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Volume 60 Supplement 4

Special Issue: Lunar Science with the SELENE “Kaguya” Mission-Prelaunch Studies-

Lunar cratering chronology: Statistical fluctuation of crater production frequency and its effect on age determination

Abstract

The crater frequency is often used to determine ages of planetary surfaces. In this study, we evaluate the statistical fluctuation of the crater frequency and its effect on age determination using a Monte Carlo simulation prior to the SELENE (KAGUYA) / Terrain Camera acquiring extensive high-resolution images over the entire Moon. We found that the ages estimated between 2.5 and 3.5 Gyr tend to be too young when there are not enough craters. Age determination for Eratosthenian units is least accurate. The errors defined with 1σ are 0.7 Gyr for units of 100 km2, 0.5 Gyr for units of 1000 km2, and 0.4 Gyr for units of 2500 km2. The maximum error exceeds 20% and is comparable with the error due to the cratering asymmetry.

References

  • Baldwin, R. B., Relative and absolute ages of individual craters and the rate of infalls on the moon in the post-imbrium period, Icarus, 61, 63–91, 1985.

    Article  Google Scholar 

  • Basilevsky, A. T., On the evolution rate of small lunar craters, Proc. Lunar Sci. Conf. 7th, 1005–1020, 1976.

    Google Scholar 

  • Chapman, C. R. and R. R. Haefner, A critique of methods for analysis of the diameter-frequency relation for craters with special application to the moon, J. Geophys. Res., 72, 549–557, 1967.

    Article  Google Scholar 

  • Crater Analysis Techniques Working Group, Standard techniques for presentation and analysis of crater size-frequency data, Icarus, 37, 467–474, 1979.

  • Dundas, C. M. and A. S. McEwen, Rays and secondary craters of Tycho, Icarus, 186, 31–40, 2006.

    Article  Google Scholar 

  • Gault, D. E., Saturation and equilibrium conditions for impact cratering on the lunar surface, Radio Sci., 5, 273–291, 1970.

    Article  Google Scholar 

  • Greeley, R., 12 colleagues, Galileo imaging observations of lunar maria and related deposites, J. Geophys. Res., 98, 17183–17205, 1993.

    Article  Google Scholar 

  • Hartmann, W. K., Lunar cratering chronology, Icarus, 13, 299–301, 1970.

    Article  Google Scholar 

  • Hartmann, W. K., Paleocratering of the Moon: Review of post-Apollo data, Astrophys. Space Sci., 17, 48–64, 1972.

    Article  Google Scholar 

  • Hartmann, W. K., Does crater “saturation equilibrium” occur in the Solar system, Icarus, 60, 56–74, 1984.

    Article  Google Scholar 

  • Hartmann, W. K. and R. W. Gaskel, Planetary cratering 2: Studies of saturation equilibrium, Meteorit. Planet. Sci, 32, 109–121, 1997.

    Article  Google Scholar 

  • Haruyama, J., H. Otake, M. Ohtake, A. Shiraishi, N. Hirata, and T. Matsunaga, LISM (Lunar Imager/SpectroMeter) mission for SELENE project, Lunar Planet. Sci. XXXI, Abstract #1317, 2000.

    Google Scholar 

  • Haruyama, J., M. Ohtake, N. Hirata, R. Nakamura, and T. Matsunaga, Expected performance of Lunar Imager/SpectroMeter on SELENE, Lunar Planet. Sci. XXXIV, Abstract #1565, 2003.

    Google Scholar 

  • Haruyama, J., M. Ohtake, T. Matsunaga, and LISM working group, Global high-resolution stereo mapping of the Moon with the SELENE Terrain Camera, Adv. Geosci., 3, 101–108, 2006a.

    Article  Google Scholar 

  • Haruyama, J., M. Ohtake, T. Matsunaga, T. Morota, A. M. Yoshizawa, and LISM working group, Planned Digital Terrain Model products from SELENE Terrain Camera data, Lunar Planet. Sci. XXXVII, Abstract #1132, 2006b.

    Google Scholar 

  • Haruyama, J., T. Matsunaga, M. Ohtake, T. Morota, C. Honda, Y. Yokota, M. Torii, Y. Ogawa, and the LISMWorking Group, Global lunar-surface mapping experiment using the Lunar Imager/Spectrometer on SELENE, Earth Planets Space, 60, this issue, 243–255, 2008.

    Article  Google Scholar 

  • Hiesinger, H., R. Jaumann, G. Neukum, and J. W. Head III, Age of mare basalts on the lunar nearside, J. Geophys. Res., 105, 29239–29275, 2000.

    Article  Google Scholar 

  • Hiesinger, H., J. W. Head III, U. Wolf, R. Jaumann, and G. Neukum, Ages and stratigraphy of mare basalts in Oceanus Procellarum, Mare Nubium, Mare Cognitum, and Mare Insularum, J. Geophys. Res., 108, doi:10.1029/2002JE001985, 2003.

  • Hiesinger, H., J. W. Head III, U. Wolf, R. Jaumann, and G. Neukum, New ages for basalts in Mare Fecunditatis based on crater size-frequency measurements, Lunar Planet. Sci. XXXVII, Abstract #1151, 2006.

    Google Scholar 

  • Hirata, N. and A. M. Nakamura, Secondary craters of Tycho: sizefrequency distributions and estimated fragment size-velocity relationships, J. Geophys. Res., 111, E03005, doi:10.1029/2005JE002484, 2006.

    Google Scholar 

  • Honda, C., T. Morota, and J. Haruyama, A determination of surface ages of small geologic units on the terrestrial planets and satellites, 36th COSPAR Scientific Assembly, Abstract #2783, 2006.

    Google Scholar 

  • Honda, C., T. Morota, Y. Yokota, J. Haruyama, M. Ohtake, T. Matsunaga, Y. Ogawa, H. Demura, N. Hirata, A. Iwasaki, S. Kodama, S. Hara, K. Hioki, and LISM working group, Preliminary test of accuracy of Digital Terrain Model derived from SELENE/LISM/TC data, Lunar Planet. Sci. XXXVIII, Abstract #1899, 2007.

    Google Scholar 

  • Ivanov, B. A., Earth/Moon impact rate comparison: searching constraints for lunar secondary/primary cratering proportion, Icarus, 183, 504–507, 2006.

    Article  Google Scholar 

  • Kreslavsky, M. A., Statistical characterization of spatial distribution of impact craters: implications to present-day cratering rate on Mars, 7th Inter. Conf. Mars, Abstract #3325, 2007.

    Google Scholar 

  • Lehmer, D. H., Mathematical methods in large-scale computing units, In Proceedings of 2nd Symposium on Large-Scale Digital Calculating Machinery, Harvard Univ. Press, pp. 141–146, 1951.

    Google Scholar 

  • Matsunaga, T., M. Ohtake, Y. Hirahara, and J. Haruyama, Development of a visible and near infrared spectrometer for Selenological and Engineering Explorer (SELENE), Proc. SPIE, 4151, 32–39, 2

    Article  Google Scholar 

  • Matsunaga, T., M. Ohtake, and T. Sugihara, Environmental test results and their implications to the performance of SELENE Spectral Profiler, Proc. 23rd Inter. Symp. Space Techn. Sci., 1922–1927, 2002.

    Google Scholar 

  • McEwen, A. S. and E. B. Bierhaus, The importance of secondary cratering to age constraints on planetary surfaces, Ann. Rev. Earth Planet. Sci., 34, 535–567, 2006.

    Article  Google Scholar 

  • McEwen, A. S., B. S. Preblich, E. P. Turtle, N. A. Artemieva, M. P. Golombek, M. Hurst, R. L. Kirk, D. M. Burr, and P. R. Christensen, The rayed crater Zunil and interpretations of small impact craters on Mars, Icarus, 176, 351–381, 2005.

    Article  Google Scholar 

  • Morota, T., T. Ukai, and M. Furumoto, Influence of the asymmetrical cratering rate on the lunar cratering chronology, Icarus, 173, 322–324, 2005.

    Article  Google Scholar 

  • Morota, T., J. Haruyama, C. Honda, Y. Yokota, M. Ohtake, and M. Furumoto, Lunar apex-antapex cratering asymmetry as an impactor recorder in the Earth-Moon system, Adv. Space Res., 2007 (in press).

    Google Scholar 

  • Namiki, N. and C. Honda, Testing hypotheses for the origin of steep slope of lunar size-frequency distribution for small craters, Earth Planets Space, 55, 39–51, 2003.

    Article  Google Scholar 

  • Neukum, G., Meteoritenbombardement und Datierung planetarer Oberflachen, Habilitation Dissertation for Faculty Membership, Ludwig Maximilianis Univ., Munich, 1983.

    Google Scholar 

  • Neukum, G. and B. A. Ivanov, Cratering size distributions and impactprobabilities on Earth from lunar, terrestrial planet, and asteroid cratering data in Hazards Due to Comet and Asteroids, edited by T. Gehrels, pp. 359–416, Univ. of Arizona Press, Tucson, 1994.

    Google Scholar 

  • Neukum, G. and B. Konig, Dating of individual lunar craters, Proc. Lunar Sci. Conf. 7th, 2867–2881, 1976.

    Google Scholar 

  • Neukum, G., B. Konig, and J. Arkani-Hamed, A study of lunar impact crater size-distributions, The Moon, 12, 201–229, 1975a.

    Article  Google Scholar 

  • Neukum, G., B. Konig, H. Fechtig, and D. Storzer, Cratering in the earthmoon system: Consequences for age determination by crater counting, Proc. Lunar Sci. Conf. 6th, 2597–2620, 1975b.

    Google Scholar 

  • Ohtake, M., J. Haruyama, H. Otake, and T. Matsunaga, LISM mission for the SELENE project, Proc. 4th Int. Conf. On the Exploration and Utilisation of the Moon, 203–206, 2000.

    Google Scholar 

  • Ohtake, M., J. Haruyama, T. Matsunaga, S. Kodama, T. Morota, and Y. Yokota, Scientific objectives and specification of the SELENE Multiband Imager, Adv. Space Res., 2007 (in press).

    Google Scholar 

  • Soderblom, L. A. and L. A. Lebofsky, Technique for rapid determination of relative ages of lunar areas from orbital photograpy, J. Geophys. Res., 77, 279–296, 1972.

    Article  Google Scholar 

  • Wilhelms, D. E., Geologic history of the Moon, U.S. Geol. Surv. Prof. Pap., 1348, 302 pp, 1987.

    Google Scholar 

  • Yokota, Y., J. Haruyama, M. Ohtake, T. Matsunaga, C. Honda, T. Morota, H. Demura, N. Hirata, and LISM working group, Kilometer scale roughness analysis of lunar digital terrain model, Lunar Planet. Sci. XXXVIII, Abstract #2430, 2007.

    Google Scholar 

  • Young, R. A., Mare crater size-frequency distributions: implications for relative surface ages and regolith, Proc. Lunar Sci. Conf. 6th, 2645–2662, 1975.

    Google Scholar 

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Correspondence to Tomokatsu Morota.

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Morota, T., Haruyama, J., Honda, C. et al. Lunar cratering chronology: Statistical fluctuation of crater production frequency and its effect on age determination. Earth Planet Sp 60, 265–270 (2008). https://doi.org/10.1186/BF03352790

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  • DOI: https://doi.org/10.1186/BF03352790

Key words

  • Moon
  • cratering chronology
  • crater size-frequency distribution
  • statistical fluctuation