have been used to suggest that protobasins and peak-ring
basins represent a continuum of morphologies (Alexopoulos and
McKinnon, 1994), in contrast to the view of Pike (1988), who favored a statistical distinction between peak-ring basins and protobasins. Alexopoulos and McKinnon (1994) identified a general
trend of continuous, non-linearly decreasing rim-crest/ring ratios
with increasing rim-crest diameter for protobasins and peak-ring
basins on Venus. The basin catalogs of Wood and Head (1976), Hale
and Head (1979b), Wood (1980), Hale and Grieve (1982), and Pike
(1988) were also used to suggest similar trends for basins on Mercury, the Moon, and Mars, although the Moon and Mars data appeared with greater scatter (Alexopoulos and McKinnon, 1994). A
recent comprehensive survey of 74 peak-ring basins and 32 protobasins on Mercury (Baker et al., 2011) further emphasized these
observations by examining the inverse, ring/rim-crest ratios, and
noted that peak-ring basins flatten to an equilibrium ring/rim-crest
ratio value of around 0.5–0.6. As in Baker et al. (2011), we also calculate ring/rim-crest ratios (in contrast to the convention of using
rim-crest/ring ratios from Alexopoulos and McKinnon (1994)), for
consistency with earlier studies (Wood and Head, 1976; Pike,
1988) and to avoid magnifying the effects of errors in small
denominators. Ring/rim-crest ratios from our refined lunar basin
catalog (Fig. 5A) have less scatter than the catalogs used in Alexopoulos and McKinnon (1994), and reveal a trend that is very similar to that observed for Mercury (Fig. 5B) (Baker et al., 2011) and
Venus (Fig. 5C) (Alexopoulos and McKinnon, 1994), although at larger rim-crest diameters. The ring/rim-crest ratios for peak-ring basins on the Moon range from 0.35 to 0.56 (arithmetic mean = 0.48),
with smaller rim-crest diameters generally having smaller ratios
than larger rim-crest diameters (Fig. 5A). The ring/rim-crest ratios
on the Moon also flatten to a value of around 0.5 for the largest
peak-ring basins. Protobasins have smaller ratios, ranging from
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D.M.H. Baker et al. / Icarus 214 (2011) 377–393
et al., 2011), which appear distinct from the general continuum
of ring/rim-crest ratios between protobasins and peak-ring basins.
The ring/rim-crest ratios for craters with ring-like central peaks are
also at very low values (range = 0.12–0.24 and arithmetic
mean = 0.17) and are similar to the ratio of Humboldt, although
they occur at much smaller rim-crest diameters.
6.3. Onset diameter of peak-ring basins
Fig. 5. Ring/rim-crest diameter ratios for peak-ring basins (red circles), protobasins
(blue squares), and ringed peak-cluster basins (green diamonds) on the Moon (A),
Mercury (B), and Venus (C). Basin data are from this study (the Moon, Tables A1–
A3), Baker et al. (2011) (Mercury), and Alexopoulos and McKinnon (1994) (Venus).
The 0.5 ratio line is drawn in each panel for reference. Also note the change in scale
of the x-axis between the Moon (A) and Mercury (B) plots. Nonlinear, curved trends
are observed for protobasins and peak-ring basins for each of the planets. The trend
is steeper at smaller rim-crest diameters and then flattens to values of 0.5–0.6 for
the Moon and Mercury (A and B) and to 0.7 for Venus (C). The continuity between
the ring/rim-crest ratios of protobasins and peak-ring basins suggest that they form
a continuum of basin morphologies that is a direct result of the process of peak-ring
basin formation. Ringed peak-cluster basins appear to diverge from the continuous
trend shared by protobasins and peak-ring basins. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
this article.)
0.33 to 0.44, with an arithmetic mean of 0.39. Since there are very
few protobasins on the Moon, the lower rim-crest diameter end of
the trend is not as well-defined as Mercury (Fig. 5B) and on Venus
(Fig. 5C). The ring/rim-crest ratio (0.16) of the lunar ringed peakcluster basin, Humboldt, is much smaller than protobasins and
peak-ring basins of similar rim-crest diameter (Fig. 5A). This is consistent with similarly small (arithmetic mean = 0.20) ring/rimcrest ratios for ringed peak-cluster basins on Mercury (Baker
Comparisons of the onset diameter for peak-ring basins on the
terrestrial planets have been complicated due to the lack of a standard method for calculating this metric. Some authors have compared only transitional diameter ranges, noting that the
transitional diameters decrease from the Moon to Mercury and
Mars (Wood and Head, 1976; Pike, 1988). Others have used the
minimum diameter of the peak-ring basin populations on the terrestrial planets to define onset diameter, yielding a similar
decreasing onset diameter ordering from the Moon (140 km) to
Mercury (75 km), Mars (45 km), and Venus (40 km) (Pike, 1983;
Alexopoulos and McKinnon, 1994). Our calculations for the onset
diameter of peak-ring basins (Table 1) do not change this general
ordering, but provide new values that are based on the most recent
and complete basin catalogs of the terrestrial planets and that are
statistical more robust compared with previous values. While the
onset diameters for the Moon and Mercury are the most reliable
due to relatively complete preservation of their crater populations,
the onset diameters for Mars and Venus are more speculative due
to the prevalence of erosional and resurfacing processes and effects
of differing target properties (e.g., volatiles and temperature) on
these planets. Mars’ smaller onset diameter for peak-ring basins
compared with Mercury, which has a similar gravitational acceleration, has traditionally been attributed to the effect of different target materials, including volatiles (e.g., Pike, 1988; Melosh, 1989;
Alexopoulos and McKinnon, 1992). Mars is also anomalous in its
large range of peak-ring basin diameters (52–442 km), suggesting
that additional parameters other than gravity and impact velocity
alone are influencing Mars’ population of peak-ring basins. The
surface of Venus has also been globally resurfaced either in a catastrophic manner or at a rate equal to the crater production rate,
and thus preserves only a 0.5 Ga crater retention age (Schaber
et al., 1992). For these reasons, we exercise caution when interpreting the peak-ring basin and protobasin populations of Mars
and Venus in context of the basin populations on the other planets.
We also do not calculate an onset diameter for the Earth due to the
obvious incompleteness of its impact basin record and the large
uncertainties associated with interpreting highly eroded basin
structures.
It has long been recognized that there is an inverse relationship
between the onset diameter of peak-ring basins and the surface
gravitational acceleration (g) of the planetary body (Pike, 1983,
1988; Melosh, 1989; Alexopoulos and McKinnon, 1992). This relationship has been used to suggest that the formation of peak rings
is largely the result of a gravity-driven process. Gravity-induced
collapse of the transient cavity has thus served as the foundation
for many current models of peak-ring basin formation, including
hydrodynamic collapse of an over-heightened central peak (Melosh, 1982, 1989; Collins et al., 2002). The dependence of peak-ring
basin onset diameter on planetary impactor velocity has been
more uncertain. Pike (1988) demonstrated that the geometric
mean diameters of peak-ring basins do not correlate with the approach velocity of asteroids and short period comets (V1) on the
terrestrial planets. An improved correlation was found when approach velocity was combined with g (i.e., g/V1), although g alone
still provided the best correlation with the geometric mean diameter of peak-ring basins.
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
387
Fig. 6. Plots of the 5th percentile onset diameters for peak-ring basins on the Moon, Mercury, Mars, and Venus (Table 1, ‘‘onset diameter, method 2’’) versus surface
p
gravitational acceleration (g) (A), mean impact velocity (Vmean) (B), the ratio of g/Vmean (C), and the ratio of g/ Vmean (D) (Table 1). Solid lines are power law fits formed by
minimizing the sum of the squared errors in the ordinate. The fits are displayed to emphasize general trends in the data and are not meant to be statistically rigorous
representations. We did not include a fit for mean impact velocity due to lack of a clear trend. A correlation between onset diameter and gravity (A) is the strongest, with little
correlation existing with mean impact velocity alone (B). The correlations of onset diameter with a combination of gravity and mean impact velocity (C and D) are more
comparable or stronger than with gravity alone, suggesting that both gravity and mean impact velocity are important in influencing the onset of peak-ring basins.
We plot our onset diameters (5th percentiles, Table 1) for peakring basins as a function of the planet’s surface gravitational acceleration (g) and the planet’s mean impact velocity (Vmean) in log–log
space (Fig. 6). The mean impact velocities are taken from recent
modeling of the distribution of planetary impactors (Le Feuvre
and Wieczorek, 2008). We also include power-law fits to the data
by minimizing the sum of the squared errors in the ordinate. Given
the uncertainties in the plotted data (especially for Mars and Venus) these fits are not meant to be statistically rigorous representations and should only be viewed as illustrating the general
trends in the plotted data, As in previous studies, the strongest correlation with peak-ring basin onset diameter is the planet’s gravitational acceleration (Fig. 6A). No correlation is observed between
onset diameter and velocity alone (Fig. 6B), although a stronger
correlation is observed when the mean impact velocity is combined with gravity (i.e., g/Vmean) (Fig. 6C). Although it may have
no physical significance, there is a very strong correlation (in
log–log space) between onset diameter and gravitational accelerap
tion over the square root of the velocity (g Vmean) (Fig. 6D). To
first-order, these comparisons suggest that gravity is likely to be
important in the process of forming peak rings. While there is no
correlation between peak-ring basin onset diameter and impact
velocity alone, a fairly strong correlation is found when impact
velocity is combined with gravity. Like gravity, this correlation is
not perfect, and the details of its physical meaning are not certain
without a more detailed examination of the parameter space of impact events. Based on these observations, we suggest that both
gravity and velocity are likely to be important in the formation
of peak rings.
6.4. Surface density of peak-ring basins
The Moon has about a factor of two fewer peak-ring basins per
unit area (4.5 107 per km2) than Mercury (9.9 107 per km2,
Baker et al., 2011) and a factor of two to five greater number of
peak-ring basins per unit area than Mars or Venus (Table 1). While
the crater size distributions for impact craters between 100 km
and 500 km in diameter are nearly the same on the Moon and Mercury (e.g., Strom et al., 2005) the mean and onset diameters for
peak-ring basins on the Moon are much higher than on Mercury.
The lower onset diameter for peak-ring basins on Mercury (Table 1)
may account for the factor of two larger number of peak-ring basins per area on Mercury than on the Moon. The large number of
peak-ring basins on Mercury has also been attributed to the high
mean impact velocities of its impactors and increased impact melt
production (Head, 2010; Baker et al., 2011). This could facilitate the
onset of peak-ring basins at smaller impactor sizes, which are more
numerous than larger-sized impactors. The surface density of craters between 100 km and 500 km in diameter is much lower on
Mars than on Mercury and the Moon due to extensive erosion
and resurfacing (Strom et al., 2005), which could partially explain
the relatively small number of peak-ring basins on Mars. Venus
has also undergone much resurfacing, which certainly has affected
the number of peak-ring basins preserved on its surface.
388
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
obliteration processes is uncertain. A much improved correlation is
found when gravitational acceleration is combined with velocity
(Fig. 7C).
7. Peak-ring basin formation models
Fig. 7. Plots of the surface density of peak-ring basins on the Moon, Mercury, Mars,
and Venus (Table 1) versus surface gravitational acceleration (g) (A), mean impact
velocity (Vmean) (B) and the ratio of g/Vmean (C). As in Fig. 6, solid lines are power law
fits formed by minimizing the sum of the squared errors in the ordinate. The fits are
displayed to emphasize general trends in the data and are not meant to be
statistically rigorous representations. We did not include a fit for gravity due to lack
of a clear trend. No correlation with gravity is observed (A), while there is a slight
correlation with velocity (B). A stronger correlation is found when gravity and
velocity are combined (C). The basin records on Venus and Mars are likely
incomplete (see discussion in Section 6.3), which complicates full understanding of
these first-order correlations.
The number of peak-ring basin per unit area is plotted versus
the planet’s mean impact velocity and gravitational acceleration
in Fig. 7. Again, power law fits to the data are given to illustrate
the general trends in the plotted data. There appears to be no correlation between the number of peak-ring basins and the planet’s
gravitational acceleration (Fig. 7A), while there is a weak correlation with mean impact velocity (Fig. 7B). Increasing the densities
of peak-ring basins on Venus and Mars, which have certainly been
affected to some degree by resurfacing events, would act to
strengthen this correlation with mean impact velocity; however,
to what degree the densities of basins have been modified by crater
While there have been numerous models attempting to explain
the transition from complex craters to multi-ring basins, a consensus on the process of ring formation in peak-ring basins and multiring basins has not been reached. Two major models for the formation of peak-ring basins have been proposed: (1) hydrodynamic
collapse of an over-heightened central peak (Melosh, 1982, 1989;
Collins et al., 2002) and (2) modification and collapse of a nested
melt cavity (Grieve and Cintala, 1992; Cintala and Grieve, 1998;
Head, 2010). As discussed by Baker et al. (2011), while much progress has been made in advancing hydrocode models simulating
the hydrodynamic collapse process (Melosh, 1989; Collins et al.,
2002, 2008; Ivanov, 2005), the model currently makes no explicit
predictions on the ring and rim-crest diameter systematics of
peak-ring basins on the terrestrial planets. This is largely due to
poor constraints on the parameters governing the timescales of fluidization of the target material and subsequent freezing of this
material to produce peak-ring structures (e.g., Wünnemann et al.,
2005). While it is possible that future models will offer more explicit predictions of ring and rim-crest spacing, the current uncertainty in the models make it difficult to test against the
morphologic trends observed from our basin catalogs.
Given these uncertainties with the hydrodynamic collapse
model, we now use our observations of the new lunar catalog to
test another model of peak-ring basin formation, the ‘‘nested
melt-cavity’’ model, which explains ring formation as the result
of nonlinear scaling between impact melt and crater dimensions.
The nested melt-cavity model is based on a suite of papers by Cintala and Grieve (Grieve and Cintala, 1992, 1997; Cintala and Grieve,
1994, 1998) who invoked a combination of terrestrial field studies
and impact and thermodynamic theory to show that for given
impactor and target materials, impact-melt volume will increase
at a rate that is greater than growth of the crater volume with
increasing energy of the impact event (Grieve and Cintala, 1992).
The maximum depth of melting was also shown to increase relative to the depth of the transient cavity with increasing transient
cavity diameter (Cintala and Grieve, 1998), approaching depths
of around 15–20 km for impact events near the onset diameters
(100–200 km) of peak-ring basins (Cintala and Grieve, 1998; Baker
et al., 2011). For further descriptions of the quantitative aspects of
this model, the reader is referred to the work by Cintala and Grieve
(1998) and references therein.
This nonlinear scaling of impact melt has been shown to be
important during the modification process in the formation of
peak-ring basins on the terrestrial planets, including Earth, the
Moon, and Venus (Grieve and Cintala, 1992, 1997; Cintala and
Grieve, 1994, 1998). Further development of this model and its
extension to multi-ring basins by Head (2010) has suggested that
a melt cavity nested within the displaced zone of the growing transient crater (the ‘‘nested melt cavity’’) exerts a major influence on
the formation of peak rings and development of exterior rings during crater modification. The volume and depth of impact melting in
complex craters is generally not sufficient to modify the uplifted
morphology of the crater interior. However, with increasing size
of the impact event and thus increasing volume of melt and depth
of melting, a melt cavity is fully formed within the displaced zone
and is sufficiently deep to retard the development of an ordinarysized central peak (Cintala and Grieve, 1998). During rebound and
collapse of the transient crater, the entire impact melt cavity is
translated upward and inward. Unlike rebound in complex craters,
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
however, the uplifted periphery of the melt cavity remains as the
only topographically prominent feature, resulting in the formation
of a peak ring (Head, 2010). At smaller crater sizes, and hence shallower depths of melting, it is still possible for a small central peak
to rise through the melt cavity, accounting for the central-peak and
peak-ring combinations that are observed in protobasins (Cintala
and Grieve, 1998; Baker et al., 2011).
One of the benefits of the nested melt-cavity model is that it
makes specific predictions that may be compared with the ring
and rim-crest diameter systematics of basin catalogs. Analysis of
a recently updated basin catalog for Mercury (Baker et al., 2011)
showed many first-order consistencies with the predictions of
the nested melt-cavity model, particularly in the observations of
(1) the surface density of peak-ring basins on the terrestrial planets, (2) the continuum of basin morphologies between protobasins
and peak-ring basins, and (3) the power-law trend of peak-ring basins. Our analysis of the new lunar catalog confirms many of these
consistencies with the nested melt-cavity model, providing additional support to the importance of impact melting in forming peak
rings.
It is important to note that the geometries of impact melting
and the transient cavity derived from theoretical calculations are
only static representations of a very dynamic process. In reality,
at no time during the impact event are these geometries fully
achieved, and the dynamics of crater formation certainly affects
how the melted portions of the displaced zone evolve and are distributed within the target material with time. However, these details of the cratering process are still poorly understood and
modeled. More certain has been various analytical and numerical
estimates of the volume and depths of melting (Grieve and Cintala,
1992; Pierazzo et al., 1997; Barr and Citron, 2011), which appear
generally consistent with each other and with estimates of melt
volumes obtained from field observations of terrestrial impact
structures. Considering the geometrical assumptions and uncertainties involved with a static model for the generation of impact
melt, our presentation of the nested melt-cavity model should be
viewed as a first-order attempt in understanding the effects of impact melting on the morphology and development of peak-ring basins. While we find many consistencies between the model and our
analysis of the basin catalogs for the Moon and Mercury, more
complex and dynamic melt-zone geometries are probably more
realistic, and future refinements to this model will be necessary,
especially in improving dynamical simulations of impact melting
during large impact events.
As stated above, Mercury has the largest number of peak-ring
basins per unit area of the terrestrial planets, with the Moon having a factor a two fewer peak-ring basins based on our new lunar
basin catalog (Table 1). Under the nested melt-cavity model, the
difference in the surface density of peak-ring basins between Mercury and the Moon may be explained by differences in mean
impactor velocities on the two bodies. Because of the higher mean
impact velocities on Mercury (40 km/s compared with 20 km/s
on the Moon), impactors of a given size will produce approximately twice as much melt on Mercury as on the Moon (Grieve
and Cintala, 1992). As a result, peak-ring basin formation will be
more effective on Mercury for smaller impactors, which are more
numerous than larger impactors (Head, 2010). If similar impactor
size-frequency fluxes for the inner planets are assumed (Strom
et al., 2005), the number of protobasins and peak-ring basins per
area should increase with the mean impact velocity at the planet.
From the new basin catalogs (Table 1), there appears to be a slight
correlation between the number of peak-ring basins per unit area
and the planet’s mean impact velocity (Fig. 7B) and an even stronger correlation with gravitational acceleration and mean impact
velocity combined (Fig. 7C). These correlations are consistent with
the predictions of the nested melt-cavity model and the correla-
389
tions in onset diameter (Fig. 6), which suggest that both gravity
and velocity are likely important in determining the onset diameter and also surface density of peak-rings on the terrestrial planets
(see discussion on onset diameter, below). The low density values
for Mars and Venus are likely to be due to planetary resurfacing
events; if the complete basin records for Mars and Venus were
available, the correlation between the number of peak-ring basins
and mean impact velocity might further be strengthened.
The nested melt-cavity model also predicts that there will be a
continuous progression of impact basin morphologies in the transition from complex craters to peak-ring basins. Under that model,
the influence of increasing melt volume and depth of impact melting becomes more important with increasing basin size. In the
transition from protobasins to peak-ring basins, uplifted central
peak material is suppressed by increasing depth of impact melting,
and the uplifted periphery of the melt cavity emerges as the dominant interior morphology (Cintala and Grieve, 1998). This results
in a continuum of basin morphologies between protobasins and
peak-ring basins, which is very apparent from our new measurements of ring and rim-crest diameters on the Moon (Figs. 4 and
5). The continuous, non-linear trends observed from plots of
ring/rim-crest ratios are very consistent between the Moon, Mercury, and Venus (Fig. 5). Ring/rim-crest ratios flatten to a near equilibrium value of around 0.5 for peak-ring basins on the Moon
(Fig. 5A), slightly larger ratios of 0.5–0.6 for Mercury (Fig. 5B),
and much larger ratios (0.7) for Venus (Fig. 5C). These differences
in shapes of the ring/rim-crest ratios may be controlled by the differences in the physical characteristics of the planet. Under the
nested melt-cavity model, these characteristics would include
those controlling the production of impact melt, such as impact
velocity and target properties such as composition, temperature,
and volatiles (Grieve and Cintala, 1997). Ringed peak-cluster basins
diverge most from this curved trend for the Moon and Mercury,
which can be explained by their similarities with complex craters.
Baker et al. (2011) and Schon et al. (2011) suggest that the interior
ring in ringed peak-cluster basins may be the result of direct modification of the central portions of the uplift structure. At the relatively small rim-crest diameters of ringed peak-cluster basins, the
depth of melting has only begun to penetrate the uplift structure
and a melt cavity has not been developed. Rebound of the transient
cavity floor therefore results in a disaggregated ring-like array of
central peak elements instead of a single central uplift structure
or a large peak ring. In this fashion, ringed peak-cluster basins represent unique transitional forms in the process of forming peak
rings.
The predictions of a growing melt cavity with increasing basin
size may also be compared to the power law trends between ring
and rim-crest diameter for peak-ring basins (Fig. 4). Since the solids making up the periphery of the melt cavity eventually translate
inward and upward to form the peak ring, relationships between
the expected melt volume at a given basin diameter and an estimate of the melt cavity geometry can give a first-order model of
how peak-ring diameters should expand with increasing rim-crest
diameter. Assuming a hemispherical melt cavity and using the
power law relationship between melt volume and diameter of
the transient cavity from Grieve and Cintala (1992) in combination
with crater modification scaling relationships (Croft, 1985; Holsapple, 1993), Baker et al. (2011) derived a power law expression
relating the diameter of the peak ring (Dring) to the diameter of
the final crater rim-crest diameter (Dr):
Dring ¼ ADpr
ð2Þ
1=3 d 1=3
where A ¼ 12
ða Þ and p ¼ bd
.
3
p c
The constants c and d are from the melt volume relation given
by Grieve and Cintala (1992), where c depends on target and
390
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
impactor properties and impact velocity and d is a power law constant equal to 3.85. For the Moon, we take c = 1.42 104 and
d = 3.85, which are appropriate to an anorthositic target composition, a chondritic impactor, and an impact velocity of 20 km/s
(Cintala and Grieve, 1998). These values, however, do not account
for the vaporized portion of the melt cavity, which, when factored
into the calculations, can increase the total volume of the melt cavity by 20–30% from a melt only calculation (M.J. Cintala, personal
communication, 2010). However, this should only produce about
a 5–10% difference in modeled peak ring diameters, which is on
the order of the uncertainty in our peak-ring diameter measurements and should not significantly affect our results. The values
for the constants a and b are dependent on the crater modification
scaling relationships used to convert transient cavity diameters to
final crater diameters. We use the constants of Croft (1985)
[a = (Dsc)0.15±0.04 and b = 0.85 ± 0.04] and Holsapple (1993)
[a = 0.980(Dsc)0.079 and b = 0.921], which were derived largely from
lunar and terrestrial data. Both of the scaling relationships for transient crater modification include a transition diameter from simple
to complex craters (Dsc) appropriate to the Moon (19 km, Pike,
1988), which tailors the relationship to planetary-specific variables
such as gravity and target strength. Holsapple (1993) also includes
two relationships that account for the transient rim-crest diameter
and the transient excavation diameter. We use the transient rimcrest diameter relationship for consistency with the melt volume
power law of Grieve and Cintala (1992).
The power-law fit to lunar peak-ring basins (Fig. 4A and Table 2)
follows the same form as Eq. (2), and the values for the constants A
and p determined from this fit may be directly compared with the
predicted values from the melt-cavity model (Table 2) (Baker et al.,
2011). The power law fit to lunar peak-ring basins is very consistent with the model predictions. The modeled value for the constant A in Eq. (4) ranges from 0.12 to 0.17 (mean = 0.14) using
the Croft (1985) scaling and is 0.11 using the Holsapple (1993)
scaling. These values fall within the uncertainty in A values determined from the power-law fit to peak-ring basin data on the Moon
(0.04–0.24) (Table 2). Modeled values for the slope of the power
law trend, p, range from 1.04 to 1.14 using the Croft (1985) scaling
and 1.18 using the Holsapple (1993) scaling, which nearly completely fall within the uncertainty of the p values determined from
lunar peak-ring basins (1.08–1.34) (Table 2). The consistency between the model predictions of a growing melt cavity and the
power law fits to peak-ring basins on the Moon and also comparisons on Mercury (Fig. 4A) (Baker et al., 2011) (Table 2) support
the first-order predictions of the nested melt-cavity model and
suggest that impact melting and melt cavity formation exhibit
important controls on the formation of impact basin rings.
Finally, while the apparent gravity dependence of the onset
diameter for peak-ring basins (Fig. 6A) has generally favored a
gravity-driven phenomenon for basin formation (e.g., Melosh,
1989), the nested melt-cavity model predicts that impact velocity
should also be important in determining the onset of peak-ring basin morphologies. The onset diameters of peak-ring basins on the
terrestrial planets do not appear to depend on mean impact velocity by itself (Fig. 6B), although a combination of gravitational acceleration and mean impact velocity provides an improved
correlation with peak-ring basin onset diameter on the terrestrial
planets (Fig. 6C and D). Thus, onset diameter is likely to be dependent on both gravitational acceleration and impact velocity. Under
the nested melt-cavity model, gravity primarily determines the
dimensions of the transient cavity and the final crater diameter,
while kinetic energy and thus impact velocity largely determines
the volume of melt that is produced during the impact event. Cintala and Grieve (Grieve and Cintala, 1992, 1997; Cintala and Grieve,
1994, 1998) have examined a variety of trends between crater
dimensions and impact melting, suggesting that the ratio of the
maximum depth of melting (dm) to the depth of the transient cavity (dtc) may be important in determining the onset of peak rings in
basins. Cintala and Grieve (1998, their Fig. 7) observed that the
depth of melting approaches the depth of the transient cavity with
dm/dtc ratios of 0.8–0.9 at the onset diameters for peak-ring basins
on the Earth, Moon, and Venus. While the predicted depths of
melting at these onset diameters do not meet or exceed the depths
of the transient cavity (dm/dtc P 1.0), as emphasized in the general
discussion of the onset of peak-ring basins in Grieve and Cintala
(1997) and Cintala and Grieve (1998), sufficient depths of melting
appear necessary for peak-ring basin formation. We used our calculated onset diameters (Table 1) and the plot of dm/dtc ratio versus
transient cavity diameter (Cintala and Grieve, 1998, their Fig. 10)
to determine the dm/dtc ratio predicted for the onset diameter of
Table A1
Catalog of peak-ring basins on the Moon. Peak-ring basins are characterized by a single interior topographic ring or a discontinuous ring of peaks with no central peak.
Number
Namea
Longitudeb
Latitude
Rim crest
(km)
Ring
(km)
Ring/rim-crest
ratio
Peak-ring arc
(deg)
Confidencec
Pike and Spudis
(1987)d
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Schwarzschild
d’Alembert
Milne
Bailly
Poincaré
Coulomb–Sarton
Planck
Schrödinger
Mendeleev
Birkhoff
Lorentz
Schiller–Zucchius
Korolev
Moscoviense
Grimaldi
Apollo
Freundlich–
Sharonov
120.09
164.84
112.77
291.20
163.15
237.47
135.09
133.53
141.14
213.42
263.00
314.82
202.53
147.36
291.31
208.28
175.00
70.36
51.05
31.25
67.18
57.32
51.35
57.39
74.90
5.44
58.88
34.30
55.72
4.44
26.34
5.01
36.07
18.35
207
232
264
299
312
316
321
326
331
334
351
361
417
421
460
492
582
71
106
114
130
175
159
160
150
144
163
173
179
206
192
234
247
318
0.35
0.46
0.43
0.43
0.56
0.50
0.50
0.46
0.44
0.49
0.49
0.50
0.49
0.46
0.51
0.50
0.55
<180
<180
>180
<180
>180
>180
<180
>180
<180
<180
<180
>180
<180
>180
>180
>180
>180
1
1
3
3
3
2
1
3
2
2
2
3
3
3
3
3
2
Protobasin
Protobasin
Protobasin
Protobasin
Peak-ring basin
Multi-ring basin
Peak-ring basin
Peak-ring basin
Protobasin
Peak-ring basin
Peak-ring basin
Peak-ring basin
Multi-ring basin
Multi-ring basin
Multi-ring basin
Multi-ring basin
Not classified
a
Names shown for basins are those approved by the IAU as of this writing (http://planetarynames.wr.usgs.gov). Names not approved by the IAU, but used by Pike and
Spudis (1987) and Wilhelms et al. (1987), are denoted by an asterisk (*).
b
Longitudes are positive eastward.
c
Confidence levels are given for ring measurements (3 = highest and 1 = lowest).
d
Basin classification of Pike and Spudis (1987).
391
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
Table A2
Catalog of protobasins on the Moon. Protobasins are characterized by the presence of both a central peak and an interior ring of peaks.
a
b
c
d
Number
Namea
Longitudeb
Latitude
Rim-crest
(km)
Ring
(km)
Ring/rim-crest
ratio
Central peak
(km)
Peak-ring arc
(deg)
Confidencec
Pike and Spudis
(1987)d
1
2
3
Antoniadi
Compton
Hausen
187.04
103.96
271.24
69.35
55.92
65.34
137
166
170
56
73
55
0.41
0.44
0.33
6
15
31
>180
>180
<180
3
3
2
Protobasin
Protobasin
Not classified
Names shown for basins are those approved by the IAU as of this writing (http://planetarynames.wr.usgs.gov).
Longitudes are positive eastward.
Confidence levels are given for ring measurements (3 = highest and 1 = lowest).
Basin classification of Pike and Spudis (1987).
Table A3
Catalog of craters with ring-like central peaks on the Moon. Also included is the ringed peak-cluster basin, Humboldt. Ringed peak-cluster basins are characterized by a ring of
central peak elements with a ring diameter that is anomalously small compared to protobasins or peak-ring basins of the same rim-crest diameter.
Number
Namea
Ringed peak-cluster basins
1
Humboldt
Craters with ring-like central peaks
1
Lindenau
2
Eistein
3
Eijkman
4
Carpenter
5
Zucchius
6
Eudoxus
7
Philolaus
8
Fabricius
9
Cantor
10
King
11
Olcott
12
Hayn
13
Unnamed
14
Colombo
15
Metius
16
Berkner
17
Atlas
18
Lobachevskiy
19
Posidonius
20
Vestine
21
Gassendi
22
Wiener
a
b
c
Longitudeb
Latitude
Rim-crest (km)
Ring (km)
Ring/rim-crest ratio
Ring arc (deg)
Confidencec
81.06
27.12
205
32
0.16
>180
3
24.85
271.80
217.42
308.78
309.48
16.33
327.29
41.79
118.65
120.48
117.84
84.07
170.29
46.10
43.37
254.72
44.33
113.07
30.00
93.71
320.00
146.63
32.33
16.70
63.23
69.52
61.38
44.25
72.24
42.80
38.02
4.92
20.61
64.47
57.24
15.17
40.42
25.14
46.71
9.76
31.86
33.86
17.49
41.02
50
51
57
61
64
66
70
76
76
77
80
82
83
83
84
86
87
87
99
99
112
114
9
8
8
12
11
10
15
18
13
15
15
14
13
16
15
15
15
15
15
13
17
14
0.18
0.16
0.15
0.19
0.17
0.16
0.22
0.24
0.17
0.19
0.19
0.17
0.16
0.19
0.18
0.17
0.17
0.17
0.15
0.13
0.15
0.12
>180
>180
>180
>180
>180
>180
>180
<180
<180
>180
>180
>180
>180
<180
<180
>180
<180
<180
<180
<180
<180
>180
1
1
2
1
3
2
1
3
1
3
2
2
2
1
2
2
2
1
1
2
2
1
Names shown for basins are those approved by the IAU as of this writing (http://planetarynames.wr.usgs.gov).
Longitudes are positive eastward.
Confidence levels are given for ring measurements (3 = highest and 1 = lowest).
peak-ring basins on the Moon. For comparison, we also determined
the dm/dtc ratio at the onset diameter of peak-ring basins on Mercury by using the maximum depth of melting calculations for Mercury derived from impedance matching of the Grieve and Cintala
(1992) model (Ernst et al., 2010, their Fig. 5). In calculating the
dm/dtc ratio for Mercury, we assumed that the depth of the transient cavity is approximately one-third of its rim-crest diameter
(Cintala and Grieve, 1998). The crater modification scaling relationship of Croft (1985) was also used to convert the measured
rim-crest diameters on the Moon and Mercury to transient cavity
diameters. We find a dm/dtc ratio of about 0.7 (dm 35 km) for
the onset diameter of peak-ring basins on the Moon (227 km)
and a dm/dtc ratio of about 0.8 (dm 20 km) for the onset diameter
of peak-ring basins on Mercury (116 km). The similar ratios for
both Mercury and the Moon suggest that sufficient depth of melting relative to the depth of the transient cavity must be achieved
before peak rings are fully developed. This is consistent with a
growing melt cavity within the displaced zone that suppresses
the formation of central peak elements to form a peak ring through
weakening of the central uplifted portions of the crater interior
(Cintala and Grieve, 1998; Head, 2010). Once the depth of melting
reaches a value close to roughly three-fourths the depth of the
transient cavity depth, complete suppression of the central peak
is achieved, and the peak ring is the only topographic feature that
remains.
For multi-ring basins on the Moon, the depth of melting generally meets or exceeds the depth of the transient cavity diameter.
For example, if we take the Outer Rook ring of Orientale basin to
be the diameter of the transient cavity (620 km) (Head et al.,
2011), the dm/dtc ratio is slightly greater than 1.0 (Cintala and
Grieve, 1998). This is consistent with a hybrid mega-terrace and
nested melt-cavity model for the onset of multi-ring basins (Head,
2010), in which deep penetration of the melt cavity past the displaced zone creates a strength discontinuity that allows mega-terraces to form through translation of crustal blocks laterally in
toward the melt cavity. Based on the above observations, critical
thresholds in the ratio between depth of melting and the dimensions of the transient cavity appear to offer plausible explanations
for the onset of basin morphologies on the terrestrial planets,
including interior peak rings and the exterior rings of multi-ring
basins. The scaling of these two parameters depends on both gravity and velocity, and is therefore consistent with the first-order
correlations shown in Fig. 6. We suggest that while gravity is
important in determining the dimensions of the transient cavity
392
D.M.H. Baker et al. / Icarus 214 (2011) 377–393
and final crater diameter, it is not the dominant process in forming
peak rings. Instead, our observations from the catalogs of basins on
the terrestrial planets suggest that velocity, and therefore kinetic
energy and subsequent melting of target material during impact
is likely to exhibit the strongest control on peak-ring basin
formation.
between our analyses of basin catalogs and the nested melt-cavity
model are promising, much work is needed to corroborate these
observations, including advanced impact simulations that are able
to model accurately impact melt production and its effects during
crater modification.
Acknowledgments
8. Conclusions
We have updated the current catalogs of protobasins and peakring basins on the Moon using new 128 pixel/degree (235 m/pixel) resolution gridded topography from the Lunar Orbiter Laser
Altimeter (LOLA). Our refined catalog includes 17 peak-ring basins,
3 protobasins, and 1 ringed peak-cluster basins. Several basins previously inferred to be multi-ring basins (Apollo, Moscoviense,
Grimaldi, Freundlich–Sharonov, Coulomb–Sarton, and Korolev)
are now re-classified as peak-ring basins due to the absence of
more than two prominent topographic rings observed in the LOLA
data or overall consistency with a peak-ring basin origin. Interplanetary comparisons of basin catalogs emphasize some previous
observations and provide new constraints on the dominant mechanisms of peak-ring basin formation. Key observations include:
(1) Onset diameter calculations for peak-ring basins suggest
correlations with a combination of both gravity and mean
impact velocity (Fig. 6). The Moon has the largest onset
diameter of the terrestrial planets (227 km), followed by
Mercury (116 km), Mars (56 km), and Venus (33 km)
(Table 1).
(2) The Moon has a surface density of peak-ring basins
(4.5 107 per km2) that is intermediate between Mercury
(9.9 107 per km2) and Mars (1.0 107 per km2) and
Venus (1.4 107 per km2) (Table 1). The differences in the
number of peak-ring basins between the Moon and Mercury
may be due to their different mean impact velocities and
onset diameters of peak-ring basins.
(3) Ring/rim-crest ratios (Fig. 5) indicate continuous, nonlinear
trends that are similar on the Moon, Mercury, and Venus
and suggest that protobasins and peak-ring basins are parts
of a continuum of basin morphologies. Ring/rim-crest ratios
flatten to values of around 0.5 for the Moon, slightly higher
values of 0.5–0.6 for Mercury, and a much higher ratio of
0.7 on Venus.
(4) Power-law fits to plots of the ring and rim-crest diameters of
peak-ring basins on the Moon and Mercury are very similar
(Fig. 4 and Table 2) and are both consistent with a power law
model of a growing melt cavity with increasing basin size
(Eq. (2)).
Our analysis of the morphological characteristics of peak-ring
basins and protobasins on the Moon and the terrestrial planets
shows many consistencies with the predictions of the nested
melt-cavity model for basin formation. Under this model, basin
rings are formed from the nonlinear scaling of impact melt and
development of an expanding melt cavity within the displaced
zone, which acts to suppress central uplift structures with increasing depth of melting. At a depth of melting approximately threefourths the depth of transient cavity, the depth of melting is sufficient to completely retard the formation of a central uplift structure and a peak ring emerges as the dominant interior
morphology. Multi-ring basins are likely to form as the melt cavity
expands to depths equal to or greater than the depth of the transient cavity, which acts to substantially weaken the basin interior
and initiates mega-terracing and formation of a topographic ring
exterior to transient cavity rim. While the first-order consistencies
We thank Ian Garrick-Bethell for use of the code to calculate the
averaged LOLA topography profiles and Sam Schon for productive
discussions on the populations of impact basins on Mercury. We
also thank Mark Cintala for helpful discussions on the scaling of
impact melting and the LOLA and LROC teams for their efforts in
acquiring and processing the data. Reviews by Gordon Osinski
and an anonymous reviewer helped to improve the quality of the
manuscript. Thanks are extended to the NASA Lunar Reconnaissance Obiter Mission, Lunar Orbiter Laser Altimeter (LOLA) instrument for financial assistance (NNX09AM54G).
Appendix A
Catalogs of all peak-ring basins, protobasins, and ringed peakcluster basins on the Moon as compiled in the present study are
presented in Tables A1–A3, respectively. LOLA gridded topography
images of each basin are also found as online supplementary
material.
Appendix B. Supplementary material
Supplementary data associated with this article can be found, in
the online version, at doi:10.1016/j.icarus.2011.05.030.
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