Icarus 226 (2013) 52–66 Contents lists available at SciVerse ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Lunar topographic roughness maps from Lunar Orbiter Laser Altimeter (LOLA) data: Scale dependence and correlation with geologic features and units ⇑ Mikhail A. Kreslavsky a, , James W. Head b, Gregory A. Neumann c, Margaret A. Rosenburg d, Oded Aharonson e, David E. Smith f, Maria T. Zuber f a Earth and Planetary Sciences, University of California, Santa Cruz, CA 95064, USA b Department of Geological Sciences, Brown University, Providence, RI 02912, USA c Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA d Division of Geological and Planetary Sciences, Caltech, Pasadena, CA 91125, USA e Center for Planetary Science, Weizmann Institute of Science, Rehovot, 76100, Israel f Department of Earth, Atmospheric and Planetary Sciences, MIT, Cambridge, MA 02139, USA article info abstract Article history: We present maps of the topographic roughness of the Moon at hectometer and kilometer scales. The Received 2 November 2012 maps are derived from range profiles obtained by the Lunar Orbiter Laser Altimeter (LOLA) instrument Revised 8 March 2013 onboard the Lunar Reconnaissance Orbiter (LRO) spacecraft. As roughness measures, we used the inter- Accepted 20 April 2013 quartile range of profile curvature at several baselines, from 115 m to 1.8 km, and plotted these in a glo- Available online 3 May 2013 bal map format. The maps provide a synoptic overview of variations of typical topographic textures and utilize the exceptional ranging precision of the LOLA instrument. We found that hectometer-scale rough- Keywords: ness poorly correlates with kilometer-scale roughness, because they reflect different sets of processes and Moon, surface time scales. Hectometer-scale roughness is controlled by regolith accumulation and modification pro- Regoliths Data reduction techniques cesses and affected by the most recent events, primarily, geologically recent (1–2 Ga) meteoritic impacts. Geological processes Kilometer-scale roughness reflects major geological (impact, volcanic and tectonic) events in earlier geo- logical history. Young large impact craters are rough, and their roughness decreases with age. The global roughness maps revealed a few unusually dense clusters of hectometer- and decameter-size impact cra- ters that differ in their morphology and settings from typical secondary crater clusters and chains; the origin of these features is enigmatic. The maps can assist in the geological mapping of the lunar maria by revealing contacts between volcanic plain units. The global roughness maps also clearly reveal cryp- tomaria, old volcanic plains superposed by younger materials, primarily crater and basin ejecta. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction and inconvenient. Roughness maps give a generalized overview of texture variations at large scale. Laser altimeter instruments onboard orbital planetary missions Second, roughness maps help to focus on typical topography rather significantly advanced our knowledge of the Moon, Mars, Mercury. than on peculiar features. When we look at topographic maps and Topographic maps derived from the laser altimeter data are widely images, our eyes see the most prominent features and often miss back- used in geological studies. In addition to the topographic maps, ground textures. For example, when we look at the lunar highlands, we synoptic maps of topographic roughness can be useful. There are see the distinctive impact craters, and it is very difficult to ignore craters a few reasons, why in some circumstances the use of roughness and focus on intercrater textures. Properly designed roughness maps maps is essential for geologic studies. display the most typical topographic textures and ignore rare features. First, roughness maps provide a convenient large-scale over- Finally, roughness maps utilize the exceptional internal preci- view of small-scale textures. To map regional variations of textures sion of laser altimeter data. The precision of the range determina- solely with topographic maps, a geologist constantly needs to tion along each spacecraft orbit is much higher than the accuracy switch from large scale to small scales, which is time-consuming of orbit knowledge, and the accuracy of the topographic maps is much worse than the internal precision of the original measure- ⇑ Corresponding author. Address: Earth and Planetary Sciences, University of ments. In addition, the gaps between orbit tracks are often wider California–Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA. Fax: +1 831 459 than the distance between elevation measurements along the or- 3074. bit, and the effective resolution of the topographic maps is worse E-mail address: [email protected] (M.A. Kreslavsky). 0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.04.027 M.A. Kreslavsky et al. / Icarus 226 (2013) 52–66 53 than measurement spacing along each orbit track. Roughness maps 0.8 km, however, the distance varies widely, and there are gaps rely on and utilize the exceptional internal precision and available as wide as 4 km. along-orbit spacing of the orbital laser altimeter data. Topographic roughness depends on spatial scale; this depen- Roughness maps have proven to be useful in planetary geology. dence bears essential information, as we will see later in the paper. Kilometer-scale topographic roughness maps of Mars (Kreslavsky To characterize it, we map roughness for a set of baselines l. Con- and Head, 2000) generated with Mars Orbiter Laser Altimeter secutive shots along each orbit are separated by 57.4 m; this dis- (MOLA) data (Smith et al., 2001) clearly showed many geomorpho- tance is conveniently constant within ±3% through the whole logic units on Mars, for example, patches of heavily cratered Noa- data set. Our roughness measure uses baselines with an even num- chian-age volcanic plains are well distinguished from surrounding ber of shot-to-shot steps. Thus, the shortest baseline we can use is heavily cratered highlands. The maps revealed a latitudinal trend 2 shot-to-shot steps, that is l = 115 m. In addition to this, we also in topographic roughness, which was important in understanding present maps of roughness at baselines of 8, 16, and 32 shot-to- the nature of recent climate change on Mars (Head et al., 2003). shot steps, that is l = 0.46 km, 0.92 km, and 1.8 km. Cord et al. (2007) used stereo-derived digital elevation models to For each shot, we calculated a proxy for the second derivative make decameter- and hectometer-scale roughness maps of some (‘‘curvature’’), c, of along-orbit topographic profiles, according to martian terrains. the equation: Kreslavsky (2010) produced maps of topographic roughness of 2 the Moon using data from laser altimeter LALT onboard Kaguya c ¼ðhþ þ hÀ À 2hÞ=l ; ð1Þ mission (Araki et al., 2008, 2009). These maps revealed the unique- ness of Orientale basin ejecta (Hevelius Formation) in comparison where h, h+, and hÀ are surface elevations at the given laser shot, to other impact basin ejecta deposits on the Moon. The use of LALT and shots a half-baseline ahead and a half-baseline behind, respec- data, however, is limited because of long distances between mea- tively. If any of h, h+, and hÀ were missing or marked as bad in the surements along the orbit and a small total amount of data. LOLA data set, we discarded such a curvature value. In total, about Due to its exceptional vertical precision, short along-orbit spac- 6% of data points were discarded in this way. For l in (1) we used ing, and large volume of data, the Lunar Orbiter Laser Altimeter actual horizontal distance between the shot locations at h+, and (LOLA) (Smith et al., 2010a,b) onboard LRO is an excellent data hÀ. As we noted above, its difference between this actual distance source for roughness mapping. The first roughness maps of the and the ‘‘nominal’’ baseline of 115 m, 0.46 km, 0.92 km, and Moon with LOLA data were produced by Rosenburg et al. (2011). 1.8 km does not exceed 3% and causes no bias. Kreslavsky and Head (2012) used LOLA-derived roughness maps We built the global maps in different map projections; nomi- to analyze the uniqueness of the Hevelius Formation roughness nally, we used the scale that correspond to 8 pixels per degree signature. Whitten et al. (2012) use LOLA-derived roughness maps sampling, in other words, 3.8  3.8 km2 pixel size at the projec- in their analysis of cryptomaria. tion’s standard point or line. For each map pixel, we found all LOLA In this paper we (1) consider the technique of roughness map- shots located within the distance R from the center of the pixel. p pix ping with LOLA data, (2) discuss the rationale for our choice of the The minimal reasonable Rpix is 2/2 of the nominal pixel side: for statistical measure of roughness, (3) present global roughness shorter Rpix some data would be unused. We used this minimal maps of the Moon, (4) analyze the appearance of major geological Rpix = 2.7 km for all maps, except the longest baseline of features in these maps, and (5) discuss primary inferences about l = 1.8 km, for which we used Rpix = 3.8 km. For the minimal Rpix surface-shaping and modifying processes. the majority of shots belong only to one pixel, but some of them belong to 2 pixels. Typically, 2–8 orbits contribute to a pixel (ex- cept high latitudes); each orbit typically adds a few tens of data 2. Mapping roughness points. Some pixels (1%, depending on the map projection used) have no data. We also considered pixels having too few points (less In this section we first describe the algorithm we used to pro- than 20) as having no data.