- Email: [email protected]
Characterization of palimpsest craters on Mars
Planetary and Space Science 72 (2012) 62–69
Contents lists available at SciVerse ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Characterization of palimpsest craters on Mars T. Barata a,n, E.I. Alves a,b, A. Machado a, G.A. Barberes a a b
Centre for Geophysics, University of Coimbra, Portugal Geophysical Institute and Department of Earth Science, University of Coimbra, Portugal
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 January 2012 Received in revised form 24 September 2012 Accepted 25 September 2012 Available online 16 October 2012
Palimpsest, ghost, or degraded craters have so far been identified on Mercury, the Earth, the Moon, Mars, Ganymede, Callisto, and possibly even Titan. We have identified at least 10 palimpsests on HiRISE image ESP_016526_2415 of Mars and developed an algorithm to automatically characterize these structures on high resolution images. Since the genesis of palimpsests may be related to freeze–thaw cycles these features might have provided habitable environments. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Palimpsest Ghost crater Periglacial terrain Mars
1. Introduction: Palimpsests, liquid water, and Mars habitability The word palimpsest originally meant a writing surface which was reused after earlier writing had been erased. Planetary Geosciences borrowed the term to describe craters whose flat topography lets them be perceived mainly by reflectance contrasts. This merely descriptive term has been used interchangeably with ‘‘ghost craters’’, ‘‘degraded craters’’, and even ‘‘pathological craters’’ to refer to features on Mercury (Harmon et al., 2007), the Earth (Deutsch et al., 2000), the Moon (Butler and Morrison, 1977), Mars (Arvidson, 1974; Hartmann and Esquerdo, 1999; Levy et al., 2010;), Ganymede and Callisto (Jones et al., 2003), and possibly even Titan (Nelson et al., 2004). In the present work we will use the term ‘‘palimpsest’’ with the strictly descriptive meaning ‘‘craters that are only perceptible by annular clusters of meter sized boulders on an otherwise almost featureless plane surface’’. Arvidson (1974) classified craters on Mars according to their morphology on images of Mariner 9. By ‘‘ghost craters’’ he means what remains of the ‘‘ghost’’ of an impact carter. Morphologically, these craters are flat-floored, rimless, extremely shallow, without central peaks, and would probably represent what remains after erosion. Arvidson (1974) also refers the need to sub-classify the ghost or degraded craters according to their smoothness or roughness, since these characteristics can imply differences in the patterns of degradation-a task that we will attempt in the present work.
n
Corresponding author. Tel.: þ351 239 793 420; fax: þ 351 239 793 428. E-mail address: [email protected] (T. Barata).
0032-0633/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pss.2012.09.015
Hartmann and Esquerdo (1999) described three low-relief circular features which they name ‘‘pathological craters’’. They notice that these features appear unique to Mars, although ‘‘ghost craters’’ are mentioned on the Moon. Three hypotheses are discussed in their work: (1) volcanic ghost crater, suggesting an analogous formation to lunar ghost craters, (2) ice lens hypothesis, suggesting ‘‘unusual interactions’’ with the ice or ground water and (3) isostatic deformation, a process that can involve viscous relaxation of craters that were formed in ice-rich permafrost layers. To Hartmann and Esquerdo (1999), the third hypothesis is the most acceptable, and the greatest importance of these structures is that they can give clues about the early geological history of Mars, especially in what concerns the presence of an ice-rich permafrost layer. Levy et al. (2010) mention that these features suggest the existence of a fluid-rich substrate. In particular, mounds with rounded bases, aligned along the crater rim, would indicate an origin related to fluid flow up the impact fracture system, which might have involved impact-related hydrothermal activity and glaciovolcanic processes. According to Levy et al. (2010) these structures, ‘‘boulder halo craters’’, were filled by latitudedependent mantle material. Orloff et al. (2011) exhaustively described boulder clusters at high Martian northern latitudes (601N–701N) in order to assess boulder movements over patterned ground. These authors postulate that impact craters are the source for many boulders, and use craters and their degradation to estimate the time scales for boulder movement. Orloff et al. (2011) arrived to the conclusion that freeze–thaw cycling could not have been responsible for boulder movements because in the last 3 Ma, with spin axis obliquities always o351 (Laskar et al., 2004), thermodynamic conditions for ice melting would
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have never been met. These authors calculate that the dayaverage maximum temperature in the northern plains (‘‘or elsewhere on Mars for that matter’’) would not have surpassed 255 K in the last 3 Ma. This temperature is relevant for the phase change of pure water, not brines: Renno´ et al. (2009) found possible physical and thermodynamical evidence of the presence of liquid water at the Phoenix landing site (681N). These authors also show that the thermodynamics of freeze–thaw cycles can lead to the formation of saline solutions with freezing temperatures lower than current summer ground temperatures at those latitudes. Renno´ et al. (2009) conclusions are consistent with the finding of perchlorates on the soil of the same site (Hecht et al., 2009) and may explain the formation of recurring slope lineae (McEwen et al., 2011), which grow during warm seasons and fade in cold seasons, albeit at lower latitudes (481S–321S). The location and characterization of boulder halos may prove to be useful in the selection of landing sites (Golombek et al., 2008; Mellon et al., 2008; Heet et al., 2009; Mangold, 2011).
2. Martian Palimpsests
Fig. 2. Close-up of the crater marked with an arrow on Fig. 1. North is up.
HiRISE image ESP_016526_2415_RED shows an area between latitudes 61.0671 and 61.2401, and longitudes 326.0821 and 326.3451. It was acquired on April 2nd 2010 with a 0.25 m per pixel resolution (Fig. 1). This image displays at least ten features which we identified as palimpsest craters and we will, first, take a closer look at the one which is marked with an arrow on Fig. 1.
Fig. 3. Close-up on the northern rim on Fig. 2. North is up.
Figs 2 and 3, both images with a 0.25 m per pixel of resolution, show the whole crater and a close-up on its northern rim. The crater is set on polygonal terrain which, on the first tens of meters on either side of the rim, is geometrically controlled by it. As we have shown above, polygonal terrains may be the result of thaw and freeze cycles of the permafrost active layer and thus these structures are possible geomarkers for habitability. Polygon areas do not seem significantly different inside and outside the crater. However, there are clear differences in the granulometry and distribution of boulders on either side of the rim: inside the crater boulders are smaller and of seemingly random distribution whereas on the rim, and up to 100 m outside of it, boulders are larger and preferentially set along polygon cracks (Alves et al., 2011). 2.1. Basic notions of Mathematical morphology
Fig. 1. HiRISE image ESP_016526_2415_RED. The crater marked with an arrow is 400 m in diameter. (Image: NASA/JPL/University of Arizona.).
In the middle 1960s, Matheron and Serra created a new theory of image analysis, mathematical morphology (Matheron, 1967; Serra, 1982). Since then, further developments allowed the construction of a solid theory with a vast field of applications (Chermant and Coster, 1989; Vincent, 1993; Meyer and Beucher, 1990; Soille and Pesaresi, 2002; Maragos and Vachier, 2009). Any operator or morphological transform implies the comparison of the features to analyze with a known object, the structuring element.
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The first morphological transforms defined by Matheron (1967), are the erosion and dilation. To gray scale images, the erosion (eB(f)) of an image f by a structuring element B of size l, is the minimum of the translations of f by the vectors b of B (Soille, 2002):
eB ðf Þ ¼ minb A B f b
ð1Þ
The dilation (dB(f)) of an image of an image f by a structuring element B of size l, is the maximum of the translations of f by the vectors b of B:
dB ðf Þ ¼ maxb A B f b
ð2Þ
Mathematical morphology operators can be used directly or applied sequentially to obtain more elaborated morphologic transformations for specific ends. According to this, erosion and dilation can be combined to perform the opening transform. An opening (g) consists on submitting an image f to an erosion followed by a dilation, both by a structuring element B of size l:
gBðf Þ ¼ dB ðf Þ½eB ðf Þ
ð3Þ
The grain size distribution (granulometry) of an image can be analyzed resorting to morphology operators (Serra, 1982). In mathematical morphology terms, the granulometry is the study of the size characteristics of sets (if the images are binary) and functions (for gray images). The idea is based on the sedimentological practice of using sieves of decreasing meshes. In image analysis the morphological granulometry Gc(X, l) is a cumulative function that defines the proportion of volume V that was eliminated by the application of a sequence of openings g (an opening is an erosion followed by a dilation) with a structuring element of increasing size l (l 40) (Pina et al., 2011): GðX, lÞ ¼ V½XV½glB ðXÞ=V½X
ð4Þ
For gray images, it is necessary to perform a correction of the granulometric distribution curve, since the final step of the application of successive openings is the minimum gray value of the image and the granulometric curve is unrealistic (Pina et al., 2011). To obtain the corrected curve, it is necessary to subtract the total gray levels sum of the last opening step (Vfinal) computed for each image, this is: GcorðX, lÞ ¼ ½VðlÞ þ V ðl þ 1Þ=½VðinitialÞVðfinalÞ
ð5Þ
2.2. Morphological algorithm to identify Martian boulder clusters
Fig. 4. Flowchart of the algorithm to identify the boulder clusters.
The ghost craters contour, from a visual analysis, is characterized by a boulder size variation: the largest boulders are concentrated along a ring. Based on this characteristic, we have developed a morphological granulometry algorithm to automatically identify the crater rim which will correspond to a region with a higher concentration of larger boulders. The first step of the algorithm consists in creating a binary image with a circular marker inside the crater. Then, this image is binarized by applying a threshold. After the binarization, all the single pixels that resist the threshold are eliminated by applying a morphological reconstruction by erosion by a disk of size one. The final result of this step is a binary image, a marker on the crater. The second step of the algorithm consists in submitting the marker image to several dilations by a disk of increasing size. At the end of each dilation, the image obtained is intersected with the original image in order to extract the original pixels gray levels. Each of these individual images will be subject to a granulometry by openings of increasing size. The structuring element used in this granulometric analysis is a square in order to better model sieve holes (Pina et al., 2011). This process is iterated until the dilated disk reaches the entire image and therefore the particle size distribution obtained is equivalent to the granulometric study for the whole image. Since our purpose was to determine the location of crater rims, and we have observed that they are marked by circular boulder clusters, we propose to use the statistic skewness of grain size distribution as a decision parameter for location of crater rims. Skewness is the third standardized moment about the mean (Kenney and Keeping, 1951) and can be naively seen as a measure of the distance between mean and median. Folk and Ward (1957) were the first to point out that ‘‘non-normal [y] skewness values are held to be the identifying characteristics of bimodal sediments even where such modes are not evident in frequency curves’’. Fig. 4 shows the flowchart for the developed algorithm.
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2.3. Testing the algorithm on a synthetic image We tested the new procedure with a purposely built synthetic image (Fig. 5) in order to evaluate the potential of our method. The grayscale (8-Byte) image, 1024 1024 pixels in size, has a background composed of grayscale Gaussian noise, with average 128 and standard deviation 30. To simulate spherical boulders we used white (255) circles whose black (0) shadows were elliptical, extending to the right a distance equal to the circle’s radius. The grain size distribution of the ‘‘boulders’’ is shown on Table 1, where | (F) is the diameter in Wentworth (1922) phi units g the relative frequency and G the cumulative frequency. As can be seen in Fig. 5, boulders were not all randomly dispersed on the background: boulders of diameter 8 pixels were randomly dispersed; those of larger diameters were dispersed so that the probability of their locations was highest along a circle centered in the figure’s center and radius 260 pixels. The whole synthetic figure was first submitted to the granulometric procedure described in the previous section, to assess its reliability. Fig. 6 shows a comparison between the original, known, input grain size distribution, and the measured distribution. The maximum difference between the two curves is 10% cumulative frequency, which is attributable to the use of a square structuring element to simulate sieve mesh while measuring Fig. 6. Grain size distributions of the synthetic ‘‘boulders’’ of Fig. 1: real and measured.
circular particles. We postulate that the same effect would have been felt in a mechanical sieving procedure, and intend to investigate this issue further in future work. Next we tested the procedure for finding the ghost crater rim. For that purpose a disk of diameter 45 pixels was visually centered on the synthetic ghost crater and successively dilated by 25 pixels increments to create masks upon each of which a grain size distribution was computed as well as the respective skewness (Fig. 7). As was theoretically expected, when reaching the ‘‘palimpsest’’ rim the skewness turns from positive (long-right-tailed), indicating predominance of smaller ‘‘boulders’’, to negative (long-lefttailed), indicating the appearance of larger ‘‘boulders’’. Correspondingly, we find that our procedure allows estimating the inner side of the simulated crater rim to be crossed by the 9th dilation, which imparts it a diameter of at least 247 pixels [(45/2)þ9 25].
2.4. Testing the algorithm on a palimpsest rim section
Fig. 5. Synthetic testing image. See text for complete description.
Table 1 Grain size distribution of the synthetic ‘‘boulders’’ of image 6. | (px)
Area (px)
| (F)
# of boulders
8 11 16 22 32 46 64
53 101 198 375 808 1663 3194
3.0 3.5 4.0 4.5 5.0 5.5 6.0
120 31 13 12 6 2 1
Sum
185
Total area
g(i)
G(i)
6360 3131 2574 4500 4848 3326 3194
0.23 0.11 0.09 0.16 0.17 0.12 0.11
0.23 0.34 0.43 0.59 0.77 0.89 1.00
27,933
1.00
As a next step we have tested the grain size distribution algorithm on a section of palimpsest I (Fig. 8). To that purpose we have visually located and measured the frequency-size distribution of boulders. These ranged between a minimum 4 pixels (1.0 m) and 22 pixels (5.5 m) in diameter. To measure the boulders, these were visually inscribed in ellipses, whose major axes were recorded (Fig. 9). It must be stressed that unlike a ‘‘true ground truth’’ this measurement procedure is highly dependent on the mapper. The manually and automatically measured grain size distributions follow the same pattern seen in the synthetic image test (Fig. 6) the former being systematically lower than the latter as can be seen in Fig. 10. Skewness variation with successive dilations (Fig. 11), on the other hand, is very different from the one found in the synthetic image test, though consistent with the whole crater analysis by our algorithm, as will be shown in the next section.
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Fig. 7. Estimating rim location based on grain size distribution skewness.
Fig. 9. Manual identification of boulders in the section of Fig. 8. North is up.
The analysis of all grain size distributions and respective skewnesses shows that the first local maxima usually mark the crater rims, as can be seen in Fig. 14.
3. Discussion
Fig. 8. Location of the section used as ‘‘ground truth‘‘ for testing the algorithm on palimpsest I (see Fig. 12). Small inset rectangle marks the position of Fig. 9. North is up.
2.5. Application of the algorithm to a HiRISE image The grain size distribution algorithm was tested on the 10 visually identified circular clusters of boulders (Fig. 12). Fig. 13 shows the variation of grain size distribution skewness with successive dilations for all the tested boulder clusters.
Looking at Fig. 14 we see that there are two broad sets of skewness curves, which we have called ‘‘type A’’ (increasing, then decreasing skewness) and ‘‘type V’’ (decreasing, then increasing), the latter confined to craters B, C, and J, which are the smallest. One possibility is that given the very small size of these craters (approximately 190, 125 and 270 m) the initial disk marker (45 pixels, or 11.25 m) would have been too large. Another interesting feature is that the cumulative distributions of grain sizes always show more than one inflection, which is an indication of a mixed population. Crater H stands out from our sample: it shows the shortest range of skewness values (between 0.05 and 0.14), and its cumulative distribution of grain sizes is concave upwards. It is
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Fig. 10. Grain size distribution of all the boulders in Fig. 9: measured by hand and by our algorithm.
Fig. 12. Location of tested boulder clusters.
Fig. 11. Variation of the grain size distribution skewnesses (manual and automatic) with dilation for the boulders in Fig. 8.
possible that our algorithm might have misidentified portions of some of the existing concentric ridges as boulders. The skewness values derived from the ‘‘ground truth’’ test in section 2.5 are consistent with those shown in Fig. 14 for crater I, also of type A. The algorithm presented in this work can only be applied to high resolutions images, like those of the HiRISE camera. Since it was developed based on the size of the boulders that mark the palimpsest border, high spatial resolution images are necessary to discriminate the boulders.
4. Conclusions and future work Palimpsest, ghost, or degraded craters are only discernible by circular boulder clusters. The importance of these structures is well described in the literature, since they can occur associated with periglacial features. We have developed an algorithm to automatically characterize circular boulder clusters in high resolution (HiRISE) images of Mars. Based on the grain size distribution of the boulders clusters, we proposed a method, with the use of morphological transforms, to automatically recognize craters rims. Our method allowed the recognition of all craters that we visually detected as palimpsests, and differentiate them according to their size and granulometry.
Fig. 13. Variation of skewness with dilation. Palimpsest H skewness is plotted on the right-hand ordinate axis.
The present work is only a first step to study these structures. In the next step, a more detailed study of Martian palimpsests will proceed along three lines: a) To produce a catalog of these features. b) To accurately define the geometrical parameters which characterize Martian palimpsests, namely, polygonal terrain geometry, boulder granulometry and shape analysis. c) To clarify the genesis of these features and their relationships with polygonal terrains. The location and characterization of boulder halos may also prove to be useful in the selection of landing sites on Mars.
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Fig. 14. Summary of test results. ID: identified dilation marking the inner crater rim.
T. Barata et al. / Planetary and Space Science 72 (2012) 62–69
Acknowledgments We are indebted to two anonymous reviewers and to our colleague Nuno Peixinho, whose commentaries and suggestions allowed us to greatly improve our work. This research is funded by FCT, the Portuguese Science Foundation, under the Contract PEst-OE/CTE/UI0611/2012—Center for Geophysics. References Alves, E.I., Barata, T., Barberes, G., Peixinho, N., 2011. Crater palimpsests on Mars. In: Proceedings of European Planetary Science Congress 6, EPSC-DPS2011-10, 2011, Nantes, France. Arvidson, R., 1974. Morphologic classification of martian craters and some implications. Icarus 22, 264–271. Butler, P.Jr., Morrison, D.A., 1977. Geology of the Luna 24 landing site. In: Proceedings of the 8th Lunar Science Conference, Houston, Texas, March 14–18. Chermant, J.L., Coster, M., 1989. Pre´cis d’analyse d’ images, 2nd ed. Presses du CNRS, Paris. Deutsch, A., Masaitis, V.L., Langenhorst, F., Richard, A.F., Grieve, R.A.F., 2000. Popigai, Siberia – Well preserved giant impact structure, national treasury, and world’s geological heritage. Episodes 23 (1), 3–11. Folk, R.L., Ward, W.C., 1957. Brazos River bar: a study in the significance of grain size parameters. Journal of Sedimentary Petrology 27 (1), 3–27. Golombek, M.P., Huertas, A., Marlow, J., McGranne, B., Klein, C., Martinez, M., Arvidson, R.E., Heet, T., Barry, L., Seelos, K., Adams, D., Li, W., Matijevic, J.R., Parker, T., Sizemore, H.G., Mellon, M., McEwen, A.S., Tamppari, L.K., Cheng, Y., 2008. Size-frequency distributions of rocks on the northern plains of mars with special reference to Phoenix landing surfaces. Journal of Geophysical Research 113, E00A09. Harmon, J.K., Slade, M.A., Butler, B.J., Head, J.W., Rice, M.S., Campbell, D.B., 2007. Mercury: radar images of the equatorial and mid latitudes zones. Icarus 187, 374–405. Hartmann, W., Esquerdo, G., 1999. ‘‘Pathological’’ martian craters: evidence for a transient obliteration event? Meteoritics and Planetary Science 34, 159–165. Hecht, M.H., Kounaves, S.P., Quinn, R.C., West, S.J., Young, S.M.M., Ming, D.W., Catling, D.C., Clark, B.C., Boynton, W.V., Hoffman, J., DeFlores, L.P., Gospodinova, K., Kapit, J., Smith, P.H., 2009. Detection of perchlorate and the soluble chemistry of martian soil at the Phoenix lander site. Science 325, 64–67. Heet, T.L., Arvidson, R.E., Cull, S.C., Mellon, M.T., Seelos, K.D., 2009. Geomorphic and geologic settings of the Phoenix lander mission landing site. J. Geophys. Res. 114, E00E04. HiRISE Team, NASA/ JPL/ University of Arizona, (retrieved on March 15), 2011 Jones, K.B., Head III, J.,.W., Pappalardo, R.T., Moore, J.M., 2003. Morphology and origin of palimpsests on Ganymede based on Galileo observations. Icarus 164, 197–212 /http://hirise.lpl.arizona.edu/PDS/RDR/ESP/ORB_ 016500_016599/ ESP_016526_2415/S.
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Kenney, J.F., Keeping, E.S., 1951. Mathematics of Statistics. Pt. 2, second ed. Van Nostrand, Princeton, NJ. Laskar, J., Correia, A.C.M., Gastineau, M., Joutel, F., Levrard, B., Robutel, P., 2004. Long term evolution and chaotic diffusion of the insolation quantities of Mars. Icarus 170, 343–364. Levy, J., Marchant, D.R., Head, J.W., 2010. Thermal contraction crack polygons on Mars: a synthesis from HiRISE, Phoenix and terrestrial analog studies. Icarus 206, 229–252. Mangold, N., 2011. Ice sublimation as a geomorphic process: a planetary perspective. Geomorphology 126, 1–17. Maragos, P., Vachier, C., 2009. Overview of adaptive morphology: trends and perspectives. In: Proceedings of IEEE International Conference Image Processing (ICIP’09), pp. 2241–2244. Matheron, G., 1967. E´le´ments pour une the´orie des milieus poreux. Masson, Paris. McEwen, A.S., Ojha, L., Dundas, C.M., Mattson, S.S., Byrne, S., Wray, J.J., Cull, S.C., Murchie, S.L., Thomas, N., Gulick, V.C., 2011. Seasonal flows on warm martian slopes. Science 333 (6043), 740–743. Mellon, M.T., Arvidson, R.E., Marlow, J.J., Phillips, R.J., Asphaug, E., 2008. Periglacial landforms at the Phoenix landing site and the northern plains of Mars. Journal of Geophysical Research 113, E00A23. Meyer, F., Beucher, S., 1990. Morphological segmentation. Journal of Visual Communication and Image Representation 1 (1), 21–46. Nelson, R.M., Brown, R.H., Hapke, B.W., Smythe, W.D., Kamp, L., Boryta, M., Baines, K.H., Giancarlo, B., Bibring, J., Buratti, B.J., Capaccioni, F., Cerroni, P., Clark, R.N., Coradini, A., Cruikshank, D.P., Drossart, P., Formisanno, V., Jaumann, R., Langevin, Y., Matson, D.L., McCord, T. B.v.Mennella, V., Nicholson, P.D., Sicardy, B. and Sotin, C., 2004. VIMS evidence for palimpsests on Titan as a constraint on widespread precipitation. In: Proceedings of American Geophysical Union Fall Meeting, 13–15 December 2004, San Francisco, USA, abstract #P41B-08. Orloff, T., Kreslavsky, M., Asphaug, E., Korteniemi, J., 2011. Boulder movement at high northern latitudes of Mars. Journal of Geophysical Research 116, E11006. Pina, P., Lira, C., Lousada, M., 2011. In-situ computation of granulometries of sedimentary grains-some preliminary results. Journal of Coastal Research-SI 64, 1227–1730. Renno´, N.O., Bos, J.B., Catling, D., Clark, B.C., Drube, l., Fisher, D., Goetz, W., Hviid, S.F., Keller, H.U., Kok, J.F., Kounaves, S.P., Leer, K., Lemmon, M., Madsen, M.B., Markiewicz, W.J., Marshall, J., McKay, C., Mehta, M., Smith, M., Zorzano, M.P., Smith, P.H., Stoker, C., Young, S.M.M., 2009. Possible physical and thermodynamical evidence for liquid water at the Phoenix landing site. Journal of Geophysical Research 114, E00E03. Serra, J., 1982. Image Analysis and Mathematical Morphology, vol. I. Academic press, London 610 p. Soille, P., 2002. Morphological Image Analysis. Principles and Applications, second ed. Springer, New York. Soille, P., Pesaresi, M., 2002. Advances in mathematical morphology applied to geoscience and remote sensing. IEEE Transactions on Geoscience 40 (9), 2042–2055. Vincent, L., 1993. Morphological grayscale reconstruction in image analysis: applications and efficient algorithms. IEEE Transactions on Geoscience and Remote Sensing 22 (2), 176–201. Wentworth, C.K., 1922. A scale of grade and class terms for clastic sediments. Journal of Geology 30, 377–392.
Contents lists available at SciVerse ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Characterization of palimpsest craters on Mars T. Barata a,n, E.I. Alves a,b, A. Machado a, G.A. Barberes a a b
Centre for Geophysics, University of Coimbra, Portugal Geophysical Institute and Department of Earth Science, University of Coimbra, Portugal
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 January 2012 Received in revised form 24 September 2012 Accepted 25 September 2012 Available online 16 October 2012
Palimpsest, ghost, or degraded craters have so far been identified on Mercury, the Earth, the Moon, Mars, Ganymede, Callisto, and possibly even Titan. We have identified at least 10 palimpsests on HiRISE image ESP_016526_2415 of Mars and developed an algorithm to automatically characterize these structures on high resolution images. Since the genesis of palimpsests may be related to freeze–thaw cycles these features might have provided habitable environments. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Palimpsest Ghost crater Periglacial terrain Mars
1. Introduction: Palimpsests, liquid water, and Mars habitability The word palimpsest originally meant a writing surface which was reused after earlier writing had been erased. Planetary Geosciences borrowed the term to describe craters whose flat topography lets them be perceived mainly by reflectance contrasts. This merely descriptive term has been used interchangeably with ‘‘ghost craters’’, ‘‘degraded craters’’, and even ‘‘pathological craters’’ to refer to features on Mercury (Harmon et al., 2007), the Earth (Deutsch et al., 2000), the Moon (Butler and Morrison, 1977), Mars (Arvidson, 1974; Hartmann and Esquerdo, 1999; Levy et al., 2010;), Ganymede and Callisto (Jones et al., 2003), and possibly even Titan (Nelson et al., 2004). In the present work we will use the term ‘‘palimpsest’’ with the strictly descriptive meaning ‘‘craters that are only perceptible by annular clusters of meter sized boulders on an otherwise almost featureless plane surface’’. Arvidson (1974) classified craters on Mars according to their morphology on images of Mariner 9. By ‘‘ghost craters’’ he means what remains of the ‘‘ghost’’ of an impact carter. Morphologically, these craters are flat-floored, rimless, extremely shallow, without central peaks, and would probably represent what remains after erosion. Arvidson (1974) also refers the need to sub-classify the ghost or degraded craters according to their smoothness or roughness, since these characteristics can imply differences in the patterns of degradation-a task that we will attempt in the present work.
n
Corresponding author. Tel.: þ351 239 793 420; fax: þ 351 239 793 428. E-mail address: [email protected] (T. Barata).
0032-0633/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.pss.2012.09.015
Hartmann and Esquerdo (1999) described three low-relief circular features which they name ‘‘pathological craters’’. They notice that these features appear unique to Mars, although ‘‘ghost craters’’ are mentioned on the Moon. Three hypotheses are discussed in their work: (1) volcanic ghost crater, suggesting an analogous formation to lunar ghost craters, (2) ice lens hypothesis, suggesting ‘‘unusual interactions’’ with the ice or ground water and (3) isostatic deformation, a process that can involve viscous relaxation of craters that were formed in ice-rich permafrost layers. To Hartmann and Esquerdo (1999), the third hypothesis is the most acceptable, and the greatest importance of these structures is that they can give clues about the early geological history of Mars, especially in what concerns the presence of an ice-rich permafrost layer. Levy et al. (2010) mention that these features suggest the existence of a fluid-rich substrate. In particular, mounds with rounded bases, aligned along the crater rim, would indicate an origin related to fluid flow up the impact fracture system, which might have involved impact-related hydrothermal activity and glaciovolcanic processes. According to Levy et al. (2010) these structures, ‘‘boulder halo craters’’, were filled by latitudedependent mantle material. Orloff et al. (2011) exhaustively described boulder clusters at high Martian northern latitudes (601N–701N) in order to assess boulder movements over patterned ground. These authors postulate that impact craters are the source for many boulders, and use craters and their degradation to estimate the time scales for boulder movement. Orloff et al. (2011) arrived to the conclusion that freeze–thaw cycling could not have been responsible for boulder movements because in the last 3 Ma, with spin axis obliquities always o351 (Laskar et al., 2004), thermodynamic conditions for ice melting would
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have never been met. These authors calculate that the dayaverage maximum temperature in the northern plains (‘‘or elsewhere on Mars for that matter’’) would not have surpassed 255 K in the last 3 Ma. This temperature is relevant for the phase change of pure water, not brines: Renno´ et al. (2009) found possible physical and thermodynamical evidence of the presence of liquid water at the Phoenix landing site (681N). These authors also show that the thermodynamics of freeze–thaw cycles can lead to the formation of saline solutions with freezing temperatures lower than current summer ground temperatures at those latitudes. Renno´ et al. (2009) conclusions are consistent with the finding of perchlorates on the soil of the same site (Hecht et al., 2009) and may explain the formation of recurring slope lineae (McEwen et al., 2011), which grow during warm seasons and fade in cold seasons, albeit at lower latitudes (481S–321S). The location and characterization of boulder halos may prove to be useful in the selection of landing sites (Golombek et al., 2008; Mellon et al., 2008; Heet et al., 2009; Mangold, 2011).
2. Martian Palimpsests
Fig. 2. Close-up of the crater marked with an arrow on Fig. 1. North is up.
HiRISE image ESP_016526_2415_RED shows an area between latitudes 61.0671 and 61.2401, and longitudes 326.0821 and 326.3451. It was acquired on April 2nd 2010 with a 0.25 m per pixel resolution (Fig. 1). This image displays at least ten features which we identified as palimpsest craters and we will, first, take a closer look at the one which is marked with an arrow on Fig. 1.
Fig. 3. Close-up on the northern rim on Fig. 2. North is up.
Figs 2 and 3, both images with a 0.25 m per pixel of resolution, show the whole crater and a close-up on its northern rim. The crater is set on polygonal terrain which, on the first tens of meters on either side of the rim, is geometrically controlled by it. As we have shown above, polygonal terrains may be the result of thaw and freeze cycles of the permafrost active layer and thus these structures are possible geomarkers for habitability. Polygon areas do not seem significantly different inside and outside the crater. However, there are clear differences in the granulometry and distribution of boulders on either side of the rim: inside the crater boulders are smaller and of seemingly random distribution whereas on the rim, and up to 100 m outside of it, boulders are larger and preferentially set along polygon cracks (Alves et al., 2011). 2.1. Basic notions of Mathematical morphology
Fig. 1. HiRISE image ESP_016526_2415_RED. The crater marked with an arrow is 400 m in diameter. (Image: NASA/JPL/University of Arizona.).
In the middle 1960s, Matheron and Serra created a new theory of image analysis, mathematical morphology (Matheron, 1967; Serra, 1982). Since then, further developments allowed the construction of a solid theory with a vast field of applications (Chermant and Coster, 1989; Vincent, 1993; Meyer and Beucher, 1990; Soille and Pesaresi, 2002; Maragos and Vachier, 2009). Any operator or morphological transform implies the comparison of the features to analyze with a known object, the structuring element.
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The first morphological transforms defined by Matheron (1967), are the erosion and dilation. To gray scale images, the erosion (eB(f)) of an image f by a structuring element B of size l, is the minimum of the translations of f by the vectors b of B (Soille, 2002):
eB ðf Þ ¼ minb A B f b
ð1Þ
The dilation (dB(f)) of an image of an image f by a structuring element B of size l, is the maximum of the translations of f by the vectors b of B:
dB ðf Þ ¼ maxb A B f b
ð2Þ
Mathematical morphology operators can be used directly or applied sequentially to obtain more elaborated morphologic transformations for specific ends. According to this, erosion and dilation can be combined to perform the opening transform. An opening (g) consists on submitting an image f to an erosion followed by a dilation, both by a structuring element B of size l:
gBðf Þ ¼ dB ðf Þ½eB ðf Þ
ð3Þ
The grain size distribution (granulometry) of an image can be analyzed resorting to morphology operators (Serra, 1982). In mathematical morphology terms, the granulometry is the study of the size characteristics of sets (if the images are binary) and functions (for gray images). The idea is based on the sedimentological practice of using sieves of decreasing meshes. In image analysis the morphological granulometry Gc(X, l) is a cumulative function that defines the proportion of volume V that was eliminated by the application of a sequence of openings g (an opening is an erosion followed by a dilation) with a structuring element of increasing size l (l 40) (Pina et al., 2011): GðX, lÞ ¼ V½XV½glB ðXÞ=V½X
ð4Þ
For gray images, it is necessary to perform a correction of the granulometric distribution curve, since the final step of the application of successive openings is the minimum gray value of the image and the granulometric curve is unrealistic (Pina et al., 2011). To obtain the corrected curve, it is necessary to subtract the total gray levels sum of the last opening step (Vfinal) computed for each image, this is: GcorðX, lÞ ¼ ½VðlÞ þ V ðl þ 1Þ=½VðinitialÞVðfinalÞ
ð5Þ
2.2. Morphological algorithm to identify Martian boulder clusters
Fig. 4. Flowchart of the algorithm to identify the boulder clusters.
The ghost craters contour, from a visual analysis, is characterized by a boulder size variation: the largest boulders are concentrated along a ring. Based on this characteristic, we have developed a morphological granulometry algorithm to automatically identify the crater rim which will correspond to a region with a higher concentration of larger boulders. The first step of the algorithm consists in creating a binary image with a circular marker inside the crater. Then, this image is binarized by applying a threshold. After the binarization, all the single pixels that resist the threshold are eliminated by applying a morphological reconstruction by erosion by a disk of size one. The final result of this step is a binary image, a marker on the crater. The second step of the algorithm consists in submitting the marker image to several dilations by a disk of increasing size. At the end of each dilation, the image obtained is intersected with the original image in order to extract the original pixels gray levels. Each of these individual images will be subject to a granulometry by openings of increasing size. The structuring element used in this granulometric analysis is a square in order to better model sieve holes (Pina et al., 2011). This process is iterated until the dilated disk reaches the entire image and therefore the particle size distribution obtained is equivalent to the granulometric study for the whole image. Since our purpose was to determine the location of crater rims, and we have observed that they are marked by circular boulder clusters, we propose to use the statistic skewness of grain size distribution as a decision parameter for location of crater rims. Skewness is the third standardized moment about the mean (Kenney and Keeping, 1951) and can be naively seen as a measure of the distance between mean and median. Folk and Ward (1957) were the first to point out that ‘‘non-normal [y] skewness values are held to be the identifying characteristics of bimodal sediments even where such modes are not evident in frequency curves’’. Fig. 4 shows the flowchart for the developed algorithm.
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2.3. Testing the algorithm on a synthetic image We tested the new procedure with a purposely built synthetic image (Fig. 5) in order to evaluate the potential of our method. The grayscale (8-Byte) image, 1024 1024 pixels in size, has a background composed of grayscale Gaussian noise, with average 128 and standard deviation 30. To simulate spherical boulders we used white (255) circles whose black (0) shadows were elliptical, extending to the right a distance equal to the circle’s radius. The grain size distribution of the ‘‘boulders’’ is shown on Table 1, where | (F) is the diameter in Wentworth (1922) phi units g the relative frequency and G the cumulative frequency. As can be seen in Fig. 5, boulders were not all randomly dispersed on the background: boulders of diameter 8 pixels were randomly dispersed; those of larger diameters were dispersed so that the probability of their locations was highest along a circle centered in the figure’s center and radius 260 pixels. The whole synthetic figure was first submitted to the granulometric procedure described in the previous section, to assess its reliability. Fig. 6 shows a comparison between the original, known, input grain size distribution, and the measured distribution. The maximum difference between the two curves is 10% cumulative frequency, which is attributable to the use of a square structuring element to simulate sieve mesh while measuring Fig. 6. Grain size distributions of the synthetic ‘‘boulders’’ of Fig. 1: real and measured.
circular particles. We postulate that the same effect would have been felt in a mechanical sieving procedure, and intend to investigate this issue further in future work. Next we tested the procedure for finding the ghost crater rim. For that purpose a disk of diameter 45 pixels was visually centered on the synthetic ghost crater and successively dilated by 25 pixels increments to create masks upon each of which a grain size distribution was computed as well as the respective skewness (Fig. 7). As was theoretically expected, when reaching the ‘‘palimpsest’’ rim the skewness turns from positive (long-right-tailed), indicating predominance of smaller ‘‘boulders’’, to negative (long-lefttailed), indicating the appearance of larger ‘‘boulders’’. Correspondingly, we find that our procedure allows estimating the inner side of the simulated crater rim to be crossed by the 9th dilation, which imparts it a diameter of at least 247 pixels [(45/2)þ9 25].
2.4. Testing the algorithm on a palimpsest rim section
Fig. 5. Synthetic testing image. See text for complete description.
Table 1 Grain size distribution of the synthetic ‘‘boulders’’ of image 6. | (px)
Area (px)
| (F)
# of boulders
8 11 16 22 32 46 64
53 101 198 375 808 1663 3194
3.0 3.5 4.0 4.5 5.0 5.5 6.0
120 31 13 12 6 2 1
Sum
185
Total area
g(i)
G(i)
6360 3131 2574 4500 4848 3326 3194
0.23 0.11 0.09 0.16 0.17 0.12 0.11
0.23 0.34 0.43 0.59 0.77 0.89 1.00
27,933
1.00
As a next step we have tested the grain size distribution algorithm on a section of palimpsest I (Fig. 8). To that purpose we have visually located and measured the frequency-size distribution of boulders. These ranged between a minimum 4 pixels (1.0 m) and 22 pixels (5.5 m) in diameter. To measure the boulders, these were visually inscribed in ellipses, whose major axes were recorded (Fig. 9). It must be stressed that unlike a ‘‘true ground truth’’ this measurement procedure is highly dependent on the mapper. The manually and automatically measured grain size distributions follow the same pattern seen in the synthetic image test (Fig. 6) the former being systematically lower than the latter as can be seen in Fig. 10. Skewness variation with successive dilations (Fig. 11), on the other hand, is very different from the one found in the synthetic image test, though consistent with the whole crater analysis by our algorithm, as will be shown in the next section.
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Fig. 7. Estimating rim location based on grain size distribution skewness.
Fig. 9. Manual identification of boulders in the section of Fig. 8. North is up.
The analysis of all grain size distributions and respective skewnesses shows that the first local maxima usually mark the crater rims, as can be seen in Fig. 14.
3. Discussion
Fig. 8. Location of the section used as ‘‘ground truth‘‘ for testing the algorithm on palimpsest I (see Fig. 12). Small inset rectangle marks the position of Fig. 9. North is up.
2.5. Application of the algorithm to a HiRISE image The grain size distribution algorithm was tested on the 10 visually identified circular clusters of boulders (Fig. 12). Fig. 13 shows the variation of grain size distribution skewness with successive dilations for all the tested boulder clusters.
Looking at Fig. 14 we see that there are two broad sets of skewness curves, which we have called ‘‘type A’’ (increasing, then decreasing skewness) and ‘‘type V’’ (decreasing, then increasing), the latter confined to craters B, C, and J, which are the smallest. One possibility is that given the very small size of these craters (approximately 190, 125 and 270 m) the initial disk marker (45 pixels, or 11.25 m) would have been too large. Another interesting feature is that the cumulative distributions of grain sizes always show more than one inflection, which is an indication of a mixed population. Crater H stands out from our sample: it shows the shortest range of skewness values (between 0.05 and 0.14), and its cumulative distribution of grain sizes is concave upwards. It is
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Fig. 10. Grain size distribution of all the boulders in Fig. 9: measured by hand and by our algorithm.
Fig. 12. Location of tested boulder clusters.
Fig. 11. Variation of the grain size distribution skewnesses (manual and automatic) with dilation for the boulders in Fig. 8.
possible that our algorithm might have misidentified portions of some of the existing concentric ridges as boulders. The skewness values derived from the ‘‘ground truth’’ test in section 2.5 are consistent with those shown in Fig. 14 for crater I, also of type A. The algorithm presented in this work can only be applied to high resolutions images, like those of the HiRISE camera. Since it was developed based on the size of the boulders that mark the palimpsest border, high spatial resolution images are necessary to discriminate the boulders.
4. Conclusions and future work Palimpsest, ghost, or degraded craters are only discernible by circular boulder clusters. The importance of these structures is well described in the literature, since they can occur associated with periglacial features. We have developed an algorithm to automatically characterize circular boulder clusters in high resolution (HiRISE) images of Mars. Based on the grain size distribution of the boulders clusters, we proposed a method, with the use of morphological transforms, to automatically recognize craters rims. Our method allowed the recognition of all craters that we visually detected as palimpsests, and differentiate them according to their size and granulometry.
Fig. 13. Variation of skewness with dilation. Palimpsest H skewness is plotted on the right-hand ordinate axis.
The present work is only a first step to study these structures. In the next step, a more detailed study of Martian palimpsests will proceed along three lines: a) To produce a catalog of these features. b) To accurately define the geometrical parameters which characterize Martian palimpsests, namely, polygonal terrain geometry, boulder granulometry and shape analysis. c) To clarify the genesis of these features and their relationships with polygonal terrains. The location and characterization of boulder halos may also prove to be useful in the selection of landing sites on Mars.
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Fig. 14. Summary of test results. ID: identified dilation marking the inner crater rim.
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