Elsevier

Icarus

Volume 387, 15 November 2022, 115200
Icarus

Catastrophic rupture of lunar rocks: Implications for lunar rock size–frequency distributions

https://doi.org/10.1016/j.icarus.2022.115200Get rights and content

Highlights

  • Model of rock size frequency evolution on the Moon.

  • Model calibration with measured rock size frequency distribution of known radiometric age.

  • Age estimation from rock size frequency distributions.

Abstract

Like many airless planetary surfaces, the surface of the Moon is scattered by populations of blocks and smaller boulders. These features decrease in abundance with increasing exposure time due to comminution by impact bombardment and produce regolith. Here we model the evolution of block size–frequency distributions by updating the model of Hörz et al. (1975) with new input functions: the size–frequency distributions of cm–scale meteoroids observed over the last few tens of years and a rock impact shattering function. The impact shattering function is calibrated using measurements of a lunar block size–frequency distribution of known age. We find that cumulative block size–frequency distributions change with time from a power–law for young populations (<~50 Myr) to an exponential distribution for older populations. The new destruction rates are within the uncertainty of the original model, although, for sizes >5 cm, they are two times faster than the original best estimate. The faster rates are broadly consistent with observations reported by other studies. Since the input functions are known for small rock sizes, the rock abundance can be determined theoretically at sizes below the current image spatial resolution (0.5 m). Surface exposure age of block fields can be estimated together with the initial block abundance from the measurement of block size–frequency distributions.

Introduction

Blocks (1˗100 m) and smaller boulders (0.1˗1 m) (Bruno and Ruban, 2017) are ubiquitous on planetary surfaces as a result of impact cratering. The common approach to study these features is the measurement of their size–frequency distribution (SFD). Impact ejecta block SFD have been measured extensively on the Moon since the Surveyor era (e.g., Shoemaker and Morris, 1970), using orbital imaging data (e.g., Cintala and McBride, 1995; Bart and Melosh, 2010; De Rosa et al., 2012; Krishna and Kumar, 2016; Pajola et al., 2019; Watkins et al., 2019) and up to recent time by Chinese lander missions (e.g., Di et al., 2016; Li et al., 2017; Li et al., 2018; and Li and Wu, 2018; Wu et al., 2018; Wu et al., 2021). SFD measurement of impact ejecta blocks have been performed on many airless bodies, such as Ida (Lee et al., 1996), Phobos (Thomas et al., 2000), Eros (e.g., Thomas et al., 2001; Dombard et al., 2010; Michikami and Hagermann, 2021), Itokawa (e.g., Saito et al., 2006; Michikami et al., 2008; Mazrouei et al., 2014; DeSouza et al., 2015), Lutetia (Küppers et al., 2011), Toutatis (Jiang et al., 2015a), Vesta (Schröder et al., 2021a), Ceres (Schulzeck et al., 2018; Schröder et al., 2021b), Ryugu (Michikami et al., 2019; Michikami and Hagermann, 2021; Sugimoto et al., 2021), Bennu (DellaGiustina et al., 2019; Burke et al., 2021), comet 67P (e.g., Pajola et al., 2015, Pajola et al., 2016), and Enceladus (Pajola et al., 2021). Power–laws are often fitted to these measurements and cumulative power–index steeper than −2 are measured, consistent with highly fragmented material (e.g., Hartmann, 1969; Dohnanyi, 1971; Michel et al., 2001; Jutzi et al., 2010). Extrapolation of the SFD measurement to small sizes have been attempted using different mathematical description of the SFD shapes, i.e., power–law (e.g., Shoemaker and Morris, 1970; Li et al., 2017; Bandfield et al., 2011; Watkins et al., 2019; Krishna and Kumar, 2016), exponential (Shoemaker and Morris, 1970; Golombek and Rapp, 1997; Di et al., 2016; Li and Wu, 2018), and with a Weibull distribution (e.g., Schröder et al., 2021a, Schröder et al., 2021b; Pajola et al., 2016). These extrapolations have been performed to compare and validate SFD measurement with thermal observations sensitive to cm and m scale blocks (e.g., Bandfield et al., 2011), and for landing site hazard analysis (e.g., Golombek and Rapp, 1997; Golombek et al., 2003; Golombek et al., 2008; Wu et al., 2018; Ruesch et al., 2021). Additionally, the relationship between boulder size and source crater has been investigated (Bart and Melosh, 2007; Jia et al., 2019).

Despite abundant SFD measurements, the understanding of sources, evolution, and relationships to surface age of these distributions is vague. Attempts to relate a block population to its exposure age have considered the population as a whole without distinction of its size distribution (Basilevsky et al., 2013; Ghent et al., 2014; Basilevsky et al., 2015; Li et al., 2018; Watkins et al., 2019; Wei et al., 2020; Ruesch et al., 2020; Bickel et al., 2020). Among these studies, the work of Basilevsky et al. (2013) and Ghent et al. (2014) have revealed how the measured destruction rate, for all size combined, is found to be higher than predicted theoretically in the study of Hörz et al. (1975). This poor understanding is in contrast with the relatively well–known erosive processes at the lunar surface, namely shattering (e.g., Hörz et al., 1975; Hörz, 1977; Cintala and Hörz, 1992; Hörz et al., 2020; Ruesch et al., 2020) and abrasion (e.g., Shoemaker et al., 1970; Gault et al., 1972; Hörz et al., 1974; Cintala and Hörz, 1992; Rüsch and Wöhler, 2022) by impact bombardment. Thus, a natural question arises: How does the SFD of a block population on the lunar surface changes with time, in particular at small sizes? This study addresses this question by demonstrating that the evolution of block SFD can be modeled with sufficient precision (in terms of size distribution and absolute time) to allow meaningful comparison with measured block abundances.

Section snippets

Overview

The model is based on an improvement of the Monte Carlo study of Hörz et al. (1975) and exploits the advances over the last 46 years in the understanding of impact shattering and meteoroid flux. Briefly, the model of Hörz et al. (1975) simulates a surface composed of isolated blocks of the same size, formed all at the same time, and subject to bombardment by meteoroids. It tracks the energy imparted to each block by multiple meteoroids and calculate when a block accumulates sufficient energy

Overall model SFD shapes

The shattering energy functions and the projectile SFDs strongly influence the shape of the block SFD and its changes with time (Fig. 4). As expected, the shattering function of BA99 (Fig. 4a, b, c) requires more energy for shattering than the function of HH99 (Fig. 4d, e, f) and so it relatively hampers the decrease of block abundance with time. The rather small differences in the projectile SFDs (Fig. 3) have great influence in the block SFD shape. The steeper projectile SFD leads to enhanced

Survival times of blocks

The plot presenting the survival times (Fig. 9) is the same as Fig. 11 of Hörz et al. (1975), including now larger diameters. The survival times for targets of about 3 cm in size are the same for both old and updated model. For diameters larger than ~5 cm the destruction rates are ~2 times higher than in the original model, i.e., survival time are shorter. This difference is however within the range of uncertainty on the crater production rates recognized in the original model. The crater

Conclusions

The model of block catastrophic rupture of Hörz et al. (1975) is revisited in light of new understanding of the functions describing the energy necessary for block shattering and improved estimates of the flux and size–frequency distributions (SFDs) of meteoroids hitting lunar blocks. The input functions that best reproduce the number and size–frequency distribution of blocks on the lunar surface are identified. With such functions, the modeled block SFD well reproduces measurements of block

Data and code availability

LROC/NAC image data are available at http://wms.lroc.asu.edu/lroc/search.

The code for the updated model is available upon request at Ottaviano Rüsch.

Declaration of Competing Interest

None.

Acknowledgment

OR, RMM, and MP are supported by a Sofja Kovalevskaja award of the Alexander von Humboldt foundation. The constructive comments by two anonymous referees are acknowledged. The authors are grateful to Friedrich Hörz for a discussion of this study. This article is dedicated to A. Elbakyan.

References (109)

  • A.J. Dombard et al.

    Boulders and ponds on the asteroid 433 Eros

    Icarus

    (2010)
  • D.D. Durda et al.

    Collisional models and scaling laws: a new interpretation of the shape of the main-belt asteroid size distribution

    Icarus

    (1998)
  • A. Fujiwara et al.

    Destruction of basaltic bodies by high-velocity impact

    Icarus

    (1977)
  • J. Gramberg

    Axial cleavage fracturing, a significant process in mining and geology

    Eng. Geol.

    (1965)
  • W.K. Hartmann

    Terrestrial, lunar, and interplanetary rock fragmentation

    Icarus

    (1969)
  • F. Hörz

    Impact cratering and regolith dynamics

    Phys. Chem. Earth

    (1977)
  • K. Housen

    Cumulative damage in strength-dominated collisions of rocky asteroids: rubble piles and brick piles

    Planet. Space Sci.

    (2009)
  • K.R. Housen et al.

    On the fragmentation of asteroids and planetary satellites

    Icarus

    (1990)
  • K.R. Housen et al.

    Scale effects in strength-dominated collisions of rocky asteroids

    Icarus

    (1999)
  • Q. Jiang et al.

    Observation of rock fragment ejection in post-failure response

    Int. J. Rock Mec. Min. Sci.

    (2015)
  • M. Jutzi et al.

    Fragment properties at the catastrophic disruption threshold: the effect of the parent body’s internal structure

    Icarus

    (2010)
  • P. Lee et al.

    Ejecta blocks on 243 Ida and on other asteroids

    Icarus

    (1996)
  • S. Mazrouei et al.

    Block distribution on Itokawa

    Icarus

    (2014)
  • T. Michikami et al.

    Boulder size and shape distributions on asteroid Ryugu

    Icarus

    (2019)
  • J.L. Molaro et al.

    Thermally induced stresses in boulders on airless body surfaces, and implications for rock breakdown

    Icarus

    (2017)
  • A. Nakamura et al.

    Velocity distribution of fragments formed simulated collisional disruption

    Icarus

    (1991)
  • J. Oberst

    The present-day flux of large meteoroids on the lunar surface-a synthesis of models and observational techniques

    Planet. Space Sci.

    (2012)
  • M. Pajola et al.

    Abundance and size-frequency distributions of boulders in Linné crater’s ejecta (moon)

    Planet. Space Sci.

    (2019)
  • O. Rüsch et al.

    Degradation of Rocks on the Moon: Insights on Abrasion from Topographic Diffusion, LRO/NAC and Apollo Images.

    (2022)
  • E.M. Shoemaker et al.

    Geology: physics of fragmental debris

    Icarus

    (1970)
  • C. Avdellidou et al.

    Impacts on the moon: analysis methods and size distribution of impactors

    Planet. Space Sci.

    (2021)
  • R.-L. Ballouz et al.

    Bennu’s near-earth lifetime of 1.75 million years inferred from craters on its boulders

    Nature

    (2020)
  • J.L. Bandfield et al.

    Lunar surface rock abundance and regolith fines temperatures derived from LRO diviner radiometer data

    J. Geophys. Res.

    (2011)
  • G.D. Bart et al.

    Using lunar boulders to distinguish primary from distant secondary impact craters

    J. Geophys. Res.

    (2007)
  • A.T. Basilevsky et al.

    Survival times of meter-sized boulders on the surface of the moon

    Planet. Space Sci.

    (2013)
  • A.T. Basilevsky et al.

    Survival times of meter-sized rock boulders on the surface of airless bodies

    Planet. Space Sci.

    (2015)
  • V.T. Bickel et al.

    Impacts drive lunar rockfalls over billions of years

    Nat. Commun.

    (2020)
  • P. Brown et al.

    The flux of small near-earth objects colliding with the earth

    Nature

    (2002)
  • K.N. Burke et al.

    Particle size-frequency distributions of the OSIRIS-Rex candidate sample sites on asteroid (101955) Bennu

    Remote Sens.

    (2021)
  • D.S. Burnett et al.

    Exposure histories of bench crater rocks

    LPSC

    (1975)
  • M.J. Cintala et al.

    An experimental evaluation of mineral specific comminution

    Meteoritics

    (1992)
  • M.J. Cintala et al.

    Block distributions on the lunar surface: A comparison between measurements obtained from surface and orbital photography

  • D.N. DellaGiustina

    Properties of rubble-pile asteroid (101955) Bennu from OSIRIS-REx imaging and thermal analysis

    Nat. Astron.

    (2019)
  • J.S. Dohnanyi

    Fragmentation and Distribution of Asteroids

    (1971)
  • D. Drolshagen et al.

    Mass accumulation of earth from interplanetary dust, meteoroids, asteroids and comets

    Planet. Space Sci.

    (2017)
  • R.J. Drozd et al.

    Cosmic-Ray Exposure History of Taurus-Littrow

    (1977)
  • D.D. Durda et al.

    Experimental investigation of the impact fragmentation of blocks embedded in regolith

    Meteorit. Planet. Sci.

    (2011)
  • G.J. Flynn et al.

    Hypervelocity cratering and disruption of porous pumice targets: implications for crater production, catastrophic disruption, and momentum transfer on porous asteroids

    Planet. Space Sci.

    (2015)
  • D.E. Gault et al.

    The destruction of tektites by micrometeoroid impact

    J. Geophys. Res.

    (1969)
  • D.E. Gault et al.

    Effects of microcratering on the lunar surface

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