We describe a new project to obtain a global characterisation of Martian impact crater morphology from the 1/16 degree MOLA topography dataset. A new mathematical method applicable to both symmetric and asymmetric craters is used

McBride, N.

Wallis, D.

English

Open Research Online (The Open University)

Open Research OnlineThe Open University’s repository of research publicationsand other research outputsThe detailed characterization of Martian impact cratersfrom the 1/16 degree MOLA global topography gridConference or Workshop ItemHow to cite:Wallis, D. and McBride, N. (2001). The detailed characterization of Martian impact craters from the 1/16degree MOLA global topography grid. In: 32nd Lunar and Planetary Science Conference, 12-16 Mar 2001, Houston,Texas, USA.For guidance on citations see FAQs.c© [not recorded]Version: [not recorded]Link(s) to article on publisher’s website:http://www.lpi.usra.edu/meetings/lpsc2001/pdf/1692.pdfCopyright and Moral Rights for the articles on this site are retained by the individual authors and/or other copyrightowners. For more information on Open Research Online’s data policy on reuse of materials please consult the policiespage.oro.open.ac.ukTHE DETAILED CHARACTERIZATION OF MARTIAN IMPACT CRATERS FROM THE 1/16 DEGREE MOLAGLOBAL TOPOGRAPHY GRID. D. Wallis, N. McBride, Planetary and Space Science Research Institute, The Open Uni-versity, Walton Hall, Milton Keynes, MK7 6AA, UK (david-wallis@bigfoot.com, N.M.McBride@open.ac.uk).The Mars Orbital Laser Altimeter (MOLA) [1][2] griddedglobal topography dataset provides an excellent opportunity tostudy the impact record of Mars. The resolution of the latestgrid is    degree, which translates to a horizontal resolutionof less than 4 km, sufficient to provide gridded elevation mapsof a vast number of Martian impact craters. We have extractedDigital Elevation Maps (DEM’s) of impact craters (for exam-ple figure 1) from the global dataset for morphological com-parison using new mathematical methods which can compare	 crater shapes (including asymmetries). By using thenew technique, we aim to extend previously published globalsurveys (for example [3][4]) of the Martian crater record. Thework is being undertaken under a new project at the Planetaryand Space Science Research Institute at the Open University,U.K. In this paper we present an outline of the methods theproject will use, and the areas of study we will undertake. Theoverall aim is to develop a more detailed understanding of theimpact history of Mars. A  	 impact history, consistingof the number of craters at each size, can be found easily fromphotographs by simply counting the craters. A more 	history would include more detail; ideally the class of objectthat hit the surface (for example comets versus asteroids).ﬁﬀﬃﬂ "!#  $&%('#*),+-/.10ﬃ#324/+657ﬀﬃﬂ ﬀ98:+0<;=0#*> +8ﬀ2'@?2A"#0B5C;?ED24=+?+!8ﬀF+'ﬀﬃ-/.+HG*8IG*!:+H8#!KJ#*)8!:+G8#KAL4M!2-N8O1# PQ K8ORA,#ﬂH!##?ES7TU%A1+H8:+<ﬂ!ﬀAWVComparisons between crater shapes will be made usingnew mathematical methods developed specifically for impactcrater analysis [5][6][7]. The DEM (consisting of many mea-surements arranged as a grid over the surface of the crater)is reduced to a set of parameters; the coefficients of a seriesorthogonal expansion,XBZY[]\D=^`_a bcﬁdﬁebgfhbBZYH[\DB D-0.0100.010.020.030.040.050.060 20 40 60 80 100AmplitudeModeZernike spectrum of mars1 craterﬁﬀﬂ,!#ji $Ik O,#<#),.1+ ',l ﬀ2 ' G2Q#*m/G*ﬀ# ' 8 l 4n2H!o+ ? +H!8ﬀ+ ' ﬀﬃ-qp.+G87G*!:+8#*!KV k O,#r8st2u0+H!ﬂ# l 8C.#K+Hv lBe"w+ ' Aedd+!#<4M2!!:+ A,ﬀ+H009x l x"-/-/#*8!ﬀﬃGy8#*!- l V k O1ﬀ l=l O12Ks l 8O+8z8O1#{-u+|}2!ﬀ98}x248O,#tA,#4n2!-u+8ﬀﬃ2 ' 2H418O,# l ,!4n+G#~O1+ l !:+A,ﬀ+0ﬃ09x l x,-/-/#8!xQV?+'xo24,8O1#y28O1#!zG2Q#*m/G*ﬀ#'8l!#*.,!#l#'8=+lx"-/-/#*8!ﬀﬃGy4M#K+Hp8,!#lJsIO1ﬀﬃG:OoGK+'r#{G*2 -/.+!#KAC+l#K+lﬀﬃ09xr+l8O1#lx,-/-/#8!ﬀGG2 -/.2'#'8lVwhere XBZY[\Drepresents the shape of the crater (the DEM, seefigure 1),fhbBZY[\Dare a set of orthogonal functions defined inplane polar geometry, andebare the coefficients of expansion,chosen such that the sum converges on XBZYH[\D. The coeffi-cientsebare unique to the shape of each crater, and provide aconvenient method of comparing crater shapes quantitatively,while considering all aspects of the crater shape (see figure 2).The expansion coefficients are analogous to the coefficients ofa Fourier series expansion.A particular advantage of the method is that asymmetriescan be quantified as easily as symmetrical features. This willenable us to search for asymmetries due to oblique impact. Al-though most impact craters have a circular rim (except for verylow angles of incidence), the circularity does not necessarilyimply radial symmetry of the crater bowl. Laboratory studieshave shown asymmetries in the crater bowl due to oblique im-pact, using the mathematical techniques applied here [5]. Weexpect similar asymmetries to be present in the Martian craters.By quantifying the asymmetries, we hope to deduce the impactangle for any crater, although at this stage is is uncluear howlarge the uncertainties will be. Although this is an interestingresult in itself, a knowledge of the impact angle could then beused to compensate for crater size variations due to obliqueimpact, and therefore make better estimates of impactor size(in other words, distinguish a large object at a shallow impactangle from a smaller object at near normal incidence). Al-though it is not possible to test this method experimentally atplanetary-scales, there are two methods which we will use toprovide some confirmation of our findings. First, asymme-Lunar and Planetary Science XXXII (2001) 1692.pdf;{z;=;y7t;0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.5−0.4−0.3−0.2−0.100.10.20.30.40.5a4γCrater shape parameter space.Central Peak Parabola Crater Rim Simple Simple Cone Hemisphere Rounded Pointed ﬁﬀﬃﬂ "!#u $ 1#K+8,!# l .1+G#uA"ﬀF+Hﬂ!:+H-4M2!o!:+ A"ﬀ+0ﬃ09x l x"-/-/#*8p!ﬀﬃG<G!:+H8#*! l V;{+HGOR.2ﬀ ' 82 ' 8O1#C4M#K+H8"!# l .+HG#o!#.,!# l # ' 8 l+q.+!8ﬀﬃG10+H! l O+H.# V k O1#oG# ' 8!:+H0U!#ﬂ ﬀﬃ2 ' A"# l G*!ﬀ  # l G*!:+H8#! 2KsI0 lBﬀ ',l ﬀFA"#j8O1#<G*!:+H8#!C!ﬀ- D sIﬀﬃ8O	-/2H!.1O,2 0ﬃ2 ﬂHxQJ+ ' A<8O1#~82.j!#ﬂ ﬀﬃ2 ' A"# l G*!ﬀ  # l G*!:+H8#!  2KsI0 l sIﬀ98Ou+7G# ' 8!:+H0.#K+HvhV k O,#C02Ks#*!!#*ﬂ ﬀﬃ2 ' GK+ ' #C l #A82/A"# l G*!ﬀ  #r+jG2 -qp.10ﬃ#*8#/G!:+H8#*!lO+H.# JﬁsIﬀ98O+ŁG!:+H8#*!r!ﬀﬃ-VL"O+H0ﬃ02KsG*!:+H8#!l+H!#2'8O1#t0ﬃ#*4F8=2418O,#-u+H.J#G2-/ﬀ'ﬂA"##.#*!z82(8O1#y!ﬀﬂOQ8KVtries in craters showing asymmetric ejecta blankets, typical ofoblique impact, will be measured and compared with craterswhose ejecta blankets are symmetrical. This will quickly showif any asymmetries are present. MOC images will be used tostudy the ejecta patterns. Secondly, the expected distributionof impact angles for bodies hitting a planetary surface can bederived theoretically [8]. Therefore the distribution of impactangles found for the Martian craters should match the predicteddistribution.We will also look at symmetrical features of the Mar-tian impact craters. Preliminary studies have shown that themathematical method described above is able to identify mor-phological variations over the range of sizes between simple(bowl shaped) and more complex morphology (craters with acentral uplift). This initial work has shown that the change inshape is gradual, and can be quantified using a ratio of twoexpansion coefficients,edd ande"w, with the Zernike polyno-mials [9] chosen for the functionsfb. The variation can beshown visually as a change in the  axis (  ^eddew) whenplotted on the radially symmetric feature space diagram (de-scribed by Wallis et al. in [7]). This feature space is shown infigure 3. Each point on the feature space represents a differentshape. Crater  I shapes appear in the top two portions ofthe feature space, and complete crater shapes (including theperimeter rim) are found in the lower part of the diagram. Thecentral region describes simple bowl shapes, and the top regionshows craters with a central peak. Shallow craters are on theleft, becoming deeper to the right. Our initial studies show, asexpected, that craters appear higher up and further to the leftof the plot as the diameter increases. The feature space shownin figure 3 provides a very convenient method of distinguish-ing simple and complex craters, and quantifying the  g ofmodification. Again, MOC images will be used to estimatethe degree of degradation.Each crater from the MOLA grid will be considered duringthis programme of research, which in total will amount toseveral hundred craters at least. We believe that a detailedexamination of crater morphology from MOLA DEM’s canmake a significant contribution to our understanding of thecomplex impact history of Mars.References[1] M.T. Zuber and D.E. Smith. The Mars observer laseraltimiter investigation. " ](, *"  * , pages 7781–7798, 1992.[2] D.E. Smith, M.T. Zuber, S.C. Solomon, R.J. Phillips, J.W.Head, J.B. Garvin, W.B. Banerdt, D.O. Muhleman, G.H.Pettengill, G.A. Neumann, F.G. Lemoine, J.B. Abshire,O. Aharonson, C.D. Brown, S.A. Hauck, A.B. Ivanov, P.J.McGovern, H.J. Zwally, and T.C. Duxbury. The globaltopography of Mars and implications for surface evolution.:, 284:1495–1503, 1999.[3] J.B. Garvin, J.J. Frawley, S.E.H. Sakimoto, and C. Schnet-zler. Global geometric properties of martian impactcraters: An assessment from Mars orbiter laser altimeter(MOLA) digital elevation models. z ( ( ﬃ ::¡(¡¡¢, 2000.[4] J.B. Garvin, S.E. Sakimoto, J.J. Frawley, and C. Schnet-zler. North polar region craterforms on Mars: Geomet-ric characteristics from the Mars orbiter laser altimeter.¢* , 144:329–352, 2000.[5] L. Kay, A. Podoleanu, M. Seeger, and C. J. Solomon. Anew approach to the measurements and analysis of impactcraters. ¢:1 ﬁ" ¢:	"£*z¤~Q , 19(8):739–753, 1997.[6] C.J. Solomon, M. Seeger, J. Curtis, and L. Kay. Automatedcompact parametric representation of impact craters. ¢:, "¢:	"£*z¤~Q, 19(8):739–753, 1998.[7] D. Wallis, C.J. Solomon, and N. McBride. Modelling radi-ally symmetric impact craters with orthogonal functions.¢:1ﬁ"¢:	"£*z¤~Q, 2000. In Press.[8] E.M. Schoemaker.       ¦¥ Z	j§]¨M1©K, pages 283–359. Acedemic Press, 1962.[9] Born and Wolf.      "   ]uªU    . Pergamon Press,1993.Lunar and Planetary Science XXXII (2001) 1692.pdf

The detailed characterization of Martian impact craters from the 1/16 degree MOLA global topography grid

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The detailed characterization of Martian impact craters from the 1/16 degree MOLA global topography grid

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