New maps of kilometer-scale topographic roughness and concavity of the Moon reveal a very distinctive roughness signature of the proximal ejecta deposits of the Orientale basin (the Hevelius Formation). No other lunar impact basin, even the just-preceding Imbrium basin, is characterized by this type of signature although most have similar types of ejecta units and secondary crater structures. The preservation of this distinctive signature, and its lack in basins formed prior to Orientale, is interpreted to be the result of seismically induced smoothing caused by this latest major basin-forming event. Intense seismic waves accompanying the Orientale basin-forming event preceded the emplacement of its ejecta in time and operated to shake and smooth steep and rough topography associated with earlier basin deposits such as Imbrium. Orientale ejecta emplaced immediately following the passage of the seismic waves formed the distinctive roughness signature that has been preserved for almost 4 billion years.
 Meteoritic impacts have long been understood to generate seismic waves, which can alter the surface of planetary bodies. For example, Houston et al.  argued that seismic shaking from impacts contributes to regolith gardening on the Moon. Seismic shaking works more effectively on small bodies [e.g., Cintala et al., 1978] and has been recognized as the primary cause of global resurfacing on them [e.g., Asphaug and Melosh, 1993; Richardson et al., 2004, 2005; Thomas and Robinson, 2005; Asphaug, 2008]. Seismic shaking can trigger global downslope mass movement, if the acceleration of the surface due to seismic waves is comparable to or exceeds gravity. On the basis of this criterion, Richardson et al. [2005, equation (7)] obtained a scaling relationship giving a minimum impactor size for the global seismic effects. We applied this scaling relationship to the Moon, assumed 1 Hz seismic frequency, at which the seismic wave attenuation of the Moon is known to be low [Nakamura and Koyama, 1982], took a conservative guess of impact seismic efficiency of 10−5, and obtained a 100 km threshold diameter of the projectile. Thus, on the Moon the global seismic effects can be caused only by the largest impacts in its geological history.
 The possibility of global seismic effects of large-scale impact events forming multiring basins on the Moon and other planetary bodies has been recognized long ago [e.g., Schultz and Gault, 1975; Hughes et al., 1977]. Several modeling studies have aimed to understand the concentration of seismic energy in the regions antipodal to impacts [e.g., Hughes et al., 1977; Watts et al., 1991; Boslough and Chael, 1994; Lü et al., 2010]. These studies were inspired by the work by Schultz and Gault , who attributed some specific morphologies in a region antipodal to Caloris basin on Mercury and possibly in regions antipodal to Imbrium and Orientale basins on the Moon to seismic effects. At the present state of knowledge, however, the balance between seismic waves and the convergence of basin ejecta [e.g., Stuart-Alexander, 1978; Wieczorek and Zuber, 2001, and references therein] is not clear in terms of the formation of different morphologies in the antipodal regions. On the other hand, as noted by Hughes et al. , even outside the antipodal regions, seismic waves can produce stresses high enough to disrupt rocks and accelerations high enough to exceed gravity, and thus there is a possibility that basin-forming impacts have a global effect on morphology not limited to the antipodal region.
 Here we present observational evidence that seismic effects of basing-forming impacts indeed resurface the Moon at km scale globally. This evidence results from mapping kilometer-scale topographic roughness and concavity.
2. Mapping Topographic Roughness and Concavity
 We used data from the laser altimeter LOLA [Smith et al., 2010a, 2010b] onboard the Lunar Reconnaissance Orbiter and mapped the statistical parameters of topographic km-scale roughness and concavity in a manner similar to that successfully applied to Mars by Kreslavsky and Head .
 A good statistical measure of roughness should correspond to an intuitive perception of “roughness,” in particular, it should not depend on large-scale tilts of the surface; it should characterize a typical surface rather than its prominent features; it should be tolerant of the heavy tails of statistical distributions of topographic quantities, typical for planetary surfaces. For example, the variance of topography at a given baseline is not a good measure of roughness, because it feels regional slopes. The variance (or standard deviation) of slope at a given baseline, a popular statistics of topography, is also not a good measure of roughness, because it, as any distribution moment, is not tolerant to heavy tails of the slope-frequency distributions: rare very steep slopes cause significant local increase of the variance. If we mapped the variance of slope on the Moon, we would see high values associated with the peculiar steepest topographic features, mostly walls of impact craters; thus, the variance of slopes is an indicator of peculiar features rather than a characteristic of typical, background topographic roughness. For many natural terrains the tails of the slope-frequency distribution are so heavy, that the variance of slope calculated over an arbitrary smaller subset of data for some uniform area is systematically lower than the variance calculated over the whole data set, thus, for such terrains, the variance of slope is not an objective characteristic of terrain at all.
 Here we used the interquartile range of profile curvature as a measure of roughness. To map it, we calculated a proxy for the second derivative (“curvature”), c, of along-orbit topographic profiles at a given baseline, l, at the location of each LOLA laser shot, according to the equation:
where h, h+, and h− are surface elevations at the given laser shot, and shots a half-baseline ahead and a half-baseline behind, respectively. We used different baselines to calculate curvature, which allows us to compare roughness at different spatial scales. For the particular maps presented in this paper, we used two baselines: l = 0.46 km, (8 consecutive LOLA shots), and l = 1.8 km (32 consecutive LOLA shots); the signatures of the impact basins that we analyze are best expressed at these baselines. For each 1/4° × 1/4° map cell (“pixel”), we selected all data points within the cell and collected the frequency distribution of the curvature, c, in the given map cell. The map cell should be much larger than the baseline. Typically, each map cell contained 20–200 data points. Then, for each map cell, we calculated the median (c1/2) and quartiles (c3/4, c1/4) of the curvature-frequency distribution in each cell. We use the interquartile range of this distribution, c3/4–c1/4 to characterize roughness. The numerical values of c3/4–c1/4 are not intuitive and difficult to conceptualize, and we normalized them by a typical value for typical highlands. Thus, we defined roughness r as:
where r0 = 1.7 × 10−5 m−1 for l = 0.48 km baseline, and r0 = 0.6 × 10−5 m−1 for l = 1.8 km baseline. Figures 1a and 1b show maps of roughness r at the longer and the shorter baselines, respectively. The brightest sites in Figure 1b are saturated: normalized roughness of several young craters significantly exceeds 2, the upper limit of the scale in this image.
 The interquartile range of curvature possesses the abovementioned qualities of a good measure of roughness. The use of the second spatial derivative of elevation (curvature) made it insensitive to regional slopes. The characteristic width of the curvature-frequency distribution characterizes sharpness of typical slope breaks and thus corresponds to intuitive concept of roughness. The use of the interquartile range, a robust estimator of the scale of frequency distributions, made our measure of roughness insensitive to the heavy tails. The maps (Figures 1a and 1b) show that typical highlands have rather uniform roughness; old large craters do not come out as individual features. This confirms that our roughness measure does characterize typical background topography rather than features well seen in the images. Another example of a good measure of roughness is the median differential slope proposed for Mars by Kreslavsky and Head  and applied to LOLA data by Rosenburg et al. . Maps of this measure of roughness at the same baselines, if properly contrasted, are almost indistinguishable from the maps we used in the present work.
 Positive values of profile curvature c correspond to concave segments of topographic profiles, while negative values correspond to convex segments. An ideal imaginary surface made of smooth bowl-shaped craters with sharp rims, would be almost entirely concave, except a very small area of rim crests. For typical highlands shaped by numerous impacts and downslope movement of regolith, concave segments are more frequent than convex segments. Figure 2 (middle, bold violet curve) shows the frequency distribution of curvature c/r0 at l = 1.8 km baseline calculated over a large area of typical highlands (∼108 data points). To illustrate the asymmetry of this distribution its left, negative (convex) branch is duplicated with a thin line flipped to the right. It is seen that the bold line is above the thin line (except for rare high curvature values), which means that the number of concave segments exceeds the number of convex segments; concave segments prevail. The same typically occurs for the curvature-frequency distributions inside the map cells, with the distinction that the total number of data points is much smaller and the distributions are much noisier.
 Concavity is a quantitative measure of prevalence of concave topographic forms over convex ones. The rationale for our choice of particular statistical measure of concavity is similar to that of roughness. For example, skewness of the curvature-frequency distribution, like any other measure based on the distribution moments, is not a good measure of concavity because it is badly affected by the heavy tails of the distribution. The median curvature c1/2 does characterize the misbalance between segments of profiles with the positive and negative values of c and is little affected by the tails. However, if we imaginarily stretched all topography vertically, all values of c would proportionally increase, and c1/2 would also proportionally increase. To obtain a statistics that characterizes the proportion of concave segments regardless of the vertical scale, we normalized the median curvature c1/2 by the characteristic scale of the curvature variations. Thus, we used the median curvature normalized by its interquartile range as a measure of concavity v:
Positive concavity values indicate the prevalence of concave segments of topographic profiles; negative concavity indicates the prevalence of convex topographic forms. For the “Highlands” distribution in Figure 2, equation (3) gives v = 0.033. We calculated concavity v for each map cell and obtained a concavity map. (The median value of concavity in cells that belong to the typical highlands is about 0.100, significantly higher than the concavity calculated for the whole distribution over the same area, 0.033; this occurs due to the nonlinear nature of the concavity measure we use.) Because concavity has a high level of inherent noise, we applied additional cosmetic filtering to this map to reduce the noise in exchange for resolution; Figure 1c shows the result.
 When we look at the surface images or simulated illuminated topography, our eyes catch the most prominent features; slope breaks associated with these features usually occupy only small proportions of the map cells and hence, due to our choice of statistics, they have a small influence on the roughness and concavity. Our measures r and v characterize the most typical, dominant topography. In a sense, the roughness and concavity maps make visible some variations of topographic properties that are not readily apparent in the images.
 Roughness at both baselines and concavity at the longer baseline are shown in Figure 3 as an RGB color composite: roughness at longer (Figure 1a) and shorter (Figure 1b) baselines is coded in the red and green channels, respectively; brighter shades denote rougher surfaces; concavity (Figure 1c) is coded in the blue channel; brighter shades denote higher concavity. The most obvious feature on this composite map is the dichotomy between the smooth (dark) maria and the rough (brighter) highlands. In the RGB color composite, typical highlands have bluish and pinkish shades, which denotes the prevalence of concave topography (high intensity in the blue channel). A few of the largest Copernican (the youngest) craters and proximal ejecta of some of them are light green in the map (Figure 3): they are extremely rough, especially at the shorter baseline, and have reduced (in comparison to typical highlands) concavity. Several of the largest Eratosthenian and Upper Imbrian craters have distinctive orange or yellowish surroundings, which indicates excessive roughness of their proximal ejecta at the longer baseline and reduced concavity.
3. The Roughness and Concavity Signature of Impact Basins
 After the mare - highlands dichotomy, the next most striking feature is the 930 km diameter Orientale multiring impact basin (Figure 4a; O in Figure 3) with its prominent zone of continuous ejecta (the Hevelius Formation [McCauley, 1967, 1977; Fassett et al., 2011b]; its typical exposures are outlined with arrows in Figure 4a) immediately surrounding and distal to the topographic rim crest (Cordillera Montes ring). The Hevelius Formation is noticeably rougher than typical highlands (by factors of 1.2 and 1.3 at the shorter and longer baselines, respectively) and hence appears brighter in Figure 3. The pronounced yellow shade that characterizes the Hevelius Formation in Figure 3 is due to its low concavity (∼0.04) in comparison to typical highlands. A set of rough near-radial ray-like features is seen outside the distal boundary of the Hevelius Formation, and occur in the position of secondary crater chains radiating from the basin and observed in images.
 Orientale basin is unique; of the many basins on the Moon [Wilhelms, 1987], no other impact basin has this prominent roughness signature in Figure 3. The Imbrium basin (Figure 4b; I in Figure 3), which is slightly larger than Orientale and is slightly older, but very close in age [Wilhelms, 1987; Stöffler and Ryder, 2001], shows no sign of such a signature. Its ejecta deposit (the Fra Mauro Formation [Wilhelms and McCauley, 1971]; its typical exposures are outlined with arrows in Figure 4b), where it is not covered with mare material and not modified by young craters, is noticeably smoother than typical highlands (its typical roughness is 0.6–0.8 at both baselines) and is characterized by moderate concavity (0.07).
 Curvature-frequency distributions calculated over the entire exposure areas (Figure 2) provide another way to characterize the striking difference between the Hevelius and Fra Mauro Formations. The distributions show clearly that the Hevelius Formation is significantly rougher than typical highlands (r = 1.20; orange curve in Figure 2 is wider than the violet curve), while the Fra Mauro Formation is smoother (r = 0.53; green curve is narrower). The Hevelius Formation has a small negative concavity (v = −0.008; the thin orange curve is above the bold orange curve in Figure 2), while the Fra Mauro Formation has a small positive concavity (v = +0.012; thin green curve is below the bold one). (The quantitative discrepancy between r and v reported in this paragraph and the median r and v over the corresponding map areas reported in the beginning of this section are due to the nonlinear nature of our definitions of r and v). What is the origin of the unique strong roughness signature characterizing the Orientale basin exterior?
 Orientale is the youngest basin of its size [Wilhelms, 1987], and the roughness signature of its ejecta is best preserved as seen in the images at visible wavelengths [Head, 1974; Head et al., 1993; Scott et al., 1977; Spudis, 1993]. Ejecta deposits of very old basins have been partly to completely modified by superposed impact craters [Head et al., 2010; Fassett et al., 2011a, 2011b] and by later nearby crater and basin ejecta (proximity degradation [Head, 1975]); at some point in their history they become indistinguishable from typical highlands. The degradation sequence alone, however, cannot account for the observed unique signature of the Orientale basin. The Imbrium basin is only slightly older than Orientale: craters larger than 20 km superposed on the Imbrium basin are only factor of 1.5 denser than those superposed on the Orientale basin, while on typical highlands they are a factor of 5 to 13 denser [Head et al., 2010]. Nevertheless, Imbrium ejecta roughness signature is strikingly different; moreover, it is not transitional between the roughness signatures of Orientale ejecta and that of typical highlands. Schrödinger, a small basin interpreted to postdate the Imbrium event and predate the Orientale event [Wilhelms, 1987, Fassett et al., 2011b] also does not show a distinctive roughness signature. Thus, some geologically rapid (because of the small age difference) and powerful (because of the major change in values) process other than simple gradual accumulation of small impacts must be responsible for the effective smoothing of all impact basin ejecta except that surrounding the Orientale basin.
 We explore the obvious possibility that the basin-forming impact itself causes such a process. In this scenario, the formation of each new basin could significantly modify the roughness signature of a preceding basin. Orientale, being the last of the large basins [Wilhelms, 1987; Head et al., 2010], is thus the only well-preserved. What factors associated with the Orientale basin-forming event could account for this degradation process? An excellent candidate for an impact-caused process is intensive global seismic shaking associated with the event. Schultz and Gault  showed that on the Moon the first (the strongest) seismic waves, both the internal p-waves and the surface-bound Rayleigh waves, always travel across the area of basin continuous ejecta before the emplacement of ejecta. The seismic shaking associated with these waves mobilizes the surface material and promotes intensive downslope movement for kilometer-scale and shorter slopes, and tends to form smooth fill in local lows. This process would cause smoothing of topography, because local highs would get lower, local lows would get higher, local elevation amplitude would decrease; therefore, typical curvatures would proportionally decrease. Simultaneously, smooth fill of local lows would tend to replace mixture of concave and convex shapes with smoother predominantly concave shapes, while convex shapes of local highs would become sharper and hence cover smaller areas; therefore the downslope movement of material would increase the proportion of area occupied by concave shapes and hence increase concavity.
 Kilometer-scale roughness of typical heavily cratered highlands results from a dynamical balance between roughening by impacts producing kilometer and larger craters, and smoothing by small impacts and by seismic shaking by distal basin-forming impacts. Similarly, kilometer-scale concavity of typical highlands results from a dynamical balance between an increase due to the formation of (concave) craters, regolith gardening, and seismic shaking, and a decrease due to emplacement of ejecta of larger craters. Cratered highlands had experienced many pre-Orientale shaking events, and thus one more event does not alter the topography significantly. Proximal ejecta of basins erase the equilibrated topography and replace it with specific ejecta topography. Orientale ejecta are rather pristine (except minor modification by regolith gardening). Imbrium ejecta were emplaced originally with a topographic signature similar to Orientale ejecta and then were modified (smoothed) by the Orientale seismic episode. They, however, are still far from the dynamic equilibrium characteristic of typical highlands: they have not been significantly roughened by kilometer-scale craters. Seismic shaking smoothed the old highlands less effectively than the fresh Imbrium ejecta, because abundant km-size and larger craters on the highlands are not erased by shaking and do contribute to kilometer-scale roughness, while for the fresh ejecta, large craters are absent and roughness is caused by features of smaller scale.
 Small, decameter-scale morphologies characteristic of seismically triggered intensive downwasting (small landslides, etc.) are likely to have been obliterated and overprinted by subsequent smaller-scale impacts and regolith gardening, but the signature of intensive downwasting would be preserved at kilometer scales and is revealed by the roughness map (Figure 3). Obliteration of old decameter-scale morphologies is obvious in high-resolution images; it is also evident from the 0.12-km baseline roughness (not shown here [see Rosenburg et al., 2011]): roughness at this small scale has a much narrower variability (the highlands and maria are similar), except for the youngest, Copernican-aged craters.
 Seismic shaking plays a role as a trigger for downslope movement of surface material. Seismic energy is expended to cause mobilization of material; its movement, smooth filling of local lows that causes the decrease of roughness and increase of concavity, occurs under the force of gravity. The downslope movement releases gravitational energy, which is partly converted to seismic and acoustic energy. In this way the resurfacing process triggered by the intensive seismic disturbance from the impact is self-supporting to some extent. If the specific morphologies in the basin antipodal regions indeed have a seismic origin, the mechanism of influence of seismic waves on topography in those regions should be different: concentrated seismic energy is expended to construct some topographic features.
 The region antipodal to Orientale shows anomalous orange shades in the composite map (arrows in Figure 3): it has an increased roughness at both scales, especially at the longer one, and a decreased concavity. This signature is rather similar to the signature of the Hevelius Formation. It might be a hint that the specific surface morphology here is caused by concentration of distal Orientale ejecta [Stuart-Alexander, 1978; Wieczorek and Zuber, 2001]. However, the genetic association of this antipodal roughness / concavity anomaly with the Orientale-forming impact is not obvious from Figure 3 alone: the anomaly can also be caused by the proximal ejecta of large Upper Imbrian crater Hubble. We would like to re-emphasize that our conclusion about the role of seismic effects is based on comparison of basin continuous ejecta, and not on any peculiarities of the antipodal regions.
 No post-Orientale impact crater on the Moon was apparently large enough to trigger global resurfacing. However, it is very probable that the seismic effects associated with these sub-basin-scale events left local observable traces in the areas adjacent to the larger impact craters and small basins. It is possible that some small-scale morphologies observed at high-resolution in association with Copernican-aged craters have a seismic origin.
 Due to stronger gravity on Mercury, the threshold for seismic amplitudes required to affect kilometer-scale topography is higher than on the Moon. The presence of a large presumably molten core causes the seismic effects of large impacts on Mercury to differ significantly from the Moon (see discussion by Lü et al. ). It is interesting to look for possible topographic indications of seismic effects associated with the youngest large impact basin on Mercury [Fassett et al., 2009]. This can be done with data from the Mercury Laser Altimeter (MLA) instrument, onboard the MESSENGER spacecraft currently in orbit around Mercury. On Mars, the largest terrestrial planet preserving ancient crust and impact basins, the roughness / concavity signature of the basin ejecta is completely overprinted by later modification [Kreslavsky and Head, 2000, 2002] associated with atmospheric and aqueous processes [e.g., Carr and Head, 2010].
 As we already mentioned, seismic shaking has been recognized as a major mechanism of global resurfacing of asteroids and other small bodies [e.g., Asphaug and Melosh, 1993; Richardson et al., 2004, 2005; Thomas and Robinson, 2005]. While on the Moon the global resurfacing affects kilometer-scale topography, but leaves 10-km scale and larger craters well recognizable, on small bodies the seismic effects can completely reset the observed geological record (see discussion by Asphaug ).
 We presented global maps of topographic roughness and concavity of the lunar surface at the kilometer scale. We compared the roughness / concavity signatures of the Hevelius and Fra Mauro Formations with typical highlands. We concluded that seismic shaking by basin-forming impacts causes significant modification of kilometer-scale topography of the Moon. During the Nectarian and Imbrian, the epochs of basin-forming impacts, seismic shaking played a significant role in shaping the surface along with cratering and volcanism.
 This work was partly funded as part of J.W.H.'s membership on the Lunar Reconnaissance Orbiter Lunar Orbiter Laser Altimeter (LOLA) team, under NASA grant NNX09AM54G to J.W.H.