Prepared on behalf of the National Aeronautics and Space Administration GEOMETRIC INTERPRETATION OF LUNAR CRATERS G23QIJQ8 MONIES ALPES MONIES ARISTILLUS SPITZBERGENSIS • < PALUS PUTREDINIS ;i Impact craters and other features on the Moon, photographed by Apollo 15 crew while in orbit 106 km above surface on July 31, 1971. Oblique view is north across eastern Mare Imbrium. The horizon lies about 500 km from the lava-flooded 80-km-diameter crater Archimedes. Out-of- focus object in lower right corner is part of Command Service Module. Sun is to right. Apollo 15 mapping-camera photograph 1540. Geometric Interpretation of Lunar Craters By RICHARD J. PIKE APOLLO 15-17 ORBITAL INVESTIGATIONS GEOLOGICAL SURVEY PROFESSIONAL PAPER 1046-C Prepared on behalf of the National Aeronautics and Space Administration UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1980 UNITED STATES DEPARTMENT OF THE INTERIOR CECIL D. ANDRUS, Secretary GEOLOGICAL SURVEY H. William Menard, Director Library of Congress Cataloging in Publication Data Pike, Richard J. Geometric interpretation of lunar craters. (Apollo 15-17 orbital investigation) (Geological Survey professional paper : 1046-C) Bibliography: p. C60-C65. Supt.ofDocs.no.: I 19.16:1046-C 1. Lunar craters-Data processing. 2. Lunar craters- Statistical methods. I. Title. II. Series. III. Series: United States. Geological Survey. Professional paper ; 1046-C. QB591.P73 559.9*1 79-607927 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 CONTENTS Abstract ________________________________ Cl Size dependence in the shape of fresh impact craters—Continued Introduction ________________________________ 1 Ratio-level variations—Continued Acknowledgments ________________________ 3 Rim height__________________________ C33 The new data __________________________________ 3 Width of rim flank _____________________ 35 Crater geometry and crater genesis ____________________ 5 Rim-wall slope ______________________ 37 Computer classification of analogs ______________ 5 Floor diameter ____ __________________ 38 Experimental methods __________________________ 6 Rim-crest circularity ______________________ 38 The crater sample _______________________ 7 Evenness of rim crest _________________ 40 Interpretation of principal components __________ 9 Nonratio variations-___________________ 41 Classification by principal components __________ 11 Index data ___________________________ 43 Classification by cluster analysis __________ 14 Frequency data____________________ 44 The caldera analogy _______________________ 17 Discussion ______________________________ 45 Predicting crater genesis ___________________ 18 Depth versus rim-wall width ___________________ 46 The Linne controversy resolved _________________ 18 Some alternative explanations_______________ 49 Secondary-impact craters _______________________ 22 Minor differences in crater shape _________________ 53 Lunar central volcanoes.-____________________ 23 Mare-terra contrasts ___________-_________ 54 Cratered domes ________________________ 23 Far side-near side contrasts ____________________ 54 Cratered cones __________________________ 25 Azimuth-dependent differences ________________ 56 Dark-halo craters________________________________ 26 Summary and conclusions.______________________ 58 Smooth-rimmed craters ___________________ 26 References cited ________________________________ 60 Summit craters on central peaks ________________ 29 Supplemental information-_____________________ 66 Size dependence in the shape of fresh impact craters ________ 30 Measuring crater dimensions __________________ 66 Ratio-level variations._________________ 31 Tabulation of the new data __________________ 66 Depth ____________________________ 32 ILLUSTRATIONS FRONTISPIECE Oblique view across Mare Imbrium of craters and other features on the Moon. Page PLATE 1. Dendrogram displaying cluster classification of 418 craters __— ———— ______ —————— _____ — ___ In pocket FIGURE 1. Cross section of crater Proclus showing six topographic dimensions _______— — — —— — -___ ———— --— C4 2. Graph showing correlations of crater types with the first principal component _____ — — —— ————— — — ———— 11 3. Diagram showing scores of crater types on the first three principal components — —— -___ ——— ——— —————— 13 4. Diagram showing cross sections of two crater classes in plate 1 ___________ — ___ —— ______ — _____—————— 15 5. Photograph of the crater Linne __________________________—__ —— ______ —— —— __ —— —— _______ 19 6. Diagrams showing linear topographic profiles and rim-crest outline of Linne —— ——— —— ______ —— _ — ——— __ 20 7-14. Photographs showing: 7. Detail of crater Linne _________________________—__ —— ——— __ —— ___- ——— -- —— --- 21 8. Secondary craters from crater Aristarchus _________-___ ——— ____________-__---_----_ ——— — 22 9. Catena Davy ________________________________________________——————— 23 10. Cratered domes in northern Mare Tranquillitatis _____________ ———— _______ ——— ___ ——— __———— 24 11. Cratered dome near crater Milichius___________________ —— —— _________ ——— __ —— ______ ——— ___ 24 12. Cratered cone in Mare Nubium ___________________-_— — —— — ——— ——— ———— - — - 25 13. Dark-halo craters on floor of crater Alphonsus _________ —— ________ ———— __ ——— ____ —— ___ 26 14. The crater Lassell ____________________________-__-___-——————— ———— --- 27 15. Graphs showing frequency distribution of rim-crest circularity, height/depth ratio, and width/diameter ratio -___ 28 16. Photograph of central peaks of crater Theophilus ________________ ___ ______ _______________ 29 17. Photograph of central peaks of crater Levi-Civita ______________ ———— ________ —— ————— __ —— ——— _——— 29 18. Photograph of central peaks of crater Tsiolkovskiy _________________ —— ———— ——— —— _____ — _____ 30 19-26. Graphs showing: 19. Relation between depth and diameter for 212 lunar craters ____________________________ 33 20. Relation between rim height and diameter for 162 lunar craters ____________________________________ 34 VI CONTENTS FIGURES 19-26. Graphs showing—Continued Page 21. Relation between flank width and diameter for 162 lunar craters ________--- —— ————— --——— C36 22. Relation between slope of rim wall and diameter for 107 lunar craters __—____ — _ ———————— -_-— 37 23. Relation between floor diameter and rim-crest diameter for 91 lunar craters ———— ————— ——— --—— 39 24. Relation between rim-crest circularity and diameter for 201 lunar craters _______———————- — — 40 25. Relation between rim-crest relief and diameter for 46 lunar craters _ _______- ———————— - —— - 41 26. Relation between coefficient of variation of rim-crest elevation and diameter for 35 lunar craters———— 42 27. Photomosaic showing the crater Aristarchus _____________---________ ——— — ———— —————— - —— - 43 28. Graph showing relation between morphology index and rim diameter for 152 lunar craters _ — ——————— — — 45 29. Graph showing transition from simple to complex morphologies in lunar craters _______ ——————— __———— 46 30. Graph showing relation between crater depth and rim-wall width for 107 lunar craters __—__ —— —————— — 47 31. Photographs of craters Diophantus and Delisle ________________________--————— — ————— --- 49 32. Graph showing relation between peak height and rim diameter for 29 lunar craters ————— ——— ——————— __ 51 33. Graph showing relation between depth and diameter for 21 terrestrial impact craters ——————— ————— ——— 52 34. Photograph of crater Humboldt ___________________________________ ——— _ —————— ____— 53 35. Graph showing relation between depth and diameter for 950 lunar craters _____________———— ——— ___— 55 36. Graph showing relation between depth and diameter for 58 far-side and 78 near-side craters __ ——— ——— ___— 56 37. Graph showing relation between rim height and diameter for 54 far-side and 78 near-side craters ——— —— _—— 57 TABLES Page TABLE 1. Measurements for a sampling of fresh lunar craters______________-_________________ —— _————— C5 2. Statistical summary of untransformed variables for 23 crater types ______— ————————— — ————— ___— 8 3. Matrix of similarity coefficients for principal-components analysis ____——————————————— —— — _____— 9 4. Principal-components results for seven variables and 418 craters ____________________--——— 9 5. Composition of clusters in plate 1 by crater type __________________________ — — _-_____---- 15 6. Numerical data for geometric model of fresh lunar craters__________-________— — — - —————— — 32 7. Morphologic index numbers of selected lunar craters _____________-____-_____—-- — ——————— 44 8. Qualitative deviations from mean rim-crest elevation ____________________________________ 58 9. Dimensions of 623 lunar craters _________________________________________________ 68 10. Dimensions of 59 terrestrial craters _______________________________________-—_____ 77 APOLLO 15-17 ORBITAL INVESTIGATIONS GEOMETRIC INTERPRETATION OF LUNAR CRATERS By RICHARD J. PIKE ABSTRACT ematically where practicable. These relations constitute a shape model that constrains interpretations of fresh craters on the Moon. Geometric properties of the Moon's craters between about 400 m The size-dependent changes reflect the occurrence of central peaks, and about 300 km across have been examined at a high and hitherto rim-wall terraces, and a flat floor within craters over 10 to 20 km unattainable level of accuracy using new topographic measurements across. Interpretation of these features remains speculative. The made on contour maps compiled