Topographic power spectra of cratered terrains: Theory and application to the Moon
Abstract
Impact cratering produces characteristic variations in the topographic power spectral density (PSD) of cratered terrains, which are controlled by the size-frequency distribution of craters and the spectral content (shape) of individual features. These variations are investigated here in two parallel approaches. First, a cratered terrain model, based on Monte Carlo emplacement of craters and benchmarked by an analytical formulation of the one-dimensional PSD, is employed to generate topographic surfaces at a range of size-frequency power law exponents and shape dependencies. For self-similar craters, the slope of the PSD, β, varies inversely with that of the production function, α, leveling off to 0 at high α (surface topography dominated by the smallest craters) and maintaining a roughly constant value (β ∼ 2) at low α (surface topography dominated by the largest craters). The effects of size-dependent shape parameters and various crater emplacement rules are also considered. Second, we compare the model-derived predictions for the behavior of the PSD with values of β calculated along transects from the Lunar Orbiter Laser Altimeter (LOLA). At small scales (∼115 m to 1 km) model predictions agree well with the PSD slope over the observed range of lunar size-frequency distributions. Differences between global PSD slopes at subkilometer and kilometer scales reflect a scale separation in roughness consistent with prior observations using a variety of surface roughness parameters. Understanding the statistical markers left by the impact cratering process on the lunar surface is useful for distinguishing between competing geological processes on planetary surfaces throughout the solar system.
Additional Information
© 2015 American Geophysical Union. Received 21 OCT 2014; Accepted 9 JAN 2015; Accepted article online 12 JAN 2015; Published online 13 FEB 2015. Topography data collected by the Lunar Orbiter Laser Altimeter (LOLA) are available at the LOLA/LRORS PDS Data Node at http://imbrium.mit.edu. The authors acknowledge support from the Lunar Reconnaissance Orbiter project, NASA LOLA grant NNX15AB23G, the Weizmann Minerva Center, I-Core, ISA, ISF, and the Packard Fellowship programs.Attached Files
Published - jgre20358.pdf
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Additional details
- Eprint ID
- 56789
- Resolver ID
- CaltechAUTHORS:20150420-150449404
- NNX15AB23G
- NASA
- Weizmann Minerva Center
- I-CORE Program
- Israel Space Agency
- Israeli Science Foundation
- David and Lucile Packard Foundation
- Created
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2015-04-20Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field