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    Pure and Applied Geophysics

    pageoph

    ISSN 0033-4553

    Pure Appl. Geophys.

    DOI 10.1007/s00024-014-0906-8

    Fractal Dimension of GeologicallyConstrained Crater Populations of Mercury

    Paolo Mancinelli, Cristina Pauselli,

    Diego Perugini, Andrea Lupattelli &

    Costanzo Federico

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    Fractal Dimension of Geologically Constrained Crater Populations of Mercury

    PAOLO MANCINELLI,1 CRISTINAPAUSELLI,1 DIEGO PERUGINI,1 ANDREA LUPATTELLI,1 and COSTANZOFEDERICO1

    AbstractData gathered during the Mariner10 and MES-

    SENGER missions are collated in this paper to classify craters into

    four geo-chronological units constrained to the geological map

    produced after MESSENGERs flybys. From the global catalogue,

    we classify craters, constraining them to the geological information

    derived from the map. We produce a size frequency distribution

    (SFD) finding that all crater classes show fractal behaviour: with

    the number of craters inversely proportional to their diameter, the

    exponent of the SFD (i.e., the fractal dimension of each class)

    shows a variation among classes. We discuss this observation aspossibly being caused by endogenic and/or exogenic phenomena.

    Finally, we produce an interpretative scenario where, assuming a

    constant flux of impactors, the slope variation could be represen-

    tative of rheological changes in the target materials.

    Key words: Mercurys geology, impact processes, primary

    and secondary crust.

    1. Introduction

    Over the last few years, new data from the

    MESSENGER spacecraft (NASA mission) have shed

    new light on the geological history of Mercury.

    Endogenic phenomena such as contractional tectonics

    and volcanism extensively affected the surface of the

    planet, defining the morphologies observed by Mar-

    iner10 and MESSENGER. Exogenic processes such

    as asteroid impact-induced cratering also altered

    Mercurys surface, and may have contributed to

    volcanic activity on the planet, at least in the larger

    basins.Data from both Mars and the Moon indicate that

    the inner solar system is characterised by two popu-

    lations of impactors: one resulting from the Late

    Heavy Bombardment (LHB) (GOMES et al. 2005;

    HARTMANN et al. 1981; NEUKUM et al. 2001; MARCHI

    et al. 2009; MINTON and MALHOTRA 2010) which

    ended about 3.8 Ga ago and was caused by migration

    of the giant planets (MORBIDELLI et al. 2001; MOR-

    BIDELLIet al. 2002; GOMES et al. 2005; MARCHIet al.

    2012), and another due to Near Earth Asteroids

    (NEA) (BOTTKE et al. 2002; MORBIDELLI et al. 2002;STROM et al. 2005; STROM et al. 2008; STROM et al.

    2011). Considering that the analysis from STROM

    et al.(2005) obtained the same results for Mercurys

    highlands and Caloris plains and because of its

    location in the inner solar system, we expected

    Mercurys crater population to show the same

    behaviour on a global-scale analysis. The decay rate

    from LHB is still considered controversial, but most

    authors believe that the cratering projectile flux has

    been more or less constant for the last 3.5 Ga, at least

    for those impactors with diameters of less than 10 km

    (HARTMANN et al. 1981; NEUKUM et al. 2001; BOTTKE

    et al. 2002; MARCHI et al. 2009; MINTON and MAL-

    HOTRA 2010). The effects of the LHB on a planetary

    body can also be constructive. In fact, LHB impactors

    have been hypothesized as providers of volatiles that

    could have contributed to the enrichment of the ter-

    restrial planets (TRIGO-RODRIGUEZand MARTINTORRES

    2012; TRIGO-RODRIGUEZ 2013).

    The crater represents the sum of the effects of

    three impact phases: coupling, excavation and mod-ification (e.g., MELOSH 1989; XIAO et al. 2014). The

    first two phases represents the transmission and

    propagation of the energy of the projectile to the

    target body, first producing melt and vaporization,

    then immediately after, the target material is

    deformed and ejected. Deformation is proportional to

    the energy of the projectile, is dependent on the target

    and projectile materials, and decreases with increas-

    ing distance from the impact. The result of these two

    1Dipartimento di Fisica e Geologia, Universitadegli Studi di

    Perugia, Via A. Pascoli, 06123 Perugia, Italy. E-mail: pamancinel-

    [email protected]; [email protected];[email protected];

    [email protected]; [email protected]

    Pure Appl. Geophys.

    2014 Springer Basel

    DOI 10.1007/s00024-014-0906-8 Pure and Applied Geophysics

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    phases is the transient crater. The last phase may last

    longer than the previous two, and involves the col-

    lapse of both the ejected material and the unstable

    portions of the crater rim, which will partially fill the

    crater basin. At the end of this phase, the final

    diameter of the crater is achieved.

    Products and morphologies resulting from an

    impact on the surface of a planet can be used as a

    proxy to infer the structure and rheology of the pla-

    nets upper crust (MASSIRONIet al.2009; MARCHIet al.

    2011), and therefore to verify whether outcropping

    material is made of primary crust or of stratified

    igneous bodies and volcanic deposits.

    Since the first data produced by the Mariner10,

    geological mapping of planet Mercury was one of the

    main goals to achieve in order to understand Mer-

    curys surface evolution. Resolution of mappingincreased with the quantity and resolution of data

    gathered by MESSENGER spacecraft (DENEVI et al.

    2009). Crater statistics followed and constrained

    geological mapping, and were produced by many

    authors for different purposes (e.g. STROMand NEUKUM

    1988; STROMet al.2005; MARCHIet al.2011). Despite

    crater statistics certainly being a valid method to

    gather information about a planetary surface, and its

    temporal evolution both in a relative and an absolute

    sense, global scale statistics were never produced for

    Mercury. The aim of this work is to present a first

    analysis of crater statistics on a global scale for the

    planet Mercury, and to test fractal behaviour of geo-

    logically constrained crater populations. In particular,

    we will present a size frequency distribution (SFD)

    constrained to geological observations, and discuss

    possible interpretations of the data, considering the

    variables that affect impact cratering.

    2. Material, Methods and Preliminary Results

    The basemap of this work (Fig.1A) covers the

    whole planet and contains both new geological

    information acquired during MESSENGERs third

    flyby and orbital insertion, and more recently pub-

    lished data on outcropping geology (DENEVI et al.

    2009). To achieve the maximum possible coverage,

    we started from that map and enlarged it in order to

    cover regions observed after MESSENGERs third

    flyby and orbital insertion. To map these areas, we

    used the same parameters and unit classification as

    defined by DENEVI et al. 2009. The term geological

    units will be used in the text to indicate outcropping

    formation grouped on the base of the reflectance that

    can be representative of a true mineralogical, and thus

    geological, change between units. The map was

    constructed in a GIS environment, by establishing a

    geological formation and a relative age value (geo-

    chronological information) for each deposit, as

    shown by DENEVI et al.2009, who classified materials

    on the basis of reflectance and cratering, and attrib-

    uted a relative timing of deposition to each unit.

    The older unit, called Intermediate Terrains (IT),

    is representative of heavily cratered old regions.

    Above these terrains, Low Reflectance Material

    (LRM) encompasses low reflectance deposits, com-prising of craters and basin ejecta. Within these LRM

    deposits there are a few darker outcrops, containing

    crater ejecta and which are defined as centres of LRM

    (LRM_C). The younger units, which are represented

    by smooth plains ranging from low to high reflec-

    tance, are subdivided into two deposits: 1) High

    Reflectance Plains (HRP) and Intermediate Plains

    (IP), with intermediate to high reflectance; and 2)

    Low Reflectance Blue Plains (LBP), which include

    later volcanic, low reflectance smooth plains. Within

    the HRP ? IP unit, according to the new data from

    Flyby 3 and orbit insertion (HEAD et al. 2011), some

    fresh deposits are also introduced. These have been

    mapped around and inside the Rachmaninoff Basin

    (Fig.1A). This new subunit (hereafter referred to as

    Late Volcanic Deposits; LVD) displays typical

    reflectance and cratering with respect to all the other

    units and is made up of smooth deposits. LVD fill

    topographic depressions, and are considered to be the

    products of volcanic activity that occurred in the

    Rachmaninoff region (PROCKTER et al. 2010), whereLVD also registered in an anomalous secondary

    cratering (CHAPMAN et al. 2012). Other than in the

    South Rachmaninoff basin, other LVD have been

    mapped in the Firdousi Plains region. The recently

    observed volcanic floods that occurred in the northern

    polar region (HEAD et al. 2011) have also been

    mapped as LVD, in view of their morphological

    characteristics and of their spectral properties similar

    to the Firdousi Plains (Fig. 1A, B). However, on a

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    global scale, we consider LVD as part of the

    HRP ? IP plains, according to previous work that

    classified the northern plains as similar to the HRP

    unit (HEADet al. 2011).

    Although the validity of this kind of geological

    mapping may be up for debate, particularly when

    terrains are classified primarily according to

    reflectance data, this classification (i.e., units HRP,

    IP, LBP, LRM, LRM_C and IT) was made by DENEVI

    et al. 2009 according to colour and spectroscopic

    variations observed and described by previous works

    using images from the Mercury Dual Imaging System

    (MDIS) (ROBINSON et al. 2008) and data from the

    Mercury Atmospheric and Surface Composition

    Spectrometer (MASCS) (MCCLINTOCK et al. 2008),

    respectively. This approach is further supported when

    the geologic map is compared to the mosaic of

    MASCS observations (Fig.1A, B).

    We assumed that terrains encompassed in the

    same unit were deposited in a brief time period (i.e.,

    each unit is representative of a time step of the glo-

    bal-scale geological evolution of Mercury). This

    assumption is supported by the work of MARCHI et al.

    (2013), who found that the planet-scale resurfacing ofMercury was produced between 4.1 and 3.55 Ga ago

    and was related to LHB, which possibly triggered

    global-scale volcanic activity. This indicates that all

    global-scale units as mapped in Fig.1A were rap-

    idly deposited within this time interval, and thus that

    all deposits encompassed in the same unit were pro-

    duced in a short time interval.

    Figure 2Overlay of geological map, planetary mosaic and crater catalogue from the region west of Rembrandt basin. T4 older fourth-order craters,T3

    third-order craters, T2 second-order craters, T1 younger first-order craters

    Figure 1A Geological map, modified after DENEVI et al. 2009, and picture

    mosaic after Mariner10 and MESSENGER flybys. IT: Intermediate

    Terrains, relative Age: IV. LRM: Low Reflectance Material,

    relative Age: III. LRM_C: Low Reflectance Material Centre,

    relative Age: III. HRP ? IP: Low Reflectance Plains and Interme-

    diate Plains, relative Age: II. LBP: Low reflectance Blue Plains,

    relative Age: I. LVD: Late Volcanic Deposits, relative age: I [1-

    0.7 Ga for Rachmaninoff infill (MASSIRONI et al. 2009)]. White

    arrow: Rachmaninoff Basin. B Ultraviolet to near-infrared spectral

    variations mapped by Mercury Atmospheric and Surface Compo-

    sition Spectrometer (MASCS) during the MESSENGER orbital

    phase modified from the file PIA14866 (link to the web page of this

    image is provided in the references). C Craters used for SFD

    analysis in Figure4 and geo-chronological characterization of each

    crater. Colors show diameter classes from 40 to 120 km [crater data

    from FASSETT et al. (2011)]. Background image resolution used

    during mapping: 0.7 km/pixel. Equidistant cylindrical projection

    used on images and sinusoidal equal-area projection for area

    calculations. GIS software: QuantumGIS 1.7.1

    b

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    Stratigraphic data is more complex to gather from

    reflectance or spectral observations. Data produced

    by instruments on board the Mariner10 and MES-

    SENGER missions did not allow for the easy building

    of a constrained model of the material in the imme-

    diate subsurface, also due to uncertainties over thelocal-scale mineralogical characterisation of out-

    cropping terrains still needing to be clarified. This

    lack of stratigraphic constraints also has effects on

    formulating a definition of correct ages for outcrop-

    ping material. However, the morphological features

    observed during GIS mapping, constrained by the

    degree of cratering of each deposit, do allow defini-

    tion of a depositional order in time.

    The above considerations allow us to assign the

    following relative ages, from the oldest to the youn-

    gest formations: Age IV for the IT, Age III for LRM

    and LRM_C, Age II for HRP, IP and LVD, and Age I

    for LBP deposits (Fig.1). These ages are purely

    indicative of the depositional steps during which themapped units were deposited from the older IT to the

    younger LBP. This order is established on the basis of

    morphological features and cratering. It is impossible

    to univocally define the absolute timing of the

    appearance of these units. However, it is clear that,

    from the beginning of the deposition of the IT unit to

    the end of the deposition of the LBP unit, a remark-

    able phase of the geological resurfacing of Mercury is

    Figure 3SFD analyses for crater classes defined with geo-chronological constraints (see text for details). Plot is built considering cumulative number

    (N) of craters with diameterDClarger or equal than comparative diameter dCfor each class, normalized by area covered by geological unit on

    the whole planet (A). T1, T2, T3, T4 classes defined in text and in Fig. 2. Table:n/Aratio between number of craters per crater class (n) and

    A(units in 10E6 km2

    ).S: exponent of the cumulative SFD for each crater class (i.e., fractal dimension of each class). Classes encompass all

    observed craters with diameters between 40 and 412 km. Errors reported for the calculation ofSare cumulative of errors resulting from linear

    fit and from data points

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    shown (i.e., a time interval). Another limitation

    coming from the lack of constrained stratigraphic

    information is that we cannot locate or estimate units

    overlaps, either in global or in local-scale analysis.

    Analysis of SFD was carried out starting from

    the recently published crater catalogue (FASSETT

    et al. 2011). From this catalogue, our analyses do

    not consider craters with diameter (DC) smaller

    than 40 km, or the nine larger basins (i.e., craters

    with diameter larger than 412 km). The lower

    bound allows us to exclude the effects of secondary

    cratering that may produce uncertainties in the

    results; the upper bound is introduced to reduce

    redundancy of the major craters on the cumulative

    plot.

    The geo-chronological data derived from the

    basemap is therefore combined with the position of

    the centre of each crater. This process organises the

    entire crater catalogue in four classes using the geo-

    chronological attributes of the basemap (i.e., out-

    cropping geology and relative ages). The GIS

    software automatically carries out this classification,

    but it is followed by a careful evaluation of each

    crater, to best characterise its relative age by con-

    sidering its morphological features, the outcropping

    unit at its centre, and the morphological relations

    between this deposit and the surroundings. Based on

    these criteria, we identify four geo-chronological

    classes of craters, from the youngest to the oldest: T1,

    T2, T3 and T4 (Fig. 2).

    Figure 4SFD analyses for crater classes defined with geo-chronological constraints and diameters between 40 and 120 km (see text for details). Plot is

    built considering cumulative number (N) of craters with diameter DClarger or equal than comparative diameter dCfor each class, normalized

    by area covered by geological unit on the whole planet (A). T1, T2, T3, T4 classes defined in text and in Figure 2. Table:n/Aratio between

    number of craters per crater class (n) and A (units in 10E6 km2). S: exponent of the cumulative SFD for each crater class (i.e., fractal

    dimension of each class). Errors reported for the calculation ofSare cumulative of errors resulting from linear fit and from data points

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    Some assumptions were made in this process of

    crater classification: (1) if a crater is surrounded by a

    unit that is younger than the unit outcropping at its

    centre, the impact occurred prior to the deposition of

    the surrounding unit, which never filled the basin

    produced by the impact; (2) if a crater is filled by a

    unit younger than the surrounding unit, the impact is

    deemed to have occurred just before filling, and thus

    infill material deposition is coeval with the impact;

    (3) if an impact occurred in a region extensively

    covered by a single unit, the impact is deemed to

    have occurred soon after unit deposition and thus is

    coeval with the target unit.

    From this classification, we obtain the number

    (n) of craters for each class, and by the re-projection

    of the map in Fig. 1A to sinusoidal equal area pro-

    jection, we obtain the area covered by each unit (A).The ratio betweenn and A represents crater density of

    craters with diameters between 40 and 412 km. We

    found a relatively constant number of craters per

    10E6 km2 from T1 to T4; in particular, 3438 for

    classes T4T2 and 23 for T1.

    The SFD analysis was performed for each geo-

    chronological class. The size-frequency plot N(DCC

    dC)/Avs. dCin Fig.3shows that crater classes T1T4

    have a fractal behaviour, with the number of craters

    inversely proportional to their diameter, and defines

    different linear trends following scale-invariant dis-

    tributions, S being the exponent of the cumulative

    crater SFD (i.e., the fractal dimension of each crater

    class). The cumulative number of craters (N) is nor-

    malised to the area covered by each geological unit to

    which each crater class refers (A). It is interesting

    to note that the value of Sdecreases across classes

    from T4 (3.38 0.08) to T3 (3.16 0.09), T2

    (2.81 0.1) and T1 (2.68 0.11), indicating a

    change in the fractal behaviour of the population. This

    change is likely driven by a variation of one or more ofthe properties affecting the impact (Eq. 1) and involves

    all the craters of the same class.

    To further constrain our analysis and to avoid

    statistical redundancy of larger craters (in particular

    for classes T3 and T1), we removed craters with

    diameters larger than 120 km (Fig.4). Reducing the

    upper limit allow us to analyse craters formed by the

    flux of asteroids of diameter (DA) within the range

    from 13 to 310 km (i.e., 12 B DC/DA B 40;

    MELOSH, 1989; OKEEFE and AHRENS 1993), and

    allows us to focus on asteroids considered to have a

    constant flux toward the terrestrial planet region over

    the last 3.5 Ga (BOTTKE et al. 2002; MINTON and

    MALHOTRA2010). This further constraint permits us to

    highlight the effects of other parameters, which affect

    craterization aside from the variation of the flux of

    impactors (e.g. the variation of rheological properties

    of target material). Also, in this case, we found a

    relatively constant number of craters per 10E6 km2

    from T4 to T1; in particular, 3234 for classes T4T2

    and 20 for T1. SFD still follows different linear trends

    with S, which is constant for classes T4 and T3

    (3.49 0.1) and decreases from classes T2

    (2.56 0.05) to T1 (2.09 0.04) (Fig.4).

    3. Discussion

    The results of the SFD analysis presented in

    Fig.4 can be explained by one or more of the fol-

    lowing hypotheses: (1) a change in the flux (number

    and/or size) of impactors through the Hermean sur-

    face, (2) the variable angle of incidence of impactors,

    (3) varying impact velocities, (4) a different rheo-

    logical response of the planetary crust to impactors.

    These results can also represent effects of the overlap

    of the mapped units. The main limitations pertaining

    to this global scale approach came from the lack of

    chronological and stratigraphic constraints on unit

    deposition. These limitations are more evident and

    efficient in a global-scale approach than in a local

    scale approach, because of the wider distribution of

    deposits and the higher complexity of the geological

    scenario. Resurfacing events (producing unit over-

    laps), if present, are certainly a limitation to crater

    statistics (MICHAEL and NEUKUM2010): increasing the

    area of interest for the analysis will increase theprobability of including regions where units overlap.

    This, in turn, means that statistics of the underlying

    unit will be incomplete if calculated after the depo-

    sition of the mantling unit. This problem is certainly

    significant, and is directly related to the uncertainties

    concerning the sub-surface geometries and distribu-

    tion of mapped units. The currently available data do

    not allow the exclusion of one or more of the

    hypotheses presented above, but the intent of this

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    paper is to contribute to the debate with an approach

    to global scale analysis by providing relevant issues

    for discussion.

    The first hypothesis cannot be excluded by the

    available data regarding the uncertainty of the

    definition of the age of deposition and the temporal

    relationships between one unit and the other.

    However, this analysis shows that the density of

    cratering [i.e., the ratio between the total number of

    craters (n) per each geological unit and the relative

    area coverage (A)] is more or less constant (Figs. 3,

    4). In the absence of absolute age data about the

    deposition of the mapped units, and considering

    that all units have likely been deposited in a rela-

    tively brief time interval (MARCHI et al. 2013), the

    above observation suggests that during the observed

    time span or, at least, after the units were depos-ited, the flux of asteroids across Mercurys surface

    has undergone negligible variation.

    Regarding the second and third hypotheses, the

    normal velocity component of an impact, depending on

    both velocity and angle of impact, is likely to directly

    affect the formation of craters (MELOSH,1989; MARCHI

    et al. 2005; HOLSAPPLE and HOUSEN 2007; MASSIRONI

    et al.2009: XIAOet al.2014) in relation to the location

    of the impact at different latitudes and longitudes.

    However, the geological units to which classes T1T4

    refer are distributed across the whole planet (Fig. 1A).

    We believe that this outcome does not allow for the

    possibility that normal velocity variation could play a

    key role in generating the observed systematic varia-

    tion of S from T4 to T1 crater populations, but

    currently, its effects cannot be precisely quantified.

    The diameter of the crater can also be affected by

    varying only the angle of impact; however, this

    would not significantly affect the statistics of the

    whole population, because non-circular craters are

    only produced for very low impact angles(i.e.,\10) (MELOSH, 1989).

    The fourth hypothesis defines the variation in

    crater size as a function of the properties of the tar-

    geted geological unit (MASSIRONI et al. 2009; XIAO

    et al.2014). The variation in Smay, according to this

    hypothesis, reflect a change in the rheology of Mer-

    curys upper crust (MARCHI et al. 2012).

    The dependence of crater size on the rheology of

    the target material is given by:

    R f g; qA; qT; m; a; U; Yf g 1

    in which R is the craters final radius, g the gravita-

    tional acceleration, qAand qTthe densities of asteroid

    and target, m the impactors mass, a the impactors

    radius, U the normal velocity component, and Y the

    strength of target material (HOLSAPPLE and HOUSEN2007).

    From the power-law relationship defining size-

    frequency distributions (Figs. 3and 4), we obtain the

    result:

    N DC dC =A CdSC 2

    in which dC= 2R. Thus, the variations ofScould be

    representative of variations in the rheological

    parameters (i.e., strength and density) of the materials

    involved in the impact, possibly indicating the pre-

    sence of a secondary crust and/or a compositional

    variation in the population of the LHB projectiles

    (MARCHIet al.2012; BROZ et al.2013). However, we

    have not found any evidence to support an interpre-

    tation of the observed change in S as caused by a

    cometary origin of part of the LHB impactor popu-

    lation, and this is in agreement with the work of

    MARCHI et al. (2012).

    Considering the results of the SFD for craters with

    diameters between 40 and 120 km (Fig.4), if we

    assume that the SFD of asteroids with diameterbetween 3 and 10 km during the observed time

    interval related to the mapped geological units was

    constant (BOTTKE et al. 2002; MARCHI et al. 2009;

    MINTON and MALHOTRA 2010), and normal velocity

    component of the impacts to do not affect signifi-

    cantly the crater populations, the stratified crust

    model could be supported by some observations:

    1. LRM and IT units (i.e., crater classes T3 and T4,

    respectively) were mapped as very similar depos-

    its (DENEVI et al. 2009), the only difference lyingin their colour properties. The slopes of their SFD

    are equal for craters with 40 B DCB 120 (Table

    in Fig.4), suggesting (in a rheology-driven sce-

    nario) that the response to the impact was similar

    for both geological units, and therefore that the

    rheological properties of the units are similar. This

    observation is not supported when the upper limit

    in crater diameter is removed, i.e., considering

    craters with 40B DCB 412 (Fig.3), because

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    Schanges from T4 to T3. However, in this case,

    Sis certainly affected by the lack of craters larger

    than 250 km found in T3, and more generally, by

    the wider population of impactors.

    2. The large number of volcanic plains, covering

    wide regions of the planets surface (MALIN,1976;

    STROM, 1977; SPUDIS and GUEST, 1988; DENEVI

    et al. 2009; HEAD et al. 2011; STOCKSTILL-CAHILL

    et al. 2012; Denevi et al. 2013), suggests that

    resurfacing involved planet-scale areas, and this

    observation is in agreement with recent works

    (MARCHIet al. 2013).

    In this interpretation, the natural conclusion is that

    Mercurys surface is younger than 3.5 Ga, and therefore

    postdates the LHB. This observation contrasts with pre-

    vious works [e.g., models proposing a differentiation in

    the origin and evolution of Mercurys impactor popula-

    tions, in comparison with data from the Moon and Mars

    (STROM etal. 2005; STROM etal. 2008; STROM etal. 2011)].

    The contrast might be resolved by considering the oldest

    unit IT (i.e., crater class T4) to be the target unit on which

    LHB acted. If this is so, LHB produced a greater number

    of impacts, and therefore an higher surface alteration

    within IT deposits, where volcanic activity was more

    intense (IVANOVet al.2002; HEADet al.2011), contrib-

    uting to the deposition of the succeeding younger units in

    a relatively brief phase after LHB. These units, fillingbasins previously created by LHB impacts, concealed

    large numbers of craters and IT deposits, leading to the

    present state in which, for population T4, the observed

    crater density is clear-cut. In this way, crater class T4 and

    therefore IT deposits become the key to definitive proof

    of the global-scale effects of LHB emplacement on

    Mercurys surface and crustal evolution (MARCHI et al.

    2009). However, improvements in the development of

    the global geological map (with particular regard to older

    terrains) and of evolutionary models of resurfacing his-

    tory will certainly contribute to refinement of our model.

    4. Conclusions

    We conclude that SFD analysis for geologically

    constrained global-scale crater classes, if properly

    constrained, will allow one to use crater statistics

    not only for in situ investigation (referring to a

    limited area and to a relative/absolute dating of

    deposits in this area), but also for wider applica-

    tions. In fact, given the global coverage, these

    applications can help us to constrain asteroid flux

    models and global resurfacing models, and improve

    characterization of target and impactor properties

    (geological and rheological). New data from

    MESSENGER and the upcoming BepiColombo

    mission will help us to more precisely define the

    geological properties and the chronology of target

    materials formation, while high-resolution images

    will improve the quality of the crater catalogue for

    low-resolution imaged areas.

    Acknowledgments

    We would like to dedicate this work to the memory of

    Angioletta Coradini, who played a leading role in

    many international scientific projects and was among

    the founders of space science in Italy. We all miss her

    enthusiasm and her contributions to planetary sci-

    ences. The authors also thank Caleb I. Fassett for

    making the crater catalogue available and for con-

    structive comments on a preliminary version of this

    paper. We want to thank the two anonymous

    reviewers for their constructive and insightful com-

    ments, which improved the quality of the manuscript.

    This work was funded by the ASI-INAF BepiCo-

    lombo agreement number I/022/10/0.

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