Photometric anomalies of the lunar surface: Results from Clementine data

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. E3, 5015, doi: /2002je001937, 2003 Photometric anomalies of the lunar surface: Results from Clementine data M. A. Kreslavsky Department of Geological Sciences, Brown University, Providence, Rhode Island, USA Kharkov Astronomical Observatory, Kharkov, Ukraine Y. G. Shkuratov Kharkov Astronomical Observatory, Kharkov, Ukraine Received 8 May 2002; revised 7 October 2002; accepted 21 November 2002; published 8 March [1] We mapped the photometric characteristics of the lunar surface for several small areas using Clementine UVVIS camera images. The maps of the phase function steepness showed several anomalous sites. Several small fresh impact craters have anomalous halos in these maps. The phase function within the halos is less steep than for the surrounding mare surface. We interpret these halos to be due to geologically recent impact-caused alteration of the equilibrium millimeter-scale regolith structure. This equilibrium structure is established through micrometeoritic bombardment at a geologically short timescale. An anomaly of the same signature was found at the Apollo 15 landing site. We interpret it as being a result of the regolith structure alteration with the lander jets. A unique photometric anomaly not correlated with albedo was found within the Reiner Gamma Formation. We suggest that this anomaly is genetically related to the formation, which indicates its young age. This favors the impact hypothesis for the nature of the Reiner Gamma Formation. Our study showed that mapping of photometric characteristics is a new powerful tool in studies of the surfaces of atmosphereless bodies. Future photometric studies of the Moon with existing and new data sets are promising for a search for traces of recent seismic events, studies of the recent population of meteoroids in the inner solar system, an advance in the understanding of swirls, etc. INDEX TERMS: 5464 Planetology: Solid Surface Planets: Remote sensing; 5421 Planetology: Solid Surface Planets: Interactions with particles and fields; 5420 Planetology: Solid Surface Planets: Impact phenomena (includes cratering); 6250 Planetology: Solar System Objects: Moon (1221) Citation: Kreslavsky, M. A., and Y. G. Shkuratov, Photometric anomalies of the lunar surface: Results from Clementine data, J. Geophys. Res., 108(E3), 5015, doi: /2002je001937, Introduction [2] Brightness of any illuminated surface depends on the illumination/observation geometry. This dependence is called the photometric properties of the surface. The photometric properties of a regolith surface are formed due to light scattering within and between regolith particles. This scattering is controlled by the regolith structure at a wide range of scales, from below-the-wavelength scales to the scale of the resolution element of observations. Variations of the photometric properties reflect variations of the regolith structure. Thus, photometric properties of the Moon s surface bear information about its structure. [3] If a surface can be considered as macroscopically flat and isotropic, that is all directions in the surface plane are physically equivalent, the photometric properties can be described with the photometric function. The photometric function is the dependence of the bidirectional reflectance F [e.g., Hapke, 1993] on three angles describing mutual Copyright 2003 by the American Geophysical Union /03/2002JE orientation of the normal to the surface, the direction of incidence, and the observation direction. The choice of these three angles is not unique. In this work we use the phase angle a, photometric latitude b, and photometric longitude l. The phase angle a is the angle between the directions from the object to the light source and from the object to the observer. The photometric latitude b is the angle between the normal to the surface and the scattering plane. The photometric longitude l is the angle in the scattering plane between the projection of the normal and the direction from the object to the observer (see Kreslavsky et al. [2000] for further details). The photometric function is often presented in a factorized form, as a product of the socalled phase and disk functions, F(a, b, l )=f (a)d(a, b, l ). This form is convenient, without a strong theoretical basis. The phase function f (a) describes the strong dependence of brightness on the phase angle: f (a) grows quickly, when a decreases. The disk function D(a, b, l ) involves a only as a subsidiary parameter to introduce the photometric coordinates b and l. The lunar phase function is studied better than the disk function. 1-1

2 1-2 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE [4] Early observations of the lunar phase function were carried out by many authors [e.g., Barabashev, 1922; Fedorets, 1952; van Diggelen, 1964; Gehrels et al., 1964]. The opposition increase of brightness, when the phase angle tends to zero, is the most exciting photometric effect of the Moon. The Moon cannot be observed from the Earth at phase angles less than 1 out of eclipse and hence one never can estimate the pure amplitude of the opposition brightness surge using ground-based observations. Data on the surge at a <1 can be obtained only with spacecrafts. During the Apollo missions, a series of photographs near opposition were obtained [e.g., Pohn et al., 1969, 1971; Wildey, 1972]. In particular, it was found that the brightness ratio I(0)/I(8 ) is within the limits No correlations with the surface albedo or other surface characteristics were found. The Clementine images of the opposition spot of the lunar surface were also analyzed [e.g., Buratti et al., 1996; Shkuratov et al., 1999; Kreslavsky et al., 2000]. It was shown, in particular, that the amplitude of the surge depends noticeably on terrain type. [5] Mapping of the photometric characteristics of the lunar surface is interesting and promising way of study the surface nature and processes. Wildey [1978], using a telescope, obtained a map of the brightness ratio I(a =2.0 )/ I(a =4.5 ) for the lunar disk. Similar studies were done by Akimov and Shkuratov [1981] for the ratio I(3.2 )/I(14.5 )at two wavelengths. Later, Shkuratov et al. [1994] analyzed the phase-ratio maps I(1 )/I(6 ), I(6 )/I(12 ), and I(12 )/ I(96 ) taken with a telescope. It turns out that many regions reveal different values of the ratios that can be related to variations of composition and age of the regions. [6] A major success in recent studies of the Moon is the high-resolution coverage of the lunar surface with multispectral images that was provided by Clementine. Multispectral data are a powerful basis to examine surface chemistry and mineralogy of the Moon [e.g., Nozette et al., 1994; Pieters et al., 1994]. We have used the Clementine UVVIS camera data for a quantitative study of the photometric properties in average and for selected sites [Shkuratov et al., 1999; Kreslavsky et al., 2000]. Here we present our results on mapping photometric properties at high resolution for several small areas, where this is possible with the Clementine data. The next section describes our approach and algorithms in detail. In section 3 we present our maps of photometric parameters and list the photometric anomalies found. In section 4 we interpret the photometric anomalies in terms of variations of the regolith characteristics. In section 5 we discuss the implications of our findings for the surface processes and features, especially for the nature of the Reiner Gamma Formation. Finally, we propose prospective studies that cam be done with extensive mapping of the photometric properties at high resolution, and consider the data sets suitable for such studies. 2. Data Processing 2.1. Approximation of the Photometric Function [7] The photometric function F(a, b, l ) being a function of 3 variables is a rather complex object, and we do not have enough data to measure it for any grid in the 3D space of variables a, b, l. We have to approximate the photometric function with an analytical expression having a small number of free parameters, and express the variations of the photometric properties as variations of these parameters. We use the following approximation proposed by Akimov [1979, 1988]: Fða; l; bþ ¼ expð haþcos a=2 ðcosðl a=2þþ naþ1 ðsin a=2 ðcos b 1 ðsin a=2þ naþ1 cos l Þ naþ1 Þ na : ð1þ As one can see Akimov s empirical formula contains two adjustable parameters: steepness of the phase function h, and a parameter of the disk function n. The factor exp( ha)cos(a/2) is the phase function. This simple exponential form is not applicable at small phase angles (a < 10 ) because of the opposition spike. The other factor in equation (1) is the disk function describing the dependence of the reflectance on the orientation of the surface relatively to the source and observer directions for a given phase angle. It contains parameter n, whose typical values are in the range [Akimov, 1988; Kreslavsky et al., 2000]. For more details about the Akimov s empirical photometric function and for the reasoning of its choice, see Kreslavsky et al. [2000]. [8] If the light source and the observer are relatively high above the local horizon, that is the angles a, b, l are noticeably smaller than 90, the disk function of the lunar surface is rather close to unity, and its variations from site to site are minor. This means that if we do not involve data for large phase angles, we cannot reliably estimate the disk function. On the other hand, this also means that reliable estimations of the phase function can be obtained without accurate knowledge of the disk function. In this work we dealt with the phase angles in the range of 10 60, and the estimation of the disk function parameter n was seldom possible. In all cases, where we could not estimate n from the data, we adopted n = 0.3. We checked that the variations of n in the range of have little effect on the relative contrasts of the derived estimates of h. In this work we express the steepness of the phase function as values of h in exp( ha), where a is in radians Approach to Data Processing [9] To map the photometric parameters we need the same scene to be imaged under several illumination/observation conditions. The technique we used to extract the photometric information from the Clementine UVVIS images was slightly different for different data sets, however, the general approach was the same. [10] We used raw UVVIS frames (Experimental Data Records, EDR) as the input data for our processing. All selected frames for a given scene underwent the standard calibration procedure [McEwen et al., 1998] including electronic offset, dark current, frame transfer, nonlinearity, flat field, and exposure duration compensation, but excluding the photometric correction. The data numbers (DN) resulted from this procedure are supposed to be proportional to the surface brightness, and the proportionality coefficients, though unknown, are supposed to be the same for all frames taken in the same filter. To reduce the effect of

3 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE 1-3 possible imperfections of the calibration procedure, we used, where it was possible, the frames obtained with the same gain, electronic offset, and exposure settings. [11] Then we coregistered all calibrated frames for the same scene. We used the frame with the smallest emergence angle as the basic frame and transformed all other frames to its layout. This coregistration was performed in two steps. (1) Each frame underwent an affine geometric transformation to compensate the difference in scale along image rows and columns between the given and basic frames, as well as the roll and shift of the camera field of view. Scale and roll data were taken from the supplementary information accompanied EDR. Camera pointing data in the EDR data set were not accurate enough to calculate the shift with accuracy of a few pixels and we identified one point on each frame to find the shift. The frames after the affine transformation became roughly coregistered. The residual coregistration errors (up to 2 5 pixels) remained due to nonlinear panoramic distortion, curvature of the lunar sphere within the frame, field of view curvature, and parallax shifts due to the scene topography. (2) We run a procedure that finds a field of these residual errors through finding maximums of the mutual correlation function of the image fragments. Then we performed the final geometric transformation to compensate these errors. [12] We calculated the illumination/observation geometry (angles a, b, l ) for each pixel in each frame. In this calculation we ignored (1) the field-of-view curvature, (2) the deviation of the lunar sphere from a plane within the frame, (3) the errors in the camera pointing data, and (4) the surface tilts due to the scene topography. The first ignored factor is negligible; the second, though minor, is formally not negligible, but its influence is small, because it does not affect a, and minor errors in b and l have little effect on the phase function estimates. The errors in the camera pointing data are smaller, but they do affect a; our estimations show that the final effect of these errors is small in comparison with the uncertainty due to possible calibration inaccuracy. In addition, these errors affect the absolute values of steepness of the phase dependence, but do not influence the spatial pattern. The surface tilts due to the scene topography are not small and affect the results strongly. [13] In the way described above, for each pixel of the scene, we obtained a set of DN values proportional to the bidirectional reflectance under a corresponding set of illumination/observation conditions. We fitted these data with the Akimov s photometric function (1) to estimate the steepness of the phase function h, and in some cases the parameter n of the disk function. The particular methods of the estimation are described in section 3. Values of h and n for each pixel form maps of photometric properties suitable for further informal analysis and search for the photometric anomalies Clementine Data Appropriated for Analysis [14] In the simplest case the image set contains only two images. In this case the ratio of the images excludes the albedo. Then the phase function steepness can be obtained by taking the logarithm of the ratio, dividing by the phase angle difference and introducing an additive correction for the disk function. Knowing the signal-to-noise ratios (S/N) of the source images, it is easy to estimate S/N of the result map of h. We found that for a pair of good UVVIS frames, with well chosen exposure and no lossy compression, the result map of h has S/N about unity or higher, if the phase angle difference of the source images is about 10 or higher. The majority of the UVVIS frames were transmitted with lossy compression, which reduces S/N and is very harmful for visual perception and quantitative analysis of the data. We found that a pair of UVVIS frames with lossy compression can hardly be used for mapping of photometric properties even if all other circumstances favor it. [15] During the regular survey a significant area of the lunar surface was imaged twice in each filter due to overlap of both consecutive frames along each orbit and frames from neighboring orbit tracks. In the former case the phase angle difference is smaller than 4, and mapping of photometric properties in the overlap area is impossible. In the latter case the phase angle difference can reach 20, but for all overlaps at least one of the frames suffer from the lossy compression. Thus the regular survey data alone cannot be effectively used for mapping of the photometric properties. [16] Before and after the regular survey Clementine took several series of frames of the same scene from different directions of observation (hence, at different phase angles). Large numbers of frames for the same scene favor the photometric studies, because this allows one to reduce the noise through explicit or implicit averaging. [17] There are also a few non-regular frames without the compression loss that overlap good frames from the regular survey; such pairs can also be used for mapping h. [18] In general, the highland surface cannot be considered as flat at the UVVIS camera resolution (100 m). Topography of the Moon has not been measured at this resolution. A reconstruction of the topography together with the photometric function is possible in principle, but this is a task of a next order of complexity and probably cannot be actually performed for the Clementine UVVIS data. Thus, the photometric properties at this resolution can be mapped for mare surfaces only. [19] Totally the photometric mapping with the Clementine UVVIS data is principally possible for approximately a dozen of small areas; in this paper we consider five of them with the best data coverage Approach to Result Assessment [20] The variations of the photometric parameters over the scene in the parameter maps presented below are due to four factors: (1) noise, (2) discrepancy in the resolution of the source frames, (3) surface tilts, and (4) true variations of the photometric properties. Understanding of these factors is necessary to distinguish the true variations of the photometric properties in the obtained maps. 1. The noise in the parameter maps comes from the noise of the source frames. It is amplified in the maps because the photometric parameters are derived from small differences between similar source images. The noise in the source frames contains three components. (a) The white noise of source measurements and quantization gives the noise close to white in the result maps. Visual inspection can reliably distinguish between features larger than several pixels across and the white noise. (b) The compression losses give noise seen as a characteristic rectangular pattern in the

4 1-4 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE maps. This noise is very harmful for visual perception of the results: for the same S/N it masks real features much more effectively than the white noise. (c) We found also a specific noise in some frames. This noise has a rather high amplitude (up to 8 in raw data numbers) and a very narrow spatial spectrum (chessboard pattern). It occurs only for a certain range of the raw DN values. Probably it is caused by some flaw in the analog-digital converter of the camera. This kind of noise can produce specific artifacts in the parameter maps, and its existence was kept in mind in the course of result interpretation. 2. Source frames, as a rule, have somewhat different spatial resolution. This leads to specific artifacts in the maps of photometric parameters. These artifacts are associated with high albedo contrasts in the scenes. They are easily distinguishable from real photometric anomalies through visual inspection. Of course, the spatial resolution of the source frames could be reduced to the same level for all frames before the parameter estimation. In principle, this allows us to avoid this kind of artifacts. Our attempts to do this showed, however, that such an approach does not give good results. The rigorous procedure demands an application of a proper linear low-pass filter that reduces the resolution to the level twice worse than the lowest resolution of the source frames. The filtration spreads harmful influence of the scene topography over flat terrains. Because of this, the maps obtained with the rigorous filtration of source data are not suitable for further analysis. We tried also to apply filters that reduce the resolution not as strongly as the rigorous procedure. In this case, however, the result maps contain residual resolutionrelated artifacts that are not easy to distinguish from real features. 3. Surface topography causes large discrepancy between calculated angles l and b and the actual illumination/ observation geometry for the tilted surface. This leads to large deviation of the estimated photometric parameters in the maps, which is seen as a pattern looking like shaded topography in the map. This pattern usually can be easily distinguished from the real variations of the parameters by visual inspection. 3. Results 3.1. Apollo 15 Landing Site [21] A long series of frames with this scene was taken by the UVVIS camera in orbit 299. The sun was at the southeast 54 above the horizon. The spacecraft moved from the southern to northern horizon almost through the local zenith. We used a set of 52 frames in each filter from this series. The illustrations (Figures 1a 1e) were made using the red (B, nm) filter frames, and the numerical results mentioned below are for this filter; the results for the other filters are qualitatively the same. The first frame in the chosen series (Figure 1a) was taken from 45 above the horizon from the south; the last one (Figure 1c) was taken from 65 above the horizon from the north. The frame taken almost from the zenith is shown in Figure 1b. The phase angle changed in the range of through the set. The image resolution changed in the range of m per pixel because of the difference in distance from the spacecraft to the scene and the perspective distortion. Changes of the photometric latitude and longitude in the series of frames are illustrated in Figure 2 from Kreslavsky et al. [2000]. The logarithmic least squares fitting procedure with equal weights of all 52 frames was applied to each pixel of the coregistered images to obtain the maps of parameters n and h. To reduce the noise and the resolution-differencerelated artifacts, the resolution of the maps was reduced two times. The resulting maps of parameters n and h are shown in Figures 1d and 1e, respectively. [22] A contrasting shadow-like pattern of mountains (Apennines) and a channel (Rima Hadley) in the maps (Figures 1d and 1e) does not reflect real variations of the photometric function parameters and should be disregarded in the analysis. These strong variations of the estimates are caused by steep surface slopes, which were not taken into account when we calculated the observation geometry. The same is the case for a number of black-and-white objects associated with the resolved craters, pits, and knobs. Several bright unresolved craters also produce small contrasting unreal features in the map of the parameters due to difference in the actual resolution of the source frames and minor imperfections in the coregistration. Only a few diffuse features on the flat mare surface are real anomalies of the photometric function. [23] The map of the parameter n of the disk dependence of brightness (Figure 1d) has a high level of noise (one standard deviation of 0.04, that is 15%) and few real features. The value of n averaged over the flat surfaces is Variations of the parameter (of the amplitude of ±0.05) are seen inside the Rima Hadley loop (arrows in Figure 1d). They may represent a photometric anomaly related to a band of brighter material (probably, a crater ray; see Figure 1b). It is more probable, however, that these variations of n are caused by a wide low ridge, so gentle that it cannot be seen even in the low-sun images of the scene (Figure 1f ). [24] The map of the parameter h of the phase dependence of brightness (Figure 1e) has lower noise level (one standard deviation is less than 1%). The value of h averaged over the flat surfaces out of the anomalies described below is 0.75 with a perfect agreement with the results by Kreslavsky et al. [2000] for this area. [25] The map shows several distinctive diffuse features in the flat surface. The most pronounced feature is a dark diffuse halo (arrow B in Figure 1d) associated with an impact crater. The well-expressed inner part of this diffuse halo has a radius of 0.7 km and approximately coincides with the area of bright ejecta. Values of h here are 10 20% lower than the typical value. A faint extension of the halo with 2 5% decrease of h can be traced over 2 km from the center. On these distances from the crater the albedo and color of the mare surface are indistinguishable from those of surroundings. A smaller (1 km in diameter) and less pronounced (up to 8% decrease of h) halo (arrow C in Figure 1d) is also associated with an impact crater. Both craters are fresh, because (1) they have sharp slope breaks seen at the full resolution in the low-sun Lunar Orbiter V image of the scene, and (2) they are bright (Figure 1b) due to the regolith immaturity. The haloes extend much farther from the crater centers than the increased albedo. There are some other fresh craters of comparable size in the scene, which do not have any associated halo of anomalous phase function steepness.

5 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE 1-5 Figure 1. The Apollo 15 landing site vicinity. The scene is centered at 26.2 N 3.4 E, the north is at the top. (a) Clementine UVVIS frame LUB3103L.299, the first frame in the series of 52 frames used for the analysis, taken from the south at 45 from local zenith. (b) Frame LUB3919L.299, the 35th frame in the series, taken approximately from the local zenith. (c) Frame LUB4327L.299, the last, 52nd frame in the series taken from the north at 25 from local zenith. (d) Map of parameter n of the disk function. Brighter shades denote higher values of n (stronger limb darkening). Arrows show the anomalous area. (e) Map of the phase function steepness h. Brighter shades denote higher values of h (steeper phase function). Arrows indicate the most prominent photometric anomalies, including the Apollo 15 landing site (arrow A). (f ) Low-sun image of the scene: portion of Lunar Orbiter V image 105M. [26] A small dark spot (arrow A in Figure 1d) is not associated with any fresh crater but exactly coincides with the Apollo 15 landing site. The value of h here is 0.66 in comparison with 0.75 in the vicinity. This object is very small (1 2 pixels in the source frames), and it is not easy to prove that it is not an occasional result of superposition of the lossy compression noise pattern in the source frames. However, our screening of all source frames and their coregistration in this place, absence of similar spots in the scene, and high S/N (10) made us sure that this is a real photometric anomaly Mare Cognitum Site [27] Similar series of images was taken in orbit 309 for an area in Mare Cognitum (Figure 2a). The Sun was at the east 60 above the horizon. Total number of frames in the series was smaller; totally 25 frames were used. The ratio S/N for these frames is lower than for Apollo 15 landing site because of less optimal exposure, and the compression loss noise is higher. The same logarithmic least squares fitting procedure gave rather noisy results even after the resolution of the maps was reduced two times. Figure 2b shows the map of the disk function parameter n resulted from this procedure. A rectangular pattern inherited from the noise of compression losses of the original frames is clearly seen. The noise level (one standard deviation) is about 30%. A systematic trend in the map from northwest to southeast resulted, at least partly, from the neglected curvature of the lunar sphere within the frames in photometric latitude and longitude calculations. The parameter n estimates are very

6 1-6 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE Figure 2. The studied site in Mare Cognitum. The scene is centered at 7.5 N E, the north is at the top. (a) Portion of Clementine UVVIS frame LUB1367I.309, the 17th frame in the series of 25 frames used in the analysis, taken approximately from the local zenith. (b) Map of parameter n of the disk function. Brighter shades denote higher values of n (stronger limb darkening). (c) Map of the phase function steepness h obtained supposing n = 0.3 uniformly. Brighter shades denote higher values of h (steeper phase function). Arrows show two craters of the same size and appearance on both high-sun (a) and low-sun (d) images, but the crater shown with the long arrow has an anomalous halo in the map. (d) Low-sun image of the scene: portion of Lunar Orbiter IV image 125H 3. sensitive to the surface tilts: the map (Figure 2b) reveals a wrinkle ridge (in the northern part of the map) not seen in a low-sun image of the same scene (Figure 2d). [28] As we mentioned, simultaneous estimation of both parameters h and n leads to high noise level in the result maps. A better map of the phase function parameter h was obtained, when we did not allow the disk function parameter n to vary. The map of the phase function steepness h in Figure 2c was obtained for uniform n = 0.3. The noise level in this map is 2%, that is higher than for the Apollo 15 landing site; this is seen in the map. All compact bright objects in the image (small bright craters, bright crater walls of larger craters, Figure 2a) appear as bright objects with tight dark outline in the map (Figure 2c). This occurs due to the difference in the resolution of the source frames. All dark rings around craters in the map have the same width defined by the resolution difference. The dark halo around the crater shown with the long arrow (Figure 2c) looks wider than the tight rings around other bright objects; this could be a photometric anomaly. It is interesting to compare this crater with the crater marked with the short arrow: both craters have the same size and the same appearance on both high-sun (Figure 2a) and low-sun (Figure 2d) images, but only one of them has a halo. A small young crater near the western edge of the scene also has an anomalous halo Reiner Gamma Site [29] A long series of frames of the Reiner Gamma Formation in Oceanus Procellarum (7 N 59 W, Figure 3) was taken in orbit 322. Among these frames there are many images transmitted without compression losses, which favor photometric study. Many images, however, were taken with non-standard camera electronic settings (gain mode 2), which potentially decreases the calibration accuracy. Results presented below were taken with no use of such frames. The camera axis did not point to the same site at the surface, and parts of the scene have different coverage of observational conditions, which limits possibility to map photometric parameters. The Sun was at the southeast 58 above the horizon. All results presented in this section were obtained in filter C (900 nm) with the data without lossy compression. Some results obtained in other filters (with compression losses) also show the most prominent photometric anomalies discussed below. [30] The results presented here were obtained with a procedure somewhat different than that used for the previously described sites. We averaged subsets of 4 8 frames taken at similar observational conditions to reduce the noise, and then calculated the ratio images of the result of averaging and recalibrated the ratio in terms of the phase function steepness h. [31] Figure 4a shows an oblique view of Reiner Gamma and adjacent part of Oceanus Procellarum taken when the spacecraft was at 24 above the horizon. Figure 4b shows the map of the phase function steepness h derived from the phase ratio image I(64 )/I(69 ). The prominent topographylike pattern seen in the map within the albedo feature results from almost two-fold difference in the resolution of the source images in the north-south direction. The noise level in the image is rather high due to the small difference in the phase angles. It is clearly seen, however, that the Reiner Gamma Formation as a whole is a negative photometric Figure 3. The Reiner Gamma Formation (7 N, 301 E). Low-sun view taken by Lunar Orbiter IV, image 157H 1.

7 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE 1-7 map is higher than in Figure 4b. The difference between the dividend and the divisor in the vertical (north-south) resolution is about 70%. This difference is at least partly responsible for a number of objects seen in the map, including thin dark lineaments shown by short arrows (Figure 5). The albedo feature in general has less steep phase function (by 10 20%) than adjacent dark mare surface. Several areas of especially low values of h are associated with local brightest areas in the southeastern part of the albedo feature. One of small craters inside the central part of the feature has a faint halo of reduced h. [33] Long arrow in Figure 5 shows a positive photometric anomaly (the phase function here is 20% steeper in comparison to the surroundings). This anomaly is associated with a compact bright object. Inspection of the best available low-sun image of this region (Lunar Orbiter IV, Figure 3) at its full resolution showed that there is no any topographic feature associated with this albedo object. The difference in the resolution could contribute a little to the observed anomaly, but cannot be solely responsible for it. Thus this compact bright albedo feature has unusually steep phase function. Figure 4. The Reiner Gamma Formation. (a) Clementine UVVIS frame LUC2445J.322, the last frame in the subset of 13 frames used for the analysis, taken from the south at 66 from local zenith. The phase angle is 64. The north is at the top. (b) Map of the phase function steepness h obtained supposing n = 0.3 uniformly. The map was derived from the 64 /69 phase ratio image. Brighter shades denote higher values of h (steeper phase function). The prominent topography-like pattern seen in the map results from almost two-fold difference in the resolution of the source images in the north-south direction. A systematic trend in the north direction results from the neglected curvature of the lunar sphere within the frames. It is seen that the Reiner Gamma Formation as a whole is a negative photometric anomaly. anomaly; it has lower h (less steep phase function) than surroundings. The difference between typical average h for the bright areas and the adjacent typical mare surface is on the order of 20%. Absolute estimates of h in this region are not reliable, because there are strong variations n here [Kreslavsky et al., 2000], and the calibration of the ratio image in the values of h is not accurate. A systematic trend in the north direction resulted from the neglected curvature of the lunar sphere within the frames. [32] Figure 5 shows an image (a) and a map of h (b) for a northern part of Reiner Gamma. The map was derived from the I(34 )/I(46 ) phase ratio image. Due to larger phase difference and smaller phase angles, the actual S/N in this Figure 5. A part of the Reiner Gamma Formation. (a) Clementine UVVIS frame LUC4294J.322, the last frame in the subset of 8 frames used for the analysis, taken from the south at 20 from local zenith. The phase angle is 34. The north is at the top. (b) Map of the phase function steepness h obtained supposing n = 0.3 uniformly. The map was derived from the 34 /46 phase ratio image. Brighter shades denote higher values of h (steeper phase function). Short arrows show dark lineaments, which may result from the resolution difference of the source frames and maybe not true photometric anomalies. Long arrow shows a positive photometric anomaly associated with a bright albedo feature.

8 1-8 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE (Figure 7b) shows a darker area just outside the rim at NW, which does not look like illuminated topography and is a weak negative photometric anomaly. The phase function steepness in this area is 4% lower than the typical values in the surrounding mare surface. The anomaly seems to associate with a small hill clearly seen in a low-sun image (Figure 7d). The color ratio image (Figure 7c) shows no noticeable color variations associated with this anomalous area. General east-west trend of h values seen in Figure 7b is due to the imperfections of compensating the influence of the illumination and observation geometry over the scene. Minor decrease of h is associated with a young bright small crater near the center of the scene (Figure 7b). It is barely seen on the background of the noise, whose amplitude (one standard deviation) is 2% Cardanus Site [36] Finally, the scene in Figure 8 is located to the northeast of crater Cardanus in the northwest of Oceanus Procellarum. The southeastern part of the scene is a gently rolling terrain; the large phase angle difference between the source frames leads to that the effect of surface topography masks all variations of the photometric properties in this area. The very northwest corner of the scene includes a part Figure 6. A part of the Reiner Gamma Formation. (a) Clementine UVVIS frame LUC4202J.322, the last frame in the subset of 12 frames used for the analysis, taken from the south at 21 from local zenith. (b) Map of the phase function steepness h obtained supposing n = 0.3 uniformly. The map was derived from the 36 /44 phase ratio image. Brighter shades denote higher values of h (steeper phase function). Arrow shows a negative anomaly not associated with albedo variations. [34] The southern part of the Reiner Gamma Formation and its h map are shown in Figure 6. The map was derived from the I(36 )/I(44 ) phase ratio image. Again, the bright areas of the Reiner Gamma Formation have 10% less steep phase function than surroundings. An interesting feature in this map is the diffuse negative anomaly shown with the arrow in Figure 6b. It has extra 12% lowered steepness of the phase function in comparison to the other bright areas. Unlike other local minima of h seen in this map and in Figure 5b, this feature is not associated with any local brightening of the surface, and there is no any impact crater in its center Krafft M Site [35] A small area containing crater Kraft M in the northwest of Oceanus Procellarum (Figure 7a) was imaged twice with no compression losses. Unlike the previous cases, the source frames were taken under different illumination direction. The brightness of tilted surfaces strongly depends on the slope orientation with respect to the source. Due to this, the ratio of the source frames (Figure 7b) looks like the image of the scene illuminated from the west. Long arrow Figure 7. Crater Krafft M and its vicinities. The scene is centered at 18 N, 75.5 W. (a) Portion of Clementine UVVIS frame LUB4322K.064. (b) Map of the phase function steepness h obtained supposing n = 0.3 uniformly. The map was derived from the 24 /36 phase ratio image obtained from frames LUB4322K.064 and LUB2263K.328. Brighter shades denote higher values of h (steeper phase function). (c) Red/blue (760 nm/415 nm) color ratio obtained from frames LUB4322K.064 and LUB4322K.064. Brighter shades denote higher values (redder color). (d) Low-sun image of the scene: portion of Lunar Orbiter IV image 174H 3.

9 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE 1-9 Figure 8. Area to the northeast of crater Cardanus. The scene is centered at 14 N, 71 W. (a) Fragment of Clementine UVVIS frame LUB4198K.062. (b) Map of the phase function steepness h obtained supposing n = 0.3 uniformly. The map was derived from the 22 /54 phase ratio image obtained from frames LUB4198K.062 and LUB1975K.328. Brighter shades denote higher values of h (steeper phase function). (c) Red/blue (760 nm/415 nm) color ratio obtained from frames LUB4198K.062 and LUA4203K.062. Brighter shades denote higher values (redder color). (d) Low-sun image of the scene: portion of Lunar Orbiter IV image 169H 2. Long arrow shows a linear bright albedo feature and associated negative photometric anomaly. Short arrows show a weak positive photometric anomaly. of a bright ray; it has lower values of the phase function steepness. A very bright linear albedo feature in the mare surface (long arrow, Figure 8a) also displays very low values of h, however, this is caused, at least partly, by the resolution difference between two source frames. [37] Short arrows in Figure 8 show an area of increased phase function steepness. This anomaly is very weak; the relative difference in the phase function steepness in comparison to the adjacent surface does not exceed 1.5%. This anomaly is clearly seen in the phase ratio image (Figure 8b) due to low noise level (1%), which is caused by the large difference in the phase angles of the source frames. The anomalous area is hardly distinguishable in the source frame (Figure 8a), however, in the Lunar Orbiter IV image (Figure 8d) taken at low sun (large phase angle) this area is seen as a dark feature. No apparent topography associated with this feature is seen in the image. The color ratio image (Figure 8c) shows some color change across the northern boundary of the anomalous area, and maybe also a subtle color change across the southern one. This indicates that the boundaries of this feature are probably boundaries of different materials, perhaps, different generations of lava flows formed the mare surface. 4. Interpretation 4.1. Preliminary Remarks [38] Anomalies of the photometric properties are basically related to anomalies of the surface structure. Photometric behavior of the regolith surface is formed by a number of interrelated physical effects of light scattering, which can be in a simplified way listed as (1) single-particle scattering, (2) incoherent multiple scattering (light diffusion between particles), (3) shadow hiding effect, (4) coherent backscatter enhancement, and (5) macroscopic surface roughness. The steepness of the phase function in range of phase angles is mostly affected by first three factors. Thus the steepness is, in particular, sensitive to structure at scales larger than the characteristic light diffusion length, which is on the order of 1 mm for the highland soils and somewhat shorter for mare soils. [39] The albedo can also play an important role. The increase of single-particle albedo and, hence, of the surface albedo enhances illumination of the shadowed areas with diffusely scattered light; in this way it weakens the shadow hiding effect and thereby decreases the phase function steepness. Thus, an inverse correlation between albedo and h should be anticipated. The same effect can be explained from a different viewpoint: in a brighter soil, the light diffusion length is greater, the onset of the shadow hiding occurs at longer scales, at which the surface roughness is lower, hence, the shadow hiding effect is weaker. [40] The observed dependence of the phase function steepness on albedo is more complicated. At small phase angles, the dependence has a horseshoe form that was found from our earlier Earth-based observations of the Moon [Shkuratov et al., 1992]. In this case the steepness has a maximum in the range of moderate lunar albedo. [41] For a surface with low or moderate albedo, the shape of the single-particle indicatrix can contribute to the phase function of the surface directly, through single scattering. It is known from many laboratory measurements and theoretical calculations that a typical single-particle indicatrix has double-lobe shape [e.g., Hapke, 1993], i.e. there are the relatively weak backscatter lobe and the usually prominent forward scattering surge. The shape and balance of the lobes depend on many physical characteristics, such as particle size, shape, composition, and internal structure. Accumulation of the submicroscopic metallic iron due to space weathering affects the shape of the indicatrix [e.g., Hapke, 2001] Albedo-Related Variations of the Phase Function Steepness [42] Several studied sites give examples of the inverse correlation between the steepness h and albedo. They are: the Reiner Gamma Formation in general (Figure 4), brightness variations within it (Figures 5 and 6), the ray material in the northwest corner of the Cardanus site (Figure 8), the innermost parts of the anomalous halos of several craters. The trend of the same sense has been seen in the astronomically obtained I(12 )/I(96 ) phase ratios of the Moon [Shkuratov et al., 1994]. As it is mentioned above, these anomalies can be easily interpreted in terms of weakening of the shadow hiding effect due to growth of multiple scattering contribution with the increase of albedo. [43] Our quantitative study of correlation between h and albedo with the Clementine data showed that this correlation is not described by a simple universal functional relationship. We have strong impression that there are significant regional variations of this dependence. The quantitative study, however, is hindered by the UVVIS

10 1-10 KRESLAVSKY AND SHKURATOV: ANOMALIES OF THE LUNAR SURFACE image calibration inaccuracy. In addition, the most pronounced albedo variations among the studied scenes are in the Reiner Gamma site, where the disk function is known to be rather atypical [Kreslavsky et al., 2000], and accuracy of the approximation (1) is not well justified. Thus the analyzed Clementine data set does not allow yet a consistent quantitative study of the correlation of the photometric properties and albedo. New astronomical and spacecraft (e.g., SMART-1) data would be helpful in these efforts. [44] From qualitative analysis of Apollo and Lunar Orbiter photographs, Schultz and Srnka [1980] noted that the swirls have higher contrast at larger phase angles, which is not the case for most crater rays. This observation and the quantitative study by Shkuratov et al. [1994] indicate that the correlation of the phase function steepness and albedo is not uniform Anomalous Crater Halos [45] The sites studied gave several examples of anomalous halos around small bright impact craters. Inner parts of these halos can be considered as a particular case of albedo-related photometric anomalies. However, the halos are usually wider than the bright ejecta areas and hence cannot be explained as only albedo-controlled features. Low-sun images of the scenes show that craters possessing the anomalous halos are morphologically fresh. Within the scenes, there are morphologically fresh bright craters of similar sizes, which do not have anomalous halos. [46] We suggest the following interpretation of these observations. The uppermost regolith layer has a specific porous openwork ( fairy castle ) millimeter-scale structure. This structure is created by space weathering factors, first of all, by the micrometeorite bombardment. Impact events can damage this structure, creating an area of less porous regolith. The decrease of porosity weakens the shadow hiding effect, which is observed as the negative photometric anomaly. At a geological timescale, the equilibrium fairy castle structure is reestablished due to the space weathering factors, and the anomalous halos disappear. The timescale of this process is shorter than the timescale of regolith gardening that erases the bright ejecta and softens the morphological appearance of the craters. This difference in the timescales is responsible for the presence of the fresh craters devoid of the halos. [47] We consider two possible particular mechanisms of the regolith structure damage with the impacts. The first mechanism is the ground shock/seismic wave produced by the forming impact, which shakes the vicinity strongly enough to cause a collapse of the uppermost porous regolith layer. The second is a sparse shower of distal ejecta that are dense enough to destroy the porous structure, but having particles too small to overturn the regolith and expose immature soil Landing Site [48] We interpret the phase function anomaly at the Apollo 15 landing site as a m-radius area, where the equilibrium porous regolith structure mentioned above was damaged by the lander jets [Kreslavsky and Shkuratov, 2001]. It is interesting that the apparent brightening of the surface in 200 m area immediately after the landing was observed from comparison of the pre-landing and postlanding images [Hinners and El-Baz, 1972]. It is possible that the very weak bright feature at the landing site seen in the Clementine frames is entirely due to the effect of the jets on the soil. The albedo increase at the landing site is too weak to be solely responsible for the photometric anomaly Other Anomalies [49] The positive anomaly in Cardanus vicinity (Figure 8b) does not seems to be related to any recent alteration of the equilibrium regolith structure. Here the difference in the photometric properties is probably related to peculiarities of the regolith source material or to increased large-scale surface roughness, e.g., due to the presence of excessive number of boulders on the surface, etc., which would make the phase function steeper [e.g., Shkuratov and Helfenstein, 2001]. [50] The weak negative anomaly in the Krafft M scene (Figure 7) is not apparently related to any fresh impact crater. There is a small (200 m in diameter) hill in the center of the anomalous area. The hill might be a volcanic edifice, and the halo might be related to pyroclastic deposits around it. This explanation is consistent with the astronomical 12 /96 phase ratio data [Shkuratov et al., 1994] that had shown a weak negative photometric anomaly at Marius Hills known to be volcanic centers with putative pyroclastic deposits [e.g., Head and Gifford, 1980]. The Krafft M anomaly, however, do not display noticeable spectral peculiarities in comparison to the surrounding mare surface (Figure 7d), which would be expected in the case of pyroclastic deposits. An alternative explanation of the anomaly is related to a 180-m-diameter crater on the top of the Krafft M rim near the anomalous place (short arrow in Figure 7). This crater is bright, and the decreased red/blue color ratio in its vicinity is consistent with immature regolith; hence it is relatively young. The interference of oblique impact and steep target topography could lead to focused ejection of high-velocity material, which produced a fan of regolith damaged in a way similar to anomalous crater halos. [51] One well-pronounced (arrow in Figure 6b) and a few weaker negative anomalies not correlated with the albedo pattern are seen in Reiner Gamma. These anomalies indicate that the regolith here have unusual and spatially variable structure. These maybe variations of the millimeter-scale structure ( porosity) of the uppermost regolith layer. 5. Discussion 5.1. Equilibrium Structure of the Uppermost Regolith Surface [52] The anomalous halos around some fresh impact craters and the anomaly at the landing site unequivocally indicate that the space weathering processes, mostly probably, the micrometeorite bombardment, alter the geometrical structure of the uppermost layer of the regolith at geologically short timescale, and this alteration is expressed in changes of photometric properties. In a simplified way we can state that the steepness of the phase function in phase angles range increases with time along this alteration that corresponds to establishing more porous structure of the uppermost regolith layer with time. Perhaps this structure is fragile enough to be damaged by the Apollo lander jets