Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps

Planetary and Space Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps Bo Li a, Zongcheng Ling a,n, Jiang Zhang a, Jian Chen a, Zhongchen Wu a, Yuheng Ni a, Haowei Zhao b a Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, Institute of Space Sciences, Shandong University, Weihai 264209, China b Downhole Service Company, Daqing Oilfield Limited Company, Daqing 163000, China

ar t ic l e i nf o

a b s t r a c t

Article history: Received 23 February 2015 Received in revised form 31 May 2015 Accepted 10 July 2015

The lunar global texture maps of roughness and entropy are derived at kilometer scales from Digital Elevation Models (DEMs) data obtained by Lunar Orbiter Laser Altimeter (LOLA) aboard on Lunar Reconnaissance Orbiter (LRO) spacecraft. We use statistical moments of a gray-level histogram of elevations in a neighborhood to compute the roughness and entropy value. Our texture descriptors measurements are shown in global maps at multi-sized square neighborhoods, whose length of side is 3, 5, 10, 20, 40 and 80 pixels, respectively. We found that large-scale topographical changes can only be displayed in maps with longer side of neighborhood, but the small scale global texture maps are more disorderly and unsystematic because of more complicated textures' details. Then, the frequency curves of texture maps are made out, whose shapes and distributions are changing as the spatial scales increases. Entropy frequency curve with minimum 3-pixel scale has large fluctuations and six peaks. According to this entropy curve we can classify lunar surface into maria, highlands, different parts of craters preliminarily. The most obvious textures in the middle-scale roughness and entropy maps are the two typical morphological units, smooth maria and rough highlands. For the impact crater, its roughness and entropy value are characterized by a multiple-ring structure obviously, and its different parts have different texture results. In the last, we made a 2D scatter plot between the two texture results of typical lunar maria and highlands. There are two clusters with largest dot density which are corresponded to the lunar highlands and maria separately. In the lunar mare regions (cluster A), there is a high correlation between roughness and entropy, but in the highlands (Cluster B), the entropy shows little change. This could be subjected to different geological processes of maria and highlands forming different landforms. & 2015 Elsevier Ltd. All rights reserved.

keywords: Texture analysis Lunar surface Roughness Entropy

1. Introduction The primary processes which develop and rework lunar surface are impact events, volcanic tectonism, and space weathering processes (Bandfield et al., 2015). They record the history of the interactions between the Moon and the outside environment and make lunar surface uneven. Thus there are many kinds of positive reliefs such as ridge, dome, crater rim and negative reliefs such as mare surface (mare, lacus or palus), rille and valles with different elevation variations (Jolliff et al., 2006). By knowing the formation histories of these geologic units, we can better understand surface processes on the Moon as well as other airless bodies in the Solar n Correspondence to: 180 Wenhua Xilu, Weihai, 264209, China. Tel.: +86 18769199363; fax: +86 631 5688751. E-mail address: [email protected] (Z. Ling).

System. Lunar orbiter Digital Elevation Models (DEMs) are main data sources for lunar morphology modeling (Wu et al., 2014). Lunar DEMs data are raster-based lunar topographic data. The raster consists of a matrix of cells (or pixels) organized into rows and columns (or a grid) where each cell contains a value representing elevation information of lunar surface. In general, textures are complex visual patterns formed by elements, or sub-patterns, that have characteristic color, slope, elevation, size, brightness, etc. (Tuceryan, 1998). Thus, lunar topographic variations can be treated as textures which contain topographical and morphological information on lunar surface. Lunar surface morphological analysis plays an important role in lunar scientific studies, such as terrain analysis, characteristics of landing site and establishment of the optical model (Cao et al., 2015). When we focus our eyes on topographic maps or images, we see the most primary features and often miss back-ground textures (Kreslavsky et al., 2013).

http://dx.doi.org/10.1016/j.pss.2015.07.004 0032-0633/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

B. Li et al. / Planetary and Space Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎

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Texture descriptors of lunar surface help us to concentrate on typical topography rather than on peculiar features in geological studies. Properly drawn lunar textures maps can show the most typical topographic textures and neglect rare features. This paper performs some new analyses that expand our understanding of lunar morphology based on kilometer-scale texture maps derived from DEM data. There are many researches about lunar surface slope maps derived from DEM or digital camera images. For example, Smith et al. (2010) used Lunar Orbiter Laser Altimeter (LOLA) data to generate quantitative global slope map with decameter and larger scales. Mahanti et al. (2014) used DEMs to characterize lunar surface slope with 2 m resolution. In addition, in-situ and photometric measurements had been applied to describe smaller scales lunar surface slope (Lumme et al., 1985; Helfenstein and Shepard, 1999; Shkuratov et al., 2005). As another important topographic factor, surface roughness has been known to be key geo-marker in lunar surface studies. Rosenburg et al. (2011) used LOLA data to make a global roughness map by computing several parameters, i.e. RMS slope, median differential slope and Hurst exponent. However, Kreslavsky et al. (2013) indicated that the RMS slope and Hurst exponent were not stable enough to show roughness variations. Instead, he had completed topographic roughness maps derived from LOLA data used inter-quartile range of profile curvature at several baselines. However, these maps considered only variations along individual LOLA profiles (approximate south– north direction orbits), and ignores differences among adjacent orbital tracks. Thus, these measurements are highly anisotropic. As the improvement, Cao et al. (2015) calculated lunar surface roughness based on morphological methods in image processing of SE (Structuring Element). Surface roughness at each pixel is defined as the difference between the results of Closing and Opening processing. Bandfield et al. (2015) applied the thermal infrared measurements from the Lunar Reconnaissance Orbiter Diviner Radiometer to derive lunar surface roughness via two observation types. These previous researchers have demonstrated slope and roughness distributions between lunar maria and highlands terrains, typical lunar topographic features, and documented the development of ejecta deposits with different ages. However, previous work mostly focused on slope and roughness measurements derived from variations among elevation of different lunar surfaces, then used these measurements to describe and extract geological information in a range of scales, and further revealed the relationships between geological process and different geological units or features. In this paper, we apply the statistic and information theory to (1) considering the methods to extract lunar surface texture descriptors from DEM data, (2) computing two new lunar texture descriptors, roughness and entropy of every cell within a multi-scale neighborhood, (3) analyzing the occurrences of major geological features in the two texture descriptors' maps, (4) discussing primary inferences about the variations between them.

downloaded from the Planetary Data System, has the best resolution of 30 m/pixel. In this paper, our work relies mainly on the LOLA data, and the global LDEM 1024 data are resampled to a raster map with resolution of about 500 m (18,432 (column) and 9216 (row) cells). The texture descriptors measurements are designed in global maps using different scales (sizes of neighborhood), such as 3, 5 and 10 pixels, with 1.5 km, 2.5 km, and 5 km length separately. Mathematical morphology and digital image processing are often applied to analyze binary and colored images (Serra, 1982, 1988). These methods also can be used for the texture descriptions because it focus on the form, shape, and size of the spatial structures in the images. DEMs are 3-dimensional expressions of topography of lunar surface. They can reflect the topographic variations that are resulting from the spatial structures of different features on the Moon. An important approach to texture description is to quantify its texture content. The three principal methods often used to analyze the texture of a region are statistical, structural, and spectral (Gonzalez and Wintz, 2011). Statistical approaches can yield characterizations of textures as smooth, coarse, uniformity, average entropy, and so on (Haralick et al., 1973). In this paper, we use statistical moments of a gray-level histogram of elevations in a neighborhood to describe lunar surface morphology. They represent the texture indirectly by the nondeterministic properties that govern the distributions and relationships between the gray levels of an neighborhood. Let z be a random variable denoting gray levels and let p(zi), i¼0, 1, 2, …, L  1, be the corresponding histogram, where L is the number of distinct gray levels. The nth moment of z about the mean is (Mukundan and Rammakrishan, 1998)

μ n (z ) =

L− 1

∑i = 0

n

( z − m) p (z ), i

i

(1)

where m is the mean value of z

m=

L− 1

∑i = 0

zi p (zi ).

(2)

The second moment is an important factor of texture description, because the variance σ 2 (z ) = μ2 (z ). We can establish descriptors of relative smoothness of lunar surface as

R=1−

1 . 1 + σ 2 (z )

(3)

The R in the areas of constant intensity is 0, and is 1 in areas of large values of s2(z). The third moment and fourth moment are measures of the skewness and kurtosis of the area's gray-level histogram. Another useful additional texture descriptor based on a histogram is the average entropy measurement which is defined as (Shannon, 1948)

e= −

L− 1

∑i = 0

p ( zi ) log2 p (zi )

(4)

Entropy is a measure of variability and is 0 for a constant image. 2. Texture descriptions of lunar surface 3. Results and discussions LOLA is one of the several instruments onboard NASA LRO mission to the Moon (Vondrak et al., 2010). It's a pulse detection time-of-flight altimeter that measures the precise distance to the lunar surface at 5 spots simultaneously (Smith et al., 2010). The LOLA measurements have a resolution of about 10 m in the alongtrack and cross-track directions and 1.5 m in the radial direction (Mazarico et al., 2011). LOLA DEMs (LDEMs) are established by gathering all effective measurements into map grid cells and then generating multi-resolution models. The LDEM 1024, can be

3.1. Analysis of texture maps with multi-scales neighborhoods In topology and related areas of mathematics, a neighborhood of a point is a set containing the point where one can move that point some amount without leaving the set (Kelley, 1975). In this paper, we used a series of simple square neighborhood about 3, 5, 10, 20, 40 and 80 pixels on a side, which determined the spatial scales of lunar surface textures were 1.5, 2.5, 5, 10, 20 and 40 km.

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

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These lunar texture maps are shown in Fig. 1, from which we can observe that heterogeneity of elevation are sensitive to the spatial scales of neighborhoods. Large-scale topographical changes can only be displayed in maps with big-size neighborhoods whose length is more than 5 km, while smaller scale maps show the small-scale textures. Some circular textures such as rims of large craters, whose diameter is more than 50 km, can only be seen in large scale maps and missed in small scale maps. In addition, the small scale global texture maps are more disordered and unsystematic compared with the larger ones because there are more detailed textures. For example, the large-scale crater floors which suffer post-impact events and have many small craters superposed on it, in small scale the post-craters are obvious and the floors show rough textures, while the floors are smoother in large scale because of the topographic homogeneity of the whole. In order to investigate the global distributions and characteristics of lunar surface textures, the frequency curves of roughness and entropy maps with multi-sized neighborhoods (3, 5, 10, 20, 40, and 80 pixels length) are derived (Fig. 2). In Fig. 2a and b, x-axis stands for the individual roughness and entropy value separately

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and the y-axis represents the number of corresponding x value. The frequency curves indicate varied data distributions with the spatial scales of texture maps increasing. The major characteristics are as follows: (1) The roughness curve of the lowest 3-pixel length neighborhood approximately obeys a normal distribution (Fig. 2a), whose peak is in the center, and respectively decreases to the left and right sides gradually. At the peak, the x value is 0.13 and y value is 6.25  106, which account for 3.65% of the total number, and the cumulative percentage is 50.162%. This also reflects the left–right symmetry of the lunar surface roughness map. This distribution result illustrates that, the maria and highlands cannot be divided from this size roughness map completely, although they are the two distinct geomorphic units with different roughness and brightness. In other words, smooth maria also have some high roughness areas, while rough highlands also have smooth regions. (2) With the increase of neighborhood scale, the peaks of roughness curves move to the negative direction of x axis, and the final value close to 0. This is due to expanding the scope of a

Fig. 1. The global texture maps of roughness and entropy in lunar surface with different neighborhood scales. (a), (c) and (e) are roughness maps with 3, 10, and 40 pixel scale, while (b) (d) and (f) are entropy maps with 3, 10, and 40 pixel scale.

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

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Fig. 2. Frequency curves of roughness (a) and entropy (b) maps with different spatial scales (3, 5, 10, 20, 40, and 80 pixels length of neighborhood’s side). The different colors of curves stand for multi-sized neighborhood.

Fig. 3. Lunar surfaces are classified into maria and highlands based on the 10-pixel scale entropy values, overlaying on the WAC global mosaic image.

Table 1 Lunar primary textures, their average entropy and roughness values, and geological processes they stand for.

Entropy Roughness Geological process

Crater

Impact basin

Ridges

Rille

Maria

Highlands

4.89 0.05 Impact events

6.47 0.06 Large impact events

6.15 0.07 Tectonic process

5.62 0.04 Volcanic process

3.83 0.03 Impact event and lava filing process

6.09 0.05 Magma ocean differentiation

neighborhood may bring a kind of smoothing effect to the calculation of roughness. In largest scale roughness map, only textures of regions with most rapidly changing topography can be preserved, but the small scale textures will be disappear. Therefore, the largest scale roughness and entropy maps cannot reflect the diversity and distributions of different topographic features, and we in the following sections only take the first three spatial scales texture maps (i.e., 3, 5 and 10 pixel scale) for analyzing. (3) Frequency curve of entropy derived from minimum 3-pixel scale has large fluctuations in the range of 2.8–3.17, where there are more than one peaks, located at x1 ¼2.971, x2¼ 3.008, x3 ¼ 3.033, x4 ¼3.071, x5¼ 3.095, and x6¼ 3.133 separately. The four peaks mean the concentrations of the entropy value data in their positions and make the frequency curve sharp and uneven. We infer that the 3-pixel frequency curve's peaks or entropy value's concentrations are caused by the interpolations of gridded

LOLA dataset. The DEM data we used to derive our entropy and roughness maps are made with the good shots of LOLA data obtained during LRO operations in the circular orbit. A typical distance between orbit tracks at low latitudes is on the order of 0.8 km, however, the distance varies widely, and there are gaps as wide as 4 km. The pixel values in the 3-pixel entropy map are calculated in a 1.5 km-wide neighborhood whose length is shorter than gaps among the orbit tracks, the discreteness and interpolation of LOLA data will affect the numerical values of the 3-pixel entropy. There are no peaks and fluctuation appear in the other larger scale(5, 10, 20, 40 and 80-pixel) entropy maps' frequency curves, and their neighborhood's length is close to or longer than 1.5 km. Therefore, similar spikiness is not seen in entropy frequency curve with more averaging (5 pixels and larger), suggesting the 3-pixel spikes are artifacts. (4) From the morphological point of view, entropy curves for higher scales are flat and smooth, and there is only one peak which offsets to the right side of the curves (Fig. 2b). Thus, they are similar to the negative skewness distribution, and this illustrates that pixels with lower entropy values are in the majority. With the increase of scales, we can see that standard deviations of entropy curves rise, and the shapes of the curves are more flat gradually while the distributions are more and more dispersed. Moreover, the central peaks of curves move forward to the positive direction of x axis. This may be because, with the growth of neighborhood, the topographic information such as landform types and relief variations contain within a single neighborhood increases. Thus, the entropy value calculated in the same location is greater and has wider range in a larger scale map.

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

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3.2. Global roughness and entropy textures of lunar surface In this paper, derived from LOLA DEM data, we obtained two texture measurements which are roughness and average entropy value. Because equirectangular projection was used in texture maps (Lliffe and Lott, 2008), the length distortions in the regions located in 72° N to 90° N and 72° S to 90° S (shown in Fig. 1) were large. The distortion was least obvious in roughness and entropy maps with all spatial scales, thus we neglect these parts of data for ease of analyzing the lunar textures. Surface roughness is a component of surface texture. It is quantified by the deviations in the direction of the normal vector of a real surface from its ideal form (Whitehouse, 2012). If these deviations are large, the surface is rough; if they are small, the surface is smooth. Roughness is typically considered to be the high-frequency, short-wavelength component of a measured surface. It plays an important role in determining how lunar surfaces interact with its environment. Rough surfaces usually wear more quickly and have greater friction coefficients than smooth surfaces. The most obvious textures in the middle-scale (10 pixel size neighborhood) roughness map (Fig. 1c) are the two typical morphological units, smooth maria and rough highlands. Typical roughness values of highlands are within the range of 0.04–0.23, and that of maria are within the range of 0.0–0.14, while mean values in maria and highlands are 0.03 and 0.05 respectively. That is to say, the roughness differences between highlands and maria are higher than the typical roughness variations in maria and in

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highlands. For larger spatial scales the differences between maria and highlands raise because of an effective noise increase. In information theory, entropy is the average amount of information contained in each message received. Thus, entropy characterizes uncertainty about source of information, which stands for a character drawn from a distribution of lunar surface elevation in our maps. From the Fig. 1d, we find the largest entropy appears on the highland region. This indicates the lunar highland has more geomorphic information than in mare region, in other word, there are more variations and details in highlands landforms. Like the roughness maps, the boundaries between mare and highlands are most obvious textures in entropy maps. Within maria, there are some kinds of flat and smooth basalt landforms generated by magma filling activities which mostly happened after Imbrium (Hiesinger et al., 2011), thus less topographic information is contained by maria. However, highlands are generally older than maria, and suffered more impact events and other geological erosions and weathering processes. They record more information about topography and geomorphology, thus have higher entropy value than maria. In the 10-pixel scale entropy map, typical highlands entropy value is from 5.66 to 6.07, while 2.68 to 4.24 in the maria, and the average entropy values of maria and highlands are 3.83 and 6.09 separately. Based on the different entropy values, we can classify lunar surfaces into maria and highlands (Fig. 3), the former have entropy value from 1.34 to 5.56, while the latter is 5.56–6.79. The division results are compared with Lunar Global Mare results from ASU

Fig. 4. The roughness and entropy maps in Kepler Crater area derived from our method and Kreslavsky's method. (a) WAC global mosaic of Kepler Crater; (b) Roughness map with 1.90km resolution based on method of Kreslavsky; (c) Roughness map with 10-pixel scale based on our method and (d) Entropy map with 10-pixel scale based on our method.

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

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(LROC Team), and they agree well in low-middle latitudinal zones of the Moon. However, there are some mismatches in the flat bottoms of large craters with high latitude or due to their shadows effects. From the view point of lunar evolution, the bright highlands terrains are generally older than the dark maria due to more greatly cratered and thus rougher surfaces. Although lower roughness values prefer to associated with maria, some mare surfaces are rougher than typical highlands. 3.3. Texture signature of lunar resurfacing process The maria and highlands are the two main geomorphic units in lunar surfaces. According to the theory of Magma Ocean, they are formed in different ages, and have unlike resurfacing events and suffered diverse geological processes. Therefore, the maria and highlands have different elevation changes and landforms, their boundaries are the most obvious textures in our multi-size entropy and roughness maps. At the 10-pixel scale, the average entropy and roughness values in maria are 3.83 and 0.03, while in highlands they are 6.09 and 0.05 respectively. But there are also some other distinct textures in maria and highlands areas, whose entropy and roughness values are clearly different from the average values of maria and highlands. These textures stand for various kinds of landforms which are different from their surroundings and may be represent the resurfacing results formed by different geological process. These abnormal entropy and roughness values in maria and highlands include craters, impact basins, other positive reliefs and negative reliefs which represent multi-scale impact events, volcanic and tectonic processes (Table 1). (1) Craters. Higher roughness and entropy textures (positive anomaly) in maria and highlands are mainly located in the crater’s rim and wall, these positions have obvious topographic differences and form sharp reliefs. In general, from outside to inside, craters can be divided into four parts: ejecta, rim, wall and bottom which

may contain a central peak or a depression. Crater ejecta and flat bottom are smooth and have smaller roughness and entropy values (negative anomaly), while rim, wall and central peak and depression in bottom have higher roughness and entropy values, this is also consistent with the crater’s topography. But if the bottom has central peaks and depressions, the entropy will increase again. Thus the youngest craters and their vicinities varies a wider range of entropy value, from 3.43 to 5.86, and roughness value, from 0.03 to 0.12. For example, from outside to inside, the roughness and entropy value of Kepler Crater gradually increase first, and then decreased, which shown in Fig. 4c and d. Although Fig. 4b and c is the topographic texture maps derived from the same data source (LOLA data) around Kepler Crater, their textures types and distributions are different. The textures in Fig. 4c are sensitive to the ring structures of Kepler Crater and have multi-ring structures, but crater's ejecta are not obvious, while in the Fig. 4b, the scope of ejecta is more obvious. It could be Kreslavsky's method considered variations along individual LOLA profiles (approximate south– north direction orbits), while our histogram statistical method can find out topographic changes in all directions of a neighborhood. (2) Impact basins. The impact basins (for example, the Apollo Basin, Orientale Basin, South Pole-Aitken basin and so on), which formed by large impact events, leading to a multi-rings structures. In these basins, each ring's rim has higher elevation than surroundings, thus they are obvious in full scale texture maps. Apart from the mare-highland dichotomy, Orientale basin as the youngest lunar impact basin, show the most highlighted roughness and entropy characteristics in global texture maps (Fig. 1). Inner depression (Whitten et al., 2011) shows the lowest roughness and entropy characteristics. A number of small melt ponds are found on the basin interior ring (Martin and Spudis, 2014) where the roughness and entropy values are small because of smooth and flat terrains. On Inner Rook Ring (480 km) and Out

Fig. 5. The entropy and roughness maps in Mare Imbrium at 10-pixel scale. (a) WAC global mosaic of Mare Imbrium; (b)10-pixel scale entropy map of Mare Imbrium and (c) 10-pixel scale roughness map of Mare Imbrium.

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

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Rook Ring (620 km), higher roughness and entropy variations are associated with distributions of massif materials (Spudis et al., 2014). Other higher roughness textures are located in the rims of craters. (3) Other positive and negative reliefs: In addition, there are some other high roughness and entropy values occurring in wrinkle ridge and rille which are the positive and negative terrains of the lunar surface. Wrinkle ridges are morphologically complex landforms and occur in maria mostly. Some investigators (Fielder, 1961; Scott, 1973) thought that wrinkle ridges were volcanic features associated with the emplacement of the mare basalts, while others (Baldwin, 1963; Sharpton and Head, 1988) concluded that wrinkle ridges are tectonic landforms. In Fig. 5, there are circular wrinkle ridges and basin-concentric ridge patterns inner Mare Imbrium derived from our texture maps, these wrinkle ridges textures are higher roughness and entropy values which are from 0.03 to 0.12 and from 5.23 to 6.37. It is cited as evidence that subsidence of the mare basalts played an important role in their formation. The maria are mostly level and smooth at all scales texture maps but contain local negative topographic reliefs such as rilles. Rilles are arrow troughs or grooves much longer than they are wide. The lunar rilles usually flow away from small pit structures and probably mark lava channels or collapsed lava tubes that formed during mare volcanism (Hurwitz et al., 2013). The Schröter's Rille lies to the north of the Aristarchus Crater. According to

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the superimposition relationship, we can judge that Schröter's Rille formed later than its underlying basalt unit. It may represent a relatively late volcanic activity in Aristarchus area. The source and flow path of Schröter's Rille show higher entropy and roughness values than its surrounding basaltic units because of larger topographic changes (Fig. 6). We calculated the mean of roughness and entropy values of these landforms at 10-pixel scale maps, and tried to find differences in their textures. But these landforms have wide range of roughness and entropy values and cannot be identified by roughness and entropy values simply at kilometer scale. The crater's rim, wrinkle ridges and sinus rilles are the textures whose entropy and roughness values are highest and obvious on the lunar surfaces. 3.4. Relationships between roughness and entropy values The roughness and entropy textures derived from DEM data are the descriptions of geomorphological information contained by lunar surface. Lunar geomorphic units and terrain features show different textures in the roughness and entropy maps. Although, different terrain features can be distinguished by both entropy and roughness, the same object may be show different textures in roughness and entropy maps. Roughness textures reflect the topographic changes, while entropy textures performance the amount of terrain information or uncertainty, therefore, there are

Fig. 6. The entropy and roughness maps in Schröter's Rille at 10-pixel scale. (a) WAC global mosaic of Schroter's Rille; (b) 10_pixel entropy map of Schoter's Rille and (c) 10pixel roughness map of schroter' s Rille.

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

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Fig. 7. The 2D scatter plot between roughness and entropy at 3-pixel scale in typical mare and highland. (a) The Sinus Iridum and a part of Mantes Jura, LROC WAC image. (b) The density map of 2D scatter plot, the white dotted line is the boundary of mare and highland, A and B are the two clusters standing for highlands and maria. (c) The ROIs (regions of interesting) of cluster A (green color) and B (red color) overlying the WAC mosaic image. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

both consistencies and differences between the two factors. In order to understand the relationships between them, we made a 2D scatter plot (Fig. 7) between the two texture results of in a typical lunar maria and highlands (Northern Imbrium including Chang'E-3 landing site). In the plot of Fig. 7, x axis and y axis express roughness and entropy value in the same position, while colors represent the dot density. We can infer that (1) There are two clusters (A and B) of points, which locate in the top and middle part of the scatter plot respectively with the largest dot density (red color). The two clusters A and B correspond to the lunar highlands and maria separately. The former has the highest entropy and roughness values; while the latter has lower entropy values but wider range of roughness distributions. (2) In the lunar mare regions (Cluster B), there is a high correlation between roughness and entropy values, with the roughness increases (from 0 to 0.22), the entropy also increases (from 0.8 to 2.88); but in the highlands (Cluster A), the entropy shows little change (from 2.88 to 3.17), and is not associated with roughness obviously. This could be that maria and highlands subjected to different geological processes which form different landforms. The highlands, which occupy about 80 percent of the entire lunar surface, are composed of rocks that formed very early in the Moon's history, soon became densely cratered by an intense bombardment of meteorites. The post-impact events formed multi-sized, superposed craters and ejecta in highlands, which caused highest and most rugged topography, where local relief in many areas is up to 5000 m (Hamblin and Christiansen, 2007). In addition, in highlands the population of craters, especially small craters, is in an equilibrium state, when ongoing emplacement of craters is balanced by ongoing obliteration of old craters by regolith gardening. Thus, the total entropy changes of the

highlands are small. The maria were formed by the extrusion of vast amounts of lava that accumulated in the lowlands of large craters or basins and, in places, overflowed and spread over parts of the lunar highlands. The maria are thus relatively young features of the lunar surface and have lower roughness and entropy. Because of post-impact resurfacing effects, the places with more intensive craters have higher roughness and entropy, so in maria the correlations between roughness and entropy are better than in highlands.

4. Conclusions Textures are complex visual patterns formed by elements, or sub-patterns, that have characteristic color, slope, elevation, size, brightness, etc. Thus, different roughness and entropy values show various textures which contained topographical and morphological information on lunar surface. In this paper, multi-sized texture maps of roughness and entropy of the global Moon are presented at kilometer scales. These maps are derived from DEM data obtained by LRO spacecraft. We use statistical moments of a graylevel histogram of elevations in a neighborhood to compute the roughness and entropy value. Our texture descriptors measurements are designed in global maps at a series of square neighborhoods, whose length of side is 3, 5, 10, 20, 40 and 80 pixels separately. Based on these multi-scale maps, we analyze the occurrences of major geological features in the two texture descriptors' maps and discuss primary inferences about their variations. Recent lunar exploration missions, such as the Chinese Chang'E-1, the Japanese SELENE and Indian Chandrayaan-1 carried

Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i

B. Li et al. / Planetary and Space Science ∎ (∎∎∎∎) ∎∎∎–∎∎∎

energy-dispersive, multi-bands or hyperspectral spectrometers for the remote sensing of lunar surface compositions. These spectral measurements using passive sensors in all wavelength ranges from high energy gamma-rays to mid infrared provide the elemental, mineralogical and physical properties of lunar surface units with different spectral and spatial resolution, whereas some geochemical details and the origin, differentiation, and evolution of the lunar rocks have been precisely determined from the returned samples (Heiken et al., 1991). These roughness and entropy maps derived in this study by utilizing the kilometer scale texture measurements of LOLA data have revealed mare and highland specific units and features of lunar topography and may be additional support and source for latter on in-depth studies of lunar surface geology. However, these maps called all attentions to topography of lunar surface and the textures only reflected the variations of topographic information. Thus, the textures derived from DEM data can reflect the variations of different morphological landform units, while derived from the spectral images can show the material composition and illumination geometry changes of different geological units. The results between the two may be distinctively different. For example, spectral texture analysis on crater ejecta are more sensitive than the results coming from DEM data, because the crater ejecta is mostly a flat terrain, but with obvious component changes (Kramer et al., 2008). In the future work, we will use the similar methods to generate texture maps derived from spectral images which are necessary and useful supplements to DEM textures.

Acknowledgments This work was supported by the National Natural Science Foundation of China (41373068, U1231103, 41473065, 41490634), the National Science and Technology Infrastructure work projects (2015FY210500), the Natural Science Foundation of Shandong Province (ZR2015DQ001, JQ201511) and Independent Innovation Foundation of Shandong University (2015ZQXM014, 2013ZRQP004).

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Please cite this article as: Li, B., et al., Texture descriptions of lunar surface derived from LOLA data: Kilometer-scale roughness and entropy maps. Planetary and Space Science (2015), http://dx.doi.org/10.1016/j.pss.2015.07.004i