- Email: [email protected]
On the distribution of large lunar craters
ICABUS 9, 197-211 (1968)
On the Distribution of Large Lunar Craters LUCIANO B. RONCA Boezng Scientific Research Laboratories, Seattle, Washington Communicatcd by Zden~!k Kopal Received December 271 1967 The raze distribution and location of all the craters of Classes I, 2, and 3 larger than 25 k m in diameter on the front face of the M o o n were studied. The diameter distribution of the craters follows approximately the distribution that would be expected from meteoritlc impact. Lateral variations m cratering over the lunar surface were determined by divldlng the lunar disk into 172 equi-areal zones, each of approximately 76.9 X I0ffik m 2. The number of craters, their average diameter, and the s u m of their diameters were measured in each zone. W h e n these parameters are contoured on the lunar surface, they outline not only the rearm but also areas on the terrac otherwme indistinguishable. O n the terrae the amount of cratering is not random; highly cratered areas occur clustered together with a correlation coefficient of 0.776. Lateral variations in size distribution were studied by di~qding the front face of the M o o n into 9 zones, each of which has at least 60 large craters and follows approximately the physiography. The main variations are due to the maria and terrae distribution; however, differences in the terrae are also indicated. It is concluded that meteoritic impact can not offer all the answers to the origin of lunar craters. Either the craters are predominantly volcanic, or some endogenic control on thp size of an impact crater exists. I NTRODUCTION
example, Baldwin (1963), in explaining lunar features in terms of the impact An un(ler.-t:~n(ting of lunar geology is not only important per se, but it i~, hkcly hypothesis. That the question is still open, that it will increase our knowledge of the however, can be surmised by reading the early history of Earth itself. On the Moon not less outstanding, but perhaps less we probably see the results of early known, work of proponents of the volcanic planetary processes that have subsequently origin, as for example, McCall (1965) and Fielder (1965b). More recently a hybrid been completely obhtcrated on the Earth but which are perhaps still reflected in the impact-volcanic hypothesis was also tectonic framework of our planet. Hypoth- presented (Ronca, 1966a,b). Other papers eses on this subject ]lave been made, for on the origin of lunar craters are listed example, by Gilvarry (1962) and Salisbury in the Reference section. The purpose of the present study is to and Ronca [1966). As important as the determine variations in the surface Moon is for theoretical geology, it is a sad fact that the origin of the most obvious distribution of the lunar craters. No a featurcs on the lunar surface, the craters, is priori choice on the process of formation was made, and at the end, the choice is still disputed. It is common for people who have not left to the reader. Only craters larger than 25 km in followed the literature to be surprised to diameter were counted, in order to have the hear that the impact versus volcanism confidence that essentially none was left controversy is not yet settled. This may be due to the outstanding work made by some out and to avoid the problem of secondary proponents of meteoritic impact, as for craters, which can not exceed 5 km in 197
198
L U C I A N 0 B. RONCA
°\
1000
Cumulahve
~a
1o0
U
u
I
Curve
"~,~ I00
Histogram
7
~ \ Theorehcal
E :~ 10 z
Io
50
mo tsO 200 Diameter of Craters m Km
]O0 D~ameter Io0o
250
3o0
Fro. 1. The distribution of the large lunar craters m shown as a semdogar~thmic histogram and as logarithmic cumulative curve. In the latter case the experimental values are compared with the distribution that would be expected from meteoritic ,mpact. diameter (Salisbury et al., 1965). If the craters are completely or partially endogenous, the large craters are better indicators of strong tectonic activity than the smaller craters. The catalog of lunar craters published by the University of Arizona (Arthur et al., 1963, 1964, 1965, 1966) were used. This invaluable work gives the designation, diameter, position, central peak information, and degree of erosion of all discernible craters in the four quadrants of the visible face of the Moon. The craters are classified on the basis of their degree of erosion on a scale of 1 to 5. Very sharp and fresh-looking craters are classed as 1; craters with blurred rims as 2; craters with more extensively broken rims as 3. Craters usually described as ruins are classed as 4, and Class 5 covers ghost craters and craters so fragmentary that they are not easily recognized. This classification is not based on a measurable parameter but is based on personal judgment; as such, complete accuracy is not to be expected. However, considering the careful work that went into the preparation of the catalog, one is confident that the classification is as accurate as is humanly possible, In the present work only craters of
Classes 1, 2, and 3 were used, omitting ruins and ghost craters. In this way problems of omission and recognition were avoided. However, one must realize that the conclusions reached are not applicable to the early part of the geological history of the lunar surface, and care must be used in the interpretations of flooded areas. For brevity, in this work craters of Classes 1, 2, and 3 with diameters larger than 25 km will be referred to simply as large craters. EXPERIMENTAL RESULTS Figure 1 shows the size distribution of the 908 large craters present in the area investigated. The distribution is given in the familiar form of a histogram with 10km intervals beginning with a diameter of 25 km. Previous workers have generally preferred to give the distribution in the form of a cumulative curve, each point of which represents the number of craters which are larger than the corresponding value on the abscissa. For comparison, the cumulative curve is also included in Fig. 1. It is generally accepted (Hartmann, 1964) that the cumulative curve is a straight line on a log-log chart; that is, d(Iog F) d(lol~D) = - S ,
LARGE
LUNAR
where F is the normalized number of crater increments, D is the diameter, and S is a constant. Hartmann (1964) shows that 8 = 2.1 and that this function remains valid down to craters of 8 km in diameter. He also shows that this curve closely approximates the predicted diameter distribution of craters, were they caused by the presently known mass distribution of meteoroids. Figure 1 shows that the distribution of large craters follows approximately the predicted curve. The apparent deficiency of craters of diameter greater than 100 km is not considered significant because of the small number of craters involved and the omission of Class 4 and 5 craters. It is also possible to calculate the average of the measured craters and then to compare it with the average as computed from a histogram built from the theoretical cumulative curve. The two valucs are approximately equal to 46.5 kin. In order to measure lateral variations in crater characteristics the surface of the Moon was divided into a grid of equi-areal surfaces. This was achieved by superimposing a linear grid on an equi-areal projection of the latitude-longitude system,
I
I 2 " i Columns Rows
3 4 ' I' '
199
CRATERS
as indicated in Fig. 2. Each of the large craters was assigned to a certain column and row (for brevity, to a block) according to the latitude and longitude of the center of the crater as given in the University of Arizona catalog. The area of each block is approximately 76.9 X 10a km 2. Table I reports the diameters of the craters belonging to each block. Three parameters appear important in the description of each block. The first is /), the average diameter of the large craters; the second is ~:D, the sum of the diameters of the large craters in the block; and the third is n, the number of large craters occurring in the block. Figure 3 shows the relationship between n a n d / ) . No simple relationship exists, but it is evident that blocks with a high n tend to have a /) between 40 and 50 kin. Figure 4 shows the distribution o f / ) . A peak is present between 45 and 55 kin, and the average is 46.5 kin. As was pointed out before, this is the same as the predicted average diameter of craters if all were produced by the meteoric impact. Figure 4 can be interpreted as indicating that a certain cratering flux is most common on
5 6 7 8 9 I0 'I' 'N ] J * ' ' ~
II 12 13 14 15 ' I' ;' ']' r
1 2 3 4 5 6 7 8
.~I/V
i I i i lMII/[~2tA I I I I II iliii]I I I, I i I J i J J li sl l Jl iIj
.I llllllll!l ill
9 10 11 12
-_~1/1/~ ~ ~ J l
! i Jl ILII/~ 11 I /1LLLV ~ V
13 14
15 s
FIo. 2. Simplified superposition of a hnear grid over an equi-areal projection. Each block of the grid has the same area and is identified by a column aud a row number.
200
LUCIANO B. RONCA TABLE I
R
C
Dmmeter of C'~raters
1 1
8 9
30 31 53 01
1
10
63 09
1 2 2 2 2
11 8 9 10 II
.54 31 ~ 36 28
'2
12
39 91
3 3 3
8 9 10
56 52 87 26 44 25
3
11
87 41
3 3 4 4 4 4 4
12 13 8 9 10 II 12
36 80 176 87 55 34 none 29 65 39 44 33 29
4 4 5 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7
13 14 8 9 10 11 12 13 ]4 8 9 l0 II 12 13 14 8 9 l0 ll 12 13 14
32.83 28 l l none none 30 70 25 74 64 03 46 22 32 78 38 60 26 91 26 32 28 24 55 95 0_,8 04 29 79 25 95 ;~t 76 30 05 '29 44 ;31 34 51 81 45 66
n
ZD
/)
5
268
54
7
398
57
9 4 3 '2 4
333 219 106 94 125
37 55 35 47 31
6
273
46
7 '2 3
312 94 184
45 47 61
6
263
44
6 5 5 4 (1 "2 "2
290 268 313 226 0 56 90
48 54 63 56 ind 28 45
II 4 4 il (1 3 5 3 1 4 1 1 3 3 1 '2 5 1 5 "2 l I "2
559 2"20 207 0 0 114 151 127 46 147 :39 27 98 100 56 61 L~26 26 190 56 29 31 108
51 55 52 md ind 38 30 42 46 37 39 27 33 33 56 30 45 26 38 28 29 31 54
6
235
39
I QUADRANT
27 67 66 99 97
26 89 57 31 25 47 37 39 32 32 30 26 43 37 67 32 67 42 26 29 29 39
80 50 34 60 05 85 38 07 69 43 16 75 82 11 14 54 04 24 14 62 37 16
26 50 30 126 47 28 6:3
92 34 94 55 38 58 37
85 26 87 10 73 63 98
55 83 36 ~)
62 12 32 71
25 38 41 49 57 86
26 02 26 63
26 77 30 28
28 71 125 II
26 33
29 01 65 18
67 60
40 05
30 07 43 I I
39 56
36 12
39 84
56 28
38 52
124 12 29 25 30 64
36 94 ~) 01 1{~ 53
40 12 :37 42
77 86 77 07 28 97 29
26 11 3906 28 12 74 22 68 14
85 48 56 ~2
43 16 42 83
50 96 39 56 36 53
32 61 34 64 26 14
25 45
26 47
5~ 59
30 80
43 19 39 89
28 38 32 19
32 61 45 68
36 88
74 32
39 58
4~ 15
31) 89
30 26
51 12
3~ 45
46 63
46 04 26 04
56 35 26 12 27 12
84 18 47 .0/'2
2564
t~
>
~-~=
~ -~_~-~
~--~__~
plL
L"
202
R
C
8 8 8 9 9 9 9 9 9 9 10 10 10 10 10
3 2 1 7 6 5 4 3 2 1 7 6 5 4 3
none 36.52 33 86 2406 none 43 89 33.02 44.79 31.29 24.54 54.72 104.76 58.94 none 34 21
10
2
41 70
10 11
1 7
49 21 39.82
11
6
37 72
11 11 11 11 11 12
5 4 3 2 1 7
59.72 44 64 32 40 29 37 43 91 63 27
12
6
26 65
12 12 12 12 13
5 4 3 2 7
27.01 29 81 5324 27 55 26.18
13
6
105 33
13
5
29 36
13 13
4 3
34 94 25 62
14
7
47 80
14
6
111.31
LUCIANO
B. R O N C A
TABLE I
(Cordznued)
Dmmeter of Craters
28 80 151 58 118.54
46 50 29.08 39 86
27 67 45 73 43.96 29 84 26 66 42 48 46 69
110 42
96 80
34.73
49.02 46.20 26.17 26.16 48.03
2583
24.66
91 16 47 76
38.20 41 39 42 78 25 85
31.72
81.54
32 10
131.58
33 22 29 10 29 42 39 44 29 01 40 46 51 31 31 29 35 96 55 57 33 91 29.15 48 79 32.09 30 59 30 21 36 21 25 38 46 90 50 92 31 36 29 15 26 09 47 36 35 56 25.24 36 38 38 03 38 47 93 58 31 48 36 64 27 85 30 71
45 07 31 20 36 52
33 34
39 51
37 63
66 45
41 56 39 89
44.06
26.25 87 01
34 19
3968
35 79 62.35 84 67 2788 33 93 145.26 37 60 31.79 33 84 28 75 26.78 28 44 47 50 40 23 48.74 124 95 37.18 45.82 91 06
52 04 46 01
162.64 57 85
31.77 29.11 30 80 226 74 27 64 68 73 37 82 225 30 2944 110 36 28 45 37 16 67 11 113 87 39 26
107 26
11442 35 21 34 78
48 81 37 30 30 30
31 13 76.19 29.98
35.39 31.60
45 90 25 59
30 05 69 54
33 51 26 47 51 64
n
ZD
0 3 3 5 0 1 3 2 5 3 3 4 3 0
0 112 215 314 0 44 171 91 175 101 108 217 154 0
ind 37 72 63 ind 44 57 45 35 34 36 54 51 ind
7
325
46
7 1
403 49
58 49
7
251
36
6 3 2 5 2 3
247 115 85 245 61 116
41 38 43 49 30 39
11
675
61
8 4 5 4 5
455 126 352 151 177
57 32 70 38 35
8
494
62
12
552
46
8 5
418 304
52 61
5
260
52
14
686
49
9
408
45
27.27 28 51 38 99 84 44 29 24
LARGE LUNAR CRATEI~ I (Cont/.u~/)
TABLE
R
C
14
5
71 37
14
4
29 17
203
Dmmeter of Craters 64 38 29 30
21 26 91 97
25 34 26 11
27.62 65 09
8540
61 98
-
ZD
10 4
677 208
68 52
3 3 1
96 119 34
32 40 34
6 0 4
229 0 239
38 ind 60
17
729
43
7
329
47
7 4 3
311 211 91
44 53 30
6 5
295 341
49 68
II
529
48
11
580
53
14 5 5
559 215 179
40 43 36
6 5 2
253 329 156
42 66 78
15
808
54
15 5
750 198
50 40
6
278
46
25.57 303 46
IV Q U A D R A N T 8 8 8 8
8 9 10 11
30 56 28 27 34 28 3042
8 8 8
12 13 14
none 34.80 35.11
9
8
13566
9
9
33 70
9 9 9
10 II 12
30 O0 28 56 60 27
9 9
13 14
41 77 42 74
I0
8
49 59
10
9
41 44
10 10 10
10 11 12
29 62 26.77 36 87
10 10 11
13 14 8
11
9
33 34 127.18 13609 60 70 25 53 87 74
11 11
10 11
53.41 26.44
11
12
25.46
36 03 37 45
29 13 53 01
29 67 70 79
39 13
43 04 50 23 29 70 37 47 26 87 44 29 31 18 61 95 31 67 100 O0 32 97 41 19 46 58 147 06 30 50 47 94 55 92 27 24 63 01 66 31 42 05 46 13 59 29 35 55 42 60 32 36 44 08 57 08 176 60 28 96 36 27 38 95 28 61 46 34 40 72 53.80 81 02 43 05 52 25 52.65 74.48
29 39 29 29 42 62 107.33 29 64 28 23 28 70 49 29 39 86 27 83 29 27 38 50 42 49 30 93 36 70 34 29 53 25
27 83
131 28 33 31 38 26
98 64 78 95 78 89
48 46
30 83
25 37 25 118 34
83 74 41 91 10
45 73
53 15 30 44
78 23
84 39 77 68 39 21
25 99 27 78 33 60
06 29 64 53 03 2O 76 13 81 12
36 94 79 85
67 70 47 92
52 98 26 25 30 94
47 73 30 54 38 52
27 13 64 45 43 75
26 16 25 05 33 86
89 29 30 71 36 92
47 07
31 62
4629
69 72 27 32 25 17 67 98 31 60 52 28 34.95 43 09 70 05
53 12 69.53 27 45 29.69 36 21 35 25
51 40 136 57 26 23 40 92 27.71 8423
26.21 27.90
32.35 49 12
50.30
26.05
29 01
204
LUCIANO B. RONCA. TABLE
R
C
11
13
41 04
11 12
14 8
201 33 31 20
12
9
114 21
12
10
29 88
12
11
31 48
12
12
42.22
12
13
29 84
13
~
29 17
13
9
27 48
13
10
42 83
13
11
66 31
13
12
35 56
I
(Continued)
D m m e t e r of C r a t e r s
82 67 56 21 30 94 43 89 58 07 40 55 38 22 37 79 29 64 42 85 35 79 82 27 27 15 42 05 30 14 30 52 25 03 189 48 78.08 46 22 27 45 42 98 56 85 44 48 30 04 42 83 31 15 26 92 37 21 50 98 27 53 26 58 29 53 70 78 40 79 25 38 41 63 26 59 28 59 33 96 36 O1 41 O0 27 88 51 15 26 73 95 55 43 18 25.93 42.25 32 43 44 41 33 65 44 90
125.15 28 16 78 88 100.95 57 05 47 42 31 50 26 75 69 46 29 24 42 46 49 57 25 93
25 29 38 62 41 49
26 78 38 90 32 33
30 44 125 32 35 58
27 25 34 35 31 10
87 64 28 11 58 26
30 35 27 39 27 79
62 82 35.53 25 32 30 02 71 92 ,r~ 78 43 77 39 75
37 63 35 53 40 88 36 31 32 30
31 81 80 71
27 36 40 74 36 08 41 89 34 45 25.15 35.02 31 84 27 25 32 40 53 29
31 25 61 34 53 27 34 29 39 42 34
39 36 29 68 41 46 28 25 28 29 42
46 83 29 05 51 76 07 45 61 90 65
75 47 50 09 60 75 48 93 76.22 29.53 52.28 38 34 48 36 55 92
3"2 89 76 36 46 98
29 94 89 18 33 13
38 67 48 09 28 61
25.66 31 76 41 58
25 Ol 25 26
35 18 62.49
66 71 32 41 42 28 75 34 40 43 58 26
62 72 59 73 86 77 59 36 62 66 07 07
/~
7
413
59
15 3
724 289
48 96
42 52 75 75 :59 69 36
16
715
45
14
663
47
14
734
52
15
698
47
16
666
42
IX
718
40
25
(,W),-5
39
"£2
736
33
15
802
53
15
622
41
66 17 29 74 27 06
83 16 33 17 42 61 24
82 34 33.89 28 96
ZD
n
70 62 08 94 81 51 94 70 18 48 17
27 85 74 72 30 73
205
LARGE LUNAR CRATERS
TABLE I (Continued) R
C
Diameter of Craters
14
8
~).55
14
9
33 93
14
10
71 65
14
11
32 10
61.72 94 69 53 10 56 25 60 30 28 66 35 49 98 14 25 53 94 94 36 10 30 92 30 89 38 97 34 26 43 66 47 47
42 36 45 36 37 24 35 25 29
60 85 02 76 21 61 91 85 32
141 54 42 43 84 36 28 97 131
29 51 53 59 30 82 30 28 26.92 29 84 26 42
the lunar surface, but areas exist where the flux has been weaker and areas where it has been stronger. These areas are the blocks with /) less than 45 k m and more than 55 kin, respectively. Figure 5 shows the distribution of ~:D, the sum of the diameters of the large craters in a block. This quantity m a y be thought of as the amount of cratering which has occurred in a certain area. The number of large craters per block gives an incomplete picture, as very large craters have the same weight as the others• The sum of the areas of all the large craters in a block will give too strong an importance to the very large craters. ~D is a more complete index on the amount of cratering which has affected an area as it includes
03 30 69 45 98 73 21 30 (~5
38 50 70 30 28 33 42 42 97
27 37 38 10 49 86 10 36 94
43 59 45 71 52 47 64 29 26 34 32.52 56 Ig
34 37 33 30 91 57
40 42 48 82 01 15
n
~D
/~
13
650
50
21
989
47
14
818
58
13
531
41
16
66~
42
both the number and size of the craters present. Figure 5 shows t h a t most commonly the visible surface of the Moon has a low ~:D; the average, however, is approximately 265 k m This is mainly due to the higher ~:D on the terrae. Figure 6 shows the relationship between n and ~:D. As is to be expected, in general there is a linear relationship between the two. However, there are areas of relatively high n and areas of relatively high ~:D. Figure 7 shows the distribution of n, the number of large craters in a block. T h e distribution is perhaps bimodal, and the most common value is thrce or four large craters per block (excluding blocks with no craters). The average is about six craters per block.
o
._c 25. *4
a tJ
"6
15
• -
•..•..-
10-
E ....~
. . . . .'
: .:"..7
o {s 3'0 35 ,b
:
.._"
,5
"
:
"''..
~'o 5'5 ~o a's ;;o 75 8o 8'5 ~
9'5 ,oo k,.
of Block
FIG• 3• T h e r e l a t i o n s h i p b e t w e e n n, t h e n u m b e r of large c r a t e r s in a block, a n d / ) , t h e s,verage d i a m e t e r of the large craters in t h e block•
206
LUCIANO B. RONCA
D~
52
28-
48
"~24 -
44
.c 20 -
40"
36-
E
U 12
32-
8 28E,
24-
Z
20-
0
Z 12
0'
,6o ~o 3~o ,6o ~o ~
76o ~o ~o ~o
'
Fla. 6. The relationship between n, the number of large craters in a block, and ZD, t h e s u m of the diameters of the large craters in the block. ,o
2'0
. . • o. . ~o
6o
. . ,oo . 7o. . . o . 90
,lo ,20
5 Fro. 4. T h e distribution of /), the average dia m e t e r of large craters in a block.
The next step is to examine the relationship between the above distributions and the location on the lunar surface. The values of n, 1), and ZD for each block of the grid have been marked on a copy of an L E M - 1 A lunar mosaic and then contoured. F~gure 8 shows the contour map of 1). As indlcatcd before, if the cratering flux has been constant everywhere, a value of /) of approximately 46 km should be found everywhere. The heavy dashed line limits areas Which contain fewer than three craters per block. With so few craters the average diameter was considered to characterize the blocks very poorly. The dashed lines outline clearly the maria, shown as shaded regions. Also it is evident that "no-data" areas are inside the 40-kin
contour. Zones of higher than average b are present, indicated by the 50 and 60 km closed contours. The behavior of the 40-kin contour is interesting, as it "noses" considerably at approximately longitude 40°E from latitude 10°S to 40°S. Figure 9 shows the contour map of ~D, which can be understood as a representation of the amount of "cratering" occurring in a given area. As in the case o f / ) , the maria are approximately outlined by the lowest contour. The same prominent "nosing" as in /) is also present, at approximately 40°E ranging from 10°S to 40°S. The most striking feature of this contour map is the similarity of the shapes of the contours. Not only the 100-kin contour outlines the maria approximately, but also 48. 4440-
A I
3632.
50 ¸
~ 24. "5 2o
40.
.1~ 16.
E
3o 2o 7
$0
4
o ~'5 ,25 225 325 425 525 625 725 825 ~ 5 1025 ~D
Fro. 5. T h e distribution of ZD, the s u m of t h e diameters of the large craters in ~ block.
6
8
I0
12 14
16 18 20 22 24 2 6
Number of Large Craters in
28
Block
Fzo. 7. T h e distribution of n, t h e n u m b e r o f large craters in a block. Blocks with no large c r a t e r s a r e excluded.
LARGE L U N A R
207
CRATERS
of the zones were chosen with two arbit r a r y criteria in mind. First, they had to follow, at least roughly, morphological provinces. Second, they had to have more than 60 large craters. Table II lists the number of craters respectively larger than 50 kin, 40 km, 30 km, and 25 km for each zone. When these values are plotted on log-log paper, they do not form a straight line. This makes it impossible to characterize each curve simply by its slope. A numerical value, index of each curve, can be obtained as follows:
the other contours appear to follow, at a larger distance, the mare shores. The "nosing" is repeated by all the contours. If we think in terms of a ~D surface, the map is not a random distribution of highs and lows, but it shows a high near the South Pole, from which it descends toward the maria. The "nosing" represents a valley with ridges on both sides of it. The maria occupy the lowest portions of the ~D surface. The contour map of n is not included, as it is very similar to the ~:D map. Lateral variations in cratering characteristics over the surface would be best shown from the diameter distribution curve for each block of the grid. This is impossible, however, due to the relatively small number of craters in each block. To obtain at least a general idea, the front face of the Moon was divided into nine zones as shown in Fig. 10. The size and position
R = n~.6 rt~
n3o n4o where n~5, nso, n,o, n~o are, respectively, the numbers of craters larger than 25, 30, 40, and 50 kin. This value R is indicated in Table II and in Fig. 10. The zones near the South Pole have a large value of R, N
I
~0
W-
-E io"
Fzo. 8. Contour map of Z), the average diameter of the large craters in a block. Dashed linee contour areas where there are less than three large craters per block. For clarity, more closely spacod contours a r e omitted, as they follow the trends.
2O8
LUCIANO B. RONCA N I
10 °
W--
--E I0 t
1"
I
S FIG. 9. Contour map of ZD, the sum of the diameters of the large craters in a block. For clarity, more closely spaced contours are omitted, as they follow the trends. which d e c r e a s e s t o w a r d t h e e q u a t o r i a l b e l t a n d t h e n i n c r e a s e s a g a i n in the n o r t h e r n h e m i s p h e r e . On t h e e q u a t o r i a l b e l t t h e cent e r h a s the h i g h e s t v a l u e . I f a c o n t o u r m a p is m a d e of R, t h e r e s u l t i n g s u r f a c e is a p proximately saddle-shapcd. I NTERPRETATIONS
I t is i m p o r t a n t to realize t h a t n, ~ D , a n d R are n o t s t a t i s t i c a l in n a t u r e . T h e y r e p r e -
s e n t t h e b e h a v i o r of a l l t h e large c r a t e r s , even if some b l o c k s h a v e few or no large craters. T h e v a l u e s a r e a n a b s o l u t e f a c t a n d n o t a s t a t i s t i c a l inference. O n l y t h e p a r a m e t e r /), t h e a v e r a g e d i a m e t e r of t h e large c r a t e r s , is s t a t i s t i c a l in n a t u r e . F o r this r e a s o n t h e b l o c k s w i t h fewer t h a n t h r e e large c r a t e r s h a v e been excluded. E v e n so, it is p r o b a b l e t h a t /) is m e a n i n g ful o n l y on t h e t e r r a e .
TABLE II NUMBER
OF C R A T E R S L A R G E R THAN A C E R T A I N D I A M E T E R
IN E A C H Z O N E
N u m b e r of craters In zone---
Larger than
A
B
C
D
E
F
G
H
I
50km 40km 30km 25 km
26 42 75 105
44 60 95 115
14 36 57 76
18 33 57 77
18 34 60 80
18 26 48 67
27 43 73 107
22 36 53 70
21 35 54 69
0 867
0 888
0 518
0.737
0 706
0 967
0 921
0 807
0 767
R
LARGE LUNAR
The problem becomes statistical when the question is raised as to whether a random b o m b a r d m e n t of meteorites on the terrae could have produced the contours. To obtain a general idea of w h a t t y p e of contour is to be expected from a random distribution, the craters present in the terrae were redistributed at random over the area. This was done by using a table of random numbers to define the rows and columns of the blocks where the craters were to bc located. The contours of ZD and /) so obtained are characterized by contorted "islands" scattered over the area. The contour map o f / ) , shown in Fig. 8, is smoother than the one artificially produced, but not sufficiently to w a r r a n t doubt t h a t random meteoritic impact and marc flooding are the responsible processes. The contour m a p of ZD, however, is definitely different from anything produced by a random process. The contours are mu-
CRATERS
209
tually influenced and are all affected by the position of the maria, as previously discussed. Quantitatively, the lack of randomness can be shown in the following way. I f the blocks are random, blocks with a high ~:D would occur near blocks of low ~ D as commonly as near blocks of high ~:D. For every block in the terrac which is not bordering with a mare and is not on the edge of the visible disk, the averagc ~D of the surrounding blocks was measured. Figure 11 shows the ~:D of these blocks plotted against the average ZD of the surrounding. A relationship clearly exists with a correlation coefficient of 0.776. The slope of the least-square straight line is 1.4. In the case of a truly random distribution the points are scattered around a vertical line, corresponding to the average value of ZD. The correlation coefficient of the artificially randomly located cratcr~ was 0.04. The
N Zone B
~ ZoneA
R=089
~
R=087
:)7
%V
-0~b / ~
ZoneD ~ R=074
ZoneC R= 0.52
ZoneE
E
R=071
/
/ 0 90 R=077 Zone F R= 097
FIG. 10. The division of the lunar disk into nine zones, arbitrarily selected so that each zone has more than 60 large craters and follows approximately the physiography. R is the distribution index of the large craters in each zone, as defined in the text. Contour lines refer to R and are purely indicative.
210
LUCtANO B. RONCA Km
800
0
°
I00
200
300
400
500
600
°
700 SO0 Km
Average T D of Surrounding Fro. 11. The ordinate represent ~ D of a block in the terrae, and the abscissa is the average ~ D of the blocks surrounding the block of the ordinate. In a random distribution the points are symmetrically scattered around the average, indicated by the vertical line. In reality the points are symmetric around the oblique line. The correlation coefficient is 0.776.
least-square straight hne for such a scatter has very little significance. Figure l l clearly shows t h a t highly cratered areas tend to cluster together and t h a t the amount of cratering in one block is not independent from the amount of cratering in the neighboring blocks. A possible explanation of the behavior of ZD could be t h a t areas of high XD are older than areas of low ZD. I f this is true, areas of high ZD should show a higher degree of erosion than areas of low ~.D. To check this possibility, the average class of the craters in each block was measured, and the values contoured. No relationship with ZD exists (at least when Class 4 and 5 craters are excluded), and the contours are of the contorted-island type, typical of a random process. Also if large areas of progressively younger ages exist, the present terrae should be reworked and obliterated m a r i a of an older generation than the present ones. Fielder (1963), from considerations on crater density, reached the con-
clusion t h a t older maria presently obliterated can not exist. The properties of ~D point very strongly toward an endogenous origin, or a t least an endogenous control, of the large lunar craters. This is also indicated b y Fielder's calculations (1965a,b) which show t h a t on the terrae craters smaller than 40 k m in diameter are nonrandomly distributed at the 2% level of significance. A great deal of work m u s t be done before a definite picture on the distribution of lunar craters is available. Craters of smaller size must be included, and the new maps of the far side of the Moon m u s t be examined. Effects of variations in the size and number of the blocks m u s t be studied. T h e r m a l d a t a of the craters m a y give a new p a r a m e t e r to define different types of craters. Relationships with the shape of the Moon are under study. A computer program to handle the d a t a is under development. At the moment, the only conclusion t h a t can be reached is t h a t meteoritic impact can not offer all the answers to the origin of lunar craters. Either the craters are predominantly volcanic, or some endogenie control on the size of an impact crater exists. ACKNOWLEDGMENTS Help in the calculations from R. R. Green and critical comments from D. F. Winter, J. C. Noyes, J. M. Saari, and R. W. Shorthill are gratefully acknowledged.
REFERENCES
ARTHUR, D. W. G., AONIEP~¢¥, A. P, HORVA~, R. A., WOOD, C. A., AND CtIAPM^X. C. R. (1963). The system of lunar craters, Quadrant I. Commun. Lunar Planet. Lab., Univ. of Arizana 2, text pp. 71-78, catalog pp. 1--60. ARTHIJR, D. W. G., AGNmRAY, A. P., HOaV~VH, R. A., WOOD, C. A., AND CHAPMAN, C. R. (1964). The system of lunar craters, Quadrant II. Cornmun. Lunar Planet. Lab. Univ. o/ Arizona 3, text pp. 1-2, catalog pp. 1~9.
A~rr~ua, D. W. G, AONIZRAY,A. P., P~LZCO~U,R. H., WOOD, C. A., .~SD WELLZR, T. (1965). The systems of lunar craters, Quadrant III. Commun. Lunar Planet. Lab. Univ. o/ Arizona 3,
text pp. 61-62, catalog pp. 1-146. Aavaua, D. W. G., PZLLIOOFU,R. It, ^~n WOOD, C. A. (1966). The system of lunar craters,
LARGE
LUNAR
CRATERS
211
KozrRgV, N. A. (1962). Spectroscopic proof for Quadrant IV. Commun. Lunar Planet. Lab. existence of volcanic processes on the Moon. Univ. o/Arizona 5, text p I, catalog pp. 1-208. In "The Moon" (Z. Kopal, and Z. K. MikB^LvwIs, R. B. (1963). "The Measure of the Moon," 488 pp. Univ. of Chicago Press, Chicago, hailov, eds.), pp. 263-271. Academic Press, New York. Ilhnois. FIELDER, G. (1961). Selected lunar observations L~oN^avI, P. (1966). Osserv~ioni Geomorfologiche made at the Pic du Midi observatory in 1956 sui Crateri Lunari e Marziani. Atti Accad. Naz. and 1959. J. Brit. Astron. Assoc. 71, 207-209. Lincei 40, 763-769. FIELnsR, G. (1963). Nature of the lunar maria. MCCALL, G. J. H. (1965). The caldera analogy Nature 198, 1256-1260. in selenology. In "Geological Problems in FIELDER, G. (196,5a) Distribution of craters on the Lunar Research," Ann. N.Y. Acad. 8ci. 123, lunar surface. Monthly Notices Roy. Astron. 843-475. Soc. 129, 351--361. Mooa~, P. A. (1953). Lunar summit craters. J. FXELVER, G. (1965b). "Lunar Geology," 184 pp. Brit. Astron. Assoc. 64, 34-39. Lutterworth Press, London. O'K~FE, J. A., AND CAMERON, W. S. (1962). GAULT, D. E., QUAIl)E, W. L, ^,xD OaZRRzeK, U. R Evidence from the Moon's surface features for (1966). Interpreting Ranger photographs from the production of lunar granites. Icarus 1, 271impact cratermg studies. In "The Nature of 285. the Lunar Surface," Proceechngs of the 1965 Ro•cA, L. B. (1966a). An introduction to the IAU-NASA Symposmm, pp 125-140. Johns geology of the Moon Proc. Geol. Assoc. London Hopkins Press, Baltimore, MaD'land. 77, 101-126. GmVAR~Y, J. J. (1962). Dimensional Correlation of RoNca, L. B. (1966b). Meteoritic impact and Lunar Maria and Terrestrial Ocean Basins. volcanism. Icarus 5, 515-520. Nature 196, 975-976. SALmSWY, J. W., ^~a RONCa, L. B. (1966). The GREEN, J. (1962). The geosciences applied to origin of continents. Nature 210, 669--670. lunar exploration. In "The Moon" (Z. Kopal, and Z. K. Mlkhailov, eds.), pp. 169--257. SaLlSSVSv, J. W., SMALLEY, V. G., AND RONC.',, L. B. (1965). Origin of linear elements of Mare Academic Press, New York. Humorum. Nature 210, 38,5-388. H^aV.~AN~;, W. K. (1964). On the distribution of SHOE.~AK~R, E. M. (1962). Interpretation of lunar lunar crater diameters. Commun. Lunar Planet. craters. In "Physics an Astronomy of the Lab. Univ. o~ Arizona 2, 194-203. Moon" (Z. Kopal, ed.), pp. 283-359. Academic IC~vrEa~a,v, G. N. (1967). Types, ages, and Press, New York. origins of lunar ring structures: statistical and W^RNZR, B. (1962). Some problems of lunar comparative geological approach. Icarus 6, 360orogeny. J. Brit. Astron. Assoc. 72, 281-285. 380.
On the Distribution of Large Lunar Craters LUCIANO B. RONCA Boezng Scientific Research Laboratories, Seattle, Washington Communicatcd by Zden~!k Kopal Received December 271 1967 The raze distribution and location of all the craters of Classes I, 2, and 3 larger than 25 k m in diameter on the front face of the M o o n were studied. The diameter distribution of the craters follows approximately the distribution that would be expected from meteoritlc impact. Lateral variations m cratering over the lunar surface were determined by divldlng the lunar disk into 172 equi-areal zones, each of approximately 76.9 X I0ffik m 2. The number of craters, their average diameter, and the s u m of their diameters were measured in each zone. W h e n these parameters are contoured on the lunar surface, they outline not only the rearm but also areas on the terrac otherwme indistinguishable. O n the terrae the amount of cratering is not random; highly cratered areas occur clustered together with a correlation coefficient of 0.776. Lateral variations in size distribution were studied by di~qding the front face of the M o o n into 9 zones, each of which has at least 60 large craters and follows approximately the physiography. The main variations are due to the maria and terrae distribution; however, differences in the terrae are also indicated. It is concluded that meteoritic impact can not offer all the answers to the origin of lunar craters. Either the craters are predominantly volcanic, or some endogenic control on thp size of an impact crater exists. I NTRODUCTION
example, Baldwin (1963), in explaining lunar features in terms of the impact An un(ler.-t:~n(ting of lunar geology is not only important per se, but it i~, hkcly hypothesis. That the question is still open, that it will increase our knowledge of the however, can be surmised by reading the early history of Earth itself. On the Moon not less outstanding, but perhaps less we probably see the results of early known, work of proponents of the volcanic planetary processes that have subsequently origin, as for example, McCall (1965) and Fielder (1965b). More recently a hybrid been completely obhtcrated on the Earth but which are perhaps still reflected in the impact-volcanic hypothesis was also tectonic framework of our planet. Hypoth- presented (Ronca, 1966a,b). Other papers eses on this subject ]lave been made, for on the origin of lunar craters are listed example, by Gilvarry (1962) and Salisbury in the Reference section. The purpose of the present study is to and Ronca [1966). As important as the determine variations in the surface Moon is for theoretical geology, it is a sad fact that the origin of the most obvious distribution of the lunar craters. No a featurcs on the lunar surface, the craters, is priori choice on the process of formation was made, and at the end, the choice is still disputed. It is common for people who have not left to the reader. Only craters larger than 25 km in followed the literature to be surprised to diameter were counted, in order to have the hear that the impact versus volcanism confidence that essentially none was left controversy is not yet settled. This may be due to the outstanding work made by some out and to avoid the problem of secondary proponents of meteoritic impact, as for craters, which can not exceed 5 km in 197
198
L U C I A N 0 B. RONCA
°\
1000
Cumulahve
~a
1o0
U
u
I
Curve
"~,~ I00
Histogram
7
~ \ Theorehcal
E :~ 10 z
Io
50
mo tsO 200 Diameter of Craters m Km
]O0 D~ameter Io0o
250
3o0
Fro. 1. The distribution of the large lunar craters m shown as a semdogar~thmic histogram and as logarithmic cumulative curve. In the latter case the experimental values are compared with the distribution that would be expected from meteoritic ,mpact. diameter (Salisbury et al., 1965). If the craters are completely or partially endogenous, the large craters are better indicators of strong tectonic activity than the smaller craters. The catalog of lunar craters published by the University of Arizona (Arthur et al., 1963, 1964, 1965, 1966) were used. This invaluable work gives the designation, diameter, position, central peak information, and degree of erosion of all discernible craters in the four quadrants of the visible face of the Moon. The craters are classified on the basis of their degree of erosion on a scale of 1 to 5. Very sharp and fresh-looking craters are classed as 1; craters with blurred rims as 2; craters with more extensively broken rims as 3. Craters usually described as ruins are classed as 4, and Class 5 covers ghost craters and craters so fragmentary that they are not easily recognized. This classification is not based on a measurable parameter but is based on personal judgment; as such, complete accuracy is not to be expected. However, considering the careful work that went into the preparation of the catalog, one is confident that the classification is as accurate as is humanly possible, In the present work only craters of
Classes 1, 2, and 3 were used, omitting ruins and ghost craters. In this way problems of omission and recognition were avoided. However, one must realize that the conclusions reached are not applicable to the early part of the geological history of the lunar surface, and care must be used in the interpretations of flooded areas. For brevity, in this work craters of Classes 1, 2, and 3 with diameters larger than 25 km will be referred to simply as large craters. EXPERIMENTAL RESULTS Figure 1 shows the size distribution of the 908 large craters present in the area investigated. The distribution is given in the familiar form of a histogram with 10km intervals beginning with a diameter of 25 km. Previous workers have generally preferred to give the distribution in the form of a cumulative curve, each point of which represents the number of craters which are larger than the corresponding value on the abscissa. For comparison, the cumulative curve is also included in Fig. 1. It is generally accepted (Hartmann, 1964) that the cumulative curve is a straight line on a log-log chart; that is, d(Iog F) d(lol~D) = - S ,
LARGE
LUNAR
where F is the normalized number of crater increments, D is the diameter, and S is a constant. Hartmann (1964) shows that 8 = 2.1 and that this function remains valid down to craters of 8 km in diameter. He also shows that this curve closely approximates the predicted diameter distribution of craters, were they caused by the presently known mass distribution of meteoroids. Figure 1 shows that the distribution of large craters follows approximately the predicted curve. The apparent deficiency of craters of diameter greater than 100 km is not considered significant because of the small number of craters involved and the omission of Class 4 and 5 craters. It is also possible to calculate the average of the measured craters and then to compare it with the average as computed from a histogram built from the theoretical cumulative curve. The two valucs are approximately equal to 46.5 kin. In order to measure lateral variations in crater characteristics the surface of the Moon was divided into a grid of equi-areal surfaces. This was achieved by superimposing a linear grid on an equi-areal projection of the latitude-longitude system,
I
I 2 " i Columns Rows
3 4 ' I' '
199
CRATERS
as indicated in Fig. 2. Each of the large craters was assigned to a certain column and row (for brevity, to a block) according to the latitude and longitude of the center of the crater as given in the University of Arizona catalog. The area of each block is approximately 76.9 X 10a km 2. Table I reports the diameters of the craters belonging to each block. Three parameters appear important in the description of each block. The first is /), the average diameter of the large craters; the second is ~:D, the sum of the diameters of the large craters in the block; and the third is n, the number of large craters occurring in the block. Figure 3 shows the relationship between n a n d / ) . No simple relationship exists, but it is evident that blocks with a high n tend to have a /) between 40 and 50 kin. Figure 4 shows the distribution o f / ) . A peak is present between 45 and 55 kin, and the average is 46.5 kin. As was pointed out before, this is the same as the predicted average diameter of craters if all were produced by the meteoric impact. Figure 4 can be interpreted as indicating that a certain cratering flux is most common on
5 6 7 8 9 I0 'I' 'N ] J * ' ' ~
II 12 13 14 15 ' I' ;' ']' r
1 2 3 4 5 6 7 8
.~I/V
i I i i lMII/[~2tA I I I I II iliii]I I I, I i I J i J J li sl l Jl iIj
.I llllllll!l ill
9 10 11 12
-_~1/1/~ ~ ~ J l
! i Jl ILII/~ 11 I /1LLLV ~ V
13 14
15 s
FIo. 2. Simplified superposition of a hnear grid over an equi-areal projection. Each block of the grid has the same area and is identified by a column aud a row number.
200
LUCIANO B. RONCA TABLE I
R
C
Dmmeter of C'~raters
1 1
8 9
30 31 53 01
1
10
63 09
1 2 2 2 2
11 8 9 10 II
.54 31 ~ 36 28
'2
12
39 91
3 3 3
8 9 10
56 52 87 26 44 25
3
11
87 41
3 3 4 4 4 4 4
12 13 8 9 10 II 12
36 80 176 87 55 34 none 29 65 39 44 33 29
4 4 5 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7
13 14 8 9 10 11 12 13 ]4 8 9 l0 II 12 13 14 8 9 l0 ll 12 13 14
32.83 28 l l none none 30 70 25 74 64 03 46 22 32 78 38 60 26 91 26 32 28 24 55 95 0_,8 04 29 79 25 95 ;~t 76 30 05 '29 44 ;31 34 51 81 45 66
n
ZD
/)
5
268
54
7
398
57
9 4 3 '2 4
333 219 106 94 125
37 55 35 47 31
6
273
46
7 '2 3
312 94 184
45 47 61
6
263
44
6 5 5 4 (1 "2 "2
290 268 313 226 0 56 90
48 54 63 56 ind 28 45
II 4 4 il (1 3 5 3 1 4 1 1 3 3 1 '2 5 1 5 "2 l I "2
559 2"20 207 0 0 114 151 127 46 147 :39 27 98 100 56 61 L~26 26 190 56 29 31 108
51 55 52 md ind 38 30 42 46 37 39 27 33 33 56 30 45 26 38 28 29 31 54
6
235
39
I QUADRANT
27 67 66 99 97
26 89 57 31 25 47 37 39 32 32 30 26 43 37 67 32 67 42 26 29 29 39
80 50 34 60 05 85 38 07 69 43 16 75 82 11 14 54 04 24 14 62 37 16
26 50 30 126 47 28 6:3
92 34 94 55 38 58 37
85 26 87 10 73 63 98
55 83 36 ~)
62 12 32 71
25 38 41 49 57 86
26 02 26 63
26 77 30 28
28 71 125 II
26 33
29 01 65 18
67 60
40 05
30 07 43 I I
39 56
36 12
39 84
56 28
38 52
124 12 29 25 30 64
36 94 ~) 01 1{~ 53
40 12 :37 42
77 86 77 07 28 97 29
26 11 3906 28 12 74 22 68 14
85 48 56 ~2
43 16 42 83
50 96 39 56 36 53
32 61 34 64 26 14
25 45
26 47
5~ 59
30 80
43 19 39 89
28 38 32 19
32 61 45 68
36 88
74 32
39 58
4~ 15
31) 89
30 26
51 12
3~ 45
46 63
46 04 26 04
56 35 26 12 27 12
84 18 47 .0/'2
2564
t~
>
~-~=
~ -~_~-~
~--~__~
plL
L"
202
R
C
8 8 8 9 9 9 9 9 9 9 10 10 10 10 10
3 2 1 7 6 5 4 3 2 1 7 6 5 4 3
none 36.52 33 86 2406 none 43 89 33.02 44.79 31.29 24.54 54.72 104.76 58.94 none 34 21
10
2
41 70
10 11
1 7
49 21 39.82
11
6
37 72
11 11 11 11 11 12
5 4 3 2 1 7
59.72 44 64 32 40 29 37 43 91 63 27
12
6
26 65
12 12 12 12 13
5 4 3 2 7
27.01 29 81 5324 27 55 26.18
13
6
105 33
13
5
29 36
13 13
4 3
34 94 25 62
14
7
47 80
14
6
111.31
LUCIANO
B. R O N C A
TABLE I
(Cordznued)
Dmmeter of Craters
28 80 151 58 118.54
46 50 29.08 39 86
27 67 45 73 43.96 29 84 26 66 42 48 46 69
110 42
96 80
34.73
49.02 46.20 26.17 26.16 48.03
2583
24.66
91 16 47 76
38.20 41 39 42 78 25 85
31.72
81.54
32 10
131.58
33 22 29 10 29 42 39 44 29 01 40 46 51 31 31 29 35 96 55 57 33 91 29.15 48 79 32.09 30 59 30 21 36 21 25 38 46 90 50 92 31 36 29 15 26 09 47 36 35 56 25.24 36 38 38 03 38 47 93 58 31 48 36 64 27 85 30 71
45 07 31 20 36 52
33 34
39 51
37 63
66 45
41 56 39 89
44.06
26.25 87 01
34 19
3968
35 79 62.35 84 67 2788 33 93 145.26 37 60 31.79 33 84 28 75 26.78 28 44 47 50 40 23 48.74 124 95 37.18 45.82 91 06
52 04 46 01
162.64 57 85
31.77 29.11 30 80 226 74 27 64 68 73 37 82 225 30 2944 110 36 28 45 37 16 67 11 113 87 39 26
107 26
11442 35 21 34 78
48 81 37 30 30 30
31 13 76.19 29.98
35.39 31.60
45 90 25 59
30 05 69 54
33 51 26 47 51 64
n
ZD
0 3 3 5 0 1 3 2 5 3 3 4 3 0
0 112 215 314 0 44 171 91 175 101 108 217 154 0
ind 37 72 63 ind 44 57 45 35 34 36 54 51 ind
7
325
46
7 1
403 49
58 49
7
251
36
6 3 2 5 2 3
247 115 85 245 61 116
41 38 43 49 30 39
11
675
61
8 4 5 4 5
455 126 352 151 177
57 32 70 38 35
8
494
62
12
552
46
8 5
418 304
52 61
5
260
52
14
686
49
9
408
45
27.27 28 51 38 99 84 44 29 24
LARGE LUNAR CRATEI~ I (Cont/.u~/)
TABLE
R
C
14
5
71 37
14
4
29 17
203
Dmmeter of Craters 64 38 29 30
21 26 91 97
25 34 26 11
27.62 65 09
8540
61 98
-
ZD
10 4
677 208
68 52
3 3 1
96 119 34
32 40 34
6 0 4
229 0 239
38 ind 60
17
729
43
7
329
47
7 4 3
311 211 91
44 53 30
6 5
295 341
49 68
II
529
48
11
580
53
14 5 5
559 215 179
40 43 36
6 5 2
253 329 156
42 66 78
15
808
54
15 5
750 198
50 40
6
278
46
25.57 303 46
IV Q U A D R A N T 8 8 8 8
8 9 10 11
30 56 28 27 34 28 3042
8 8 8
12 13 14
none 34.80 35.11
9
8
13566
9
9
33 70
9 9 9
10 II 12
30 O0 28 56 60 27
9 9
13 14
41 77 42 74
I0
8
49 59
10
9
41 44
10 10 10
10 11 12
29 62 26.77 36 87
10 10 11
13 14 8
11
9
33 34 127.18 13609 60 70 25 53 87 74
11 11
10 11
53.41 26.44
11
12
25.46
36 03 37 45
29 13 53 01
29 67 70 79
39 13
43 04 50 23 29 70 37 47 26 87 44 29 31 18 61 95 31 67 100 O0 32 97 41 19 46 58 147 06 30 50 47 94 55 92 27 24 63 01 66 31 42 05 46 13 59 29 35 55 42 60 32 36 44 08 57 08 176 60 28 96 36 27 38 95 28 61 46 34 40 72 53.80 81 02 43 05 52 25 52.65 74.48
29 39 29 29 42 62 107.33 29 64 28 23 28 70 49 29 39 86 27 83 29 27 38 50 42 49 30 93 36 70 34 29 53 25
27 83
131 28 33 31 38 26
98 64 78 95 78 89
48 46
30 83
25 37 25 118 34
83 74 41 91 10
45 73
53 15 30 44
78 23
84 39 77 68 39 21
25 99 27 78 33 60
06 29 64 53 03 2O 76 13 81 12
36 94 79 85
67 70 47 92
52 98 26 25 30 94
47 73 30 54 38 52
27 13 64 45 43 75
26 16 25 05 33 86
89 29 30 71 36 92
47 07
31 62
4629
69 72 27 32 25 17 67 98 31 60 52 28 34.95 43 09 70 05
53 12 69.53 27 45 29.69 36 21 35 25
51 40 136 57 26 23 40 92 27.71 8423
26.21 27.90
32.35 49 12
50.30
26.05
29 01
204
LUCIANO B. RONCA. TABLE
R
C
11
13
41 04
11 12
14 8
201 33 31 20
12
9
114 21
12
10
29 88
12
11
31 48
12
12
42.22
12
13
29 84
13
~
29 17
13
9
27 48
13
10
42 83
13
11
66 31
13
12
35 56
I
(Continued)
D m m e t e r of C r a t e r s
82 67 56 21 30 94 43 89 58 07 40 55 38 22 37 79 29 64 42 85 35 79 82 27 27 15 42 05 30 14 30 52 25 03 189 48 78.08 46 22 27 45 42 98 56 85 44 48 30 04 42 83 31 15 26 92 37 21 50 98 27 53 26 58 29 53 70 78 40 79 25 38 41 63 26 59 28 59 33 96 36 O1 41 O0 27 88 51 15 26 73 95 55 43 18 25.93 42.25 32 43 44 41 33 65 44 90
125.15 28 16 78 88 100.95 57 05 47 42 31 50 26 75 69 46 29 24 42 46 49 57 25 93
25 29 38 62 41 49
26 78 38 90 32 33
30 44 125 32 35 58
27 25 34 35 31 10
87 64 28 11 58 26
30 35 27 39 27 79
62 82 35.53 25 32 30 02 71 92 ,r~ 78 43 77 39 75
37 63 35 53 40 88 36 31 32 30
31 81 80 71
27 36 40 74 36 08 41 89 34 45 25.15 35.02 31 84 27 25 32 40 53 29
31 25 61 34 53 27 34 29 39 42 34
39 36 29 68 41 46 28 25 28 29 42
46 83 29 05 51 76 07 45 61 90 65
75 47 50 09 60 75 48 93 76.22 29.53 52.28 38 34 48 36 55 92
3"2 89 76 36 46 98
29 94 89 18 33 13
38 67 48 09 28 61
25.66 31 76 41 58
25 Ol 25 26
35 18 62.49
66 71 32 41 42 28 75 34 40 43 58 26
62 72 59 73 86 77 59 36 62 66 07 07
/~
7
413
59
15 3
724 289
48 96
42 52 75 75 :59 69 36
16
715
45
14
663
47
14
734
52
15
698
47
16
666
42
IX
718
40
25
(,W),-5
39
"£2
736
33
15
802
53
15
622
41
66 17 29 74 27 06
83 16 33 17 42 61 24
82 34 33.89 28 96
ZD
n
70 62 08 94 81 51 94 70 18 48 17
27 85 74 72 30 73
205
LARGE LUNAR CRATERS
TABLE I (Continued) R
C
Diameter of Craters
14
8
~).55
14
9
33 93
14
10
71 65
14
11
32 10
61.72 94 69 53 10 56 25 60 30 28 66 35 49 98 14 25 53 94 94 36 10 30 92 30 89 38 97 34 26 43 66 47 47
42 36 45 36 37 24 35 25 29
60 85 02 76 21 61 91 85 32
141 54 42 43 84 36 28 97 131
29 51 53 59 30 82 30 28 26.92 29 84 26 42
the lunar surface, but areas exist where the flux has been weaker and areas where it has been stronger. These areas are the blocks with /) less than 45 k m and more than 55 kin, respectively. Figure 5 shows the distribution of ~:D, the sum of the diameters of the large craters in a block. This quantity m a y be thought of as the amount of cratering which has occurred in a certain area. The number of large craters per block gives an incomplete picture, as very large craters have the same weight as the others• The sum of the areas of all the large craters in a block will give too strong an importance to the very large craters. ~D is a more complete index on the amount of cratering which has affected an area as it includes
03 30 69 45 98 73 21 30 (~5
38 50 70 30 28 33 42 42 97
27 37 38 10 49 86 10 36 94
43 59 45 71 52 47 64 29 26 34 32.52 56 Ig
34 37 33 30 91 57
40 42 48 82 01 15
n
~D
/~
13
650
50
21
989
47
14
818
58
13
531
41
16
66~
42
both the number and size of the craters present. Figure 5 shows t h a t most commonly the visible surface of the Moon has a low ~:D; the average, however, is approximately 265 k m This is mainly due to the higher ~:D on the terrae. Figure 6 shows the relationship between n and ~:D. As is to be expected, in general there is a linear relationship between the two. However, there are areas of relatively high n and areas of relatively high ~:D. Figure 7 shows the distribution of n, the number of large craters in a block. T h e distribution is perhaps bimodal, and the most common value is thrce or four large craters per block (excluding blocks with no craters). The average is about six craters per block.
o
._c 25. *4
a tJ
"6
15
• -
•..•..-
10-
E ....~
. . . . .'
: .:"..7
o {s 3'0 35 ,b
:
.._"
,5
"
:
"''..
~'o 5'5 ~o a's ;;o 75 8o 8'5 ~
9'5 ,oo k,.
of Block
FIG• 3• T h e r e l a t i o n s h i p b e t w e e n n, t h e n u m b e r of large c r a t e r s in a block, a n d / ) , t h e s,verage d i a m e t e r of the large craters in t h e block•
206
LUCIANO B. RONCA
D~
52
28-
48
"~24 -
44
.c 20 -
40"
36-
E
U 12
32-
8 28E,
24-
Z
20-
0
Z 12
0'
,6o ~o 3~o ,6o ~o ~
76o ~o ~o ~o
'
Fla. 6. The relationship between n, the number of large craters in a block, and ZD, t h e s u m of the diameters of the large craters in the block. ,o
2'0
. . • o. . ~o
6o
. . ,oo . 7o. . . o . 90
,lo ,20
5 Fro. 4. T h e distribution of /), the average dia m e t e r of large craters in a block.
The next step is to examine the relationship between the above distributions and the location on the lunar surface. The values of n, 1), and ZD for each block of the grid have been marked on a copy of an L E M - 1 A lunar mosaic and then contoured. F~gure 8 shows the contour map of 1). As indlcatcd before, if the cratering flux has been constant everywhere, a value of /) of approximately 46 km should be found everywhere. The heavy dashed line limits areas Which contain fewer than three craters per block. With so few craters the average diameter was considered to characterize the blocks very poorly. The dashed lines outline clearly the maria, shown as shaded regions. Also it is evident that "no-data" areas are inside the 40-kin
contour. Zones of higher than average b are present, indicated by the 50 and 60 km closed contours. The behavior of the 40-kin contour is interesting, as it "noses" considerably at approximately longitude 40°E from latitude 10°S to 40°S. Figure 9 shows the contour map of ~D, which can be understood as a representation of the amount of "cratering" occurring in a given area. As in the case o f / ) , the maria are approximately outlined by the lowest contour. The same prominent "nosing" as in /) is also present, at approximately 40°E ranging from 10°S to 40°S. The most striking feature of this contour map is the similarity of the shapes of the contours. Not only the 100-kin contour outlines the maria approximately, but also 48. 4440-
A I
3632.
50 ¸
~ 24. "5 2o
40.
.1~ 16.
E
3o 2o 7
$0
4
o ~'5 ,25 225 325 425 525 625 725 825 ~ 5 1025 ~D
Fro. 5. T h e distribution of ZD, the s u m of t h e diameters of the large craters in ~ block.
6
8
I0
12 14
16 18 20 22 24 2 6
Number of Large Craters in
28
Block
Fzo. 7. T h e distribution of n, t h e n u m b e r o f large craters in a block. Blocks with no large c r a t e r s a r e excluded.
LARGE L U N A R
207
CRATERS
of the zones were chosen with two arbit r a r y criteria in mind. First, they had to follow, at least roughly, morphological provinces. Second, they had to have more than 60 large craters. Table II lists the number of craters respectively larger than 50 kin, 40 km, 30 km, and 25 km for each zone. When these values are plotted on log-log paper, they do not form a straight line. This makes it impossible to characterize each curve simply by its slope. A numerical value, index of each curve, can be obtained as follows:
the other contours appear to follow, at a larger distance, the mare shores. The "nosing" is repeated by all the contours. If we think in terms of a ~D surface, the map is not a random distribution of highs and lows, but it shows a high near the South Pole, from which it descends toward the maria. The "nosing" represents a valley with ridges on both sides of it. The maria occupy the lowest portions of the ~D surface. The contour map of n is not included, as it is very similar to the ~:D map. Lateral variations in cratering characteristics over the surface would be best shown from the diameter distribution curve for each block of the grid. This is impossible, however, due to the relatively small number of craters in each block. To obtain at least a general idea, the front face of the Moon was divided into nine zones as shown in Fig. 10. The size and position
R = n~.6 rt~
n3o n4o where n~5, nso, n,o, n~o are, respectively, the numbers of craters larger than 25, 30, 40, and 50 kin. This value R is indicated in Table II and in Fig. 10. The zones near the South Pole have a large value of R, N
I
~0
W-
-E io"
Fzo. 8. Contour map of Z), the average diameter of the large craters in a block. Dashed linee contour areas where there are less than three large craters per block. For clarity, more closely spacod contours a r e omitted, as they follow the trends.
2O8
LUCIANO B. RONCA N I
10 °
W--
--E I0 t
1"
I
S FIG. 9. Contour map of ZD, the sum of the diameters of the large craters in a block. For clarity, more closely spaced contours are omitted, as they follow the trends. which d e c r e a s e s t o w a r d t h e e q u a t o r i a l b e l t a n d t h e n i n c r e a s e s a g a i n in the n o r t h e r n h e m i s p h e r e . On t h e e q u a t o r i a l b e l t t h e cent e r h a s the h i g h e s t v a l u e . I f a c o n t o u r m a p is m a d e of R, t h e r e s u l t i n g s u r f a c e is a p proximately saddle-shapcd. I NTERPRETATIONS
I t is i m p o r t a n t to realize t h a t n, ~ D , a n d R are n o t s t a t i s t i c a l in n a t u r e . T h e y r e p r e -
s e n t t h e b e h a v i o r of a l l t h e large c r a t e r s , even if some b l o c k s h a v e few or no large craters. T h e v a l u e s a r e a n a b s o l u t e f a c t a n d n o t a s t a t i s t i c a l inference. O n l y t h e p a r a m e t e r /), t h e a v e r a g e d i a m e t e r of t h e large c r a t e r s , is s t a t i s t i c a l in n a t u r e . F o r this r e a s o n t h e b l o c k s w i t h fewer t h a n t h r e e large c r a t e r s h a v e been excluded. E v e n so, it is p r o b a b l e t h a t /) is m e a n i n g ful o n l y on t h e t e r r a e .
TABLE II NUMBER
OF C R A T E R S L A R G E R THAN A C E R T A I N D I A M E T E R
IN E A C H Z O N E
N u m b e r of craters In zone---
Larger than
A
B
C
D
E
F
G
H
I
50km 40km 30km 25 km
26 42 75 105
44 60 95 115
14 36 57 76
18 33 57 77
18 34 60 80
18 26 48 67
27 43 73 107
22 36 53 70
21 35 54 69
0 867
0 888
0 518
0.737
0 706
0 967
0 921
0 807
0 767
R
LARGE LUNAR
The problem becomes statistical when the question is raised as to whether a random b o m b a r d m e n t of meteorites on the terrae could have produced the contours. To obtain a general idea of w h a t t y p e of contour is to be expected from a random distribution, the craters present in the terrae were redistributed at random over the area. This was done by using a table of random numbers to define the rows and columns of the blocks where the craters were to bc located. The contours of ZD and /) so obtained are characterized by contorted "islands" scattered over the area. The contour map o f / ) , shown in Fig. 8, is smoother than the one artificially produced, but not sufficiently to w a r r a n t doubt t h a t random meteoritic impact and marc flooding are the responsible processes. The contour m a p of ZD, however, is definitely different from anything produced by a random process. The contours are mu-
CRATERS
209
tually influenced and are all affected by the position of the maria, as previously discussed. Quantitatively, the lack of randomness can be shown in the following way. I f the blocks are random, blocks with a high ~:D would occur near blocks of low ~ D as commonly as near blocks of high ~:D. For every block in the terrac which is not bordering with a mare and is not on the edge of the visible disk, the averagc ~D of the surrounding blocks was measured. Figure 11 shows the ~:D of these blocks plotted against the average ZD of the surrounding. A relationship clearly exists with a correlation coefficient of 0.776. The slope of the least-square straight line is 1.4. In the case of a truly random distribution the points are scattered around a vertical line, corresponding to the average value of ZD. The correlation coefficient of the artificially randomly located cratcr~ was 0.04. The
N Zone B
~ ZoneA
R=089
~
R=087
:)7
%V
-0~b / ~
ZoneD ~ R=074
ZoneC R= 0.52
ZoneE
E
R=071
/
/ 0 90 R=077 Zone F R= 097
FIG. 10. The division of the lunar disk into nine zones, arbitrarily selected so that each zone has more than 60 large craters and follows approximately the physiography. R is the distribution index of the large craters in each zone, as defined in the text. Contour lines refer to R and are purely indicative.
210
LUCtANO B. RONCA Km
800
0
°
I00
200
300
400
500
600
°
700 SO0 Km
Average T D of Surrounding Fro. 11. The ordinate represent ~ D of a block in the terrae, and the abscissa is the average ~ D of the blocks surrounding the block of the ordinate. In a random distribution the points are symmetrically scattered around the average, indicated by the vertical line. In reality the points are symmetric around the oblique line. The correlation coefficient is 0.776.
least-square straight hne for such a scatter has very little significance. Figure l l clearly shows t h a t highly cratered areas tend to cluster together and t h a t the amount of cratering in one block is not independent from the amount of cratering in the neighboring blocks. A possible explanation of the behavior of ZD could be t h a t areas of high XD are older than areas of low ZD. I f this is true, areas of high ZD should show a higher degree of erosion than areas of low ~.D. To check this possibility, the average class of the craters in each block was measured, and the values contoured. No relationship with ZD exists (at least when Class 4 and 5 craters are excluded), and the contours are of the contorted-island type, typical of a random process. Also if large areas of progressively younger ages exist, the present terrae should be reworked and obliterated m a r i a of an older generation than the present ones. Fielder (1963), from considerations on crater density, reached the con-
clusion t h a t older maria presently obliterated can not exist. The properties of ~D point very strongly toward an endogenous origin, or a t least an endogenous control, of the large lunar craters. This is also indicated b y Fielder's calculations (1965a,b) which show t h a t on the terrae craters smaller than 40 k m in diameter are nonrandomly distributed at the 2% level of significance. A great deal of work m u s t be done before a definite picture on the distribution of lunar craters is available. Craters of smaller size must be included, and the new maps of the far side of the Moon m u s t be examined. Effects of variations in the size and number of the blocks m u s t be studied. T h e r m a l d a t a of the craters m a y give a new p a r a m e t e r to define different types of craters. Relationships with the shape of the Moon are under study. A computer program to handle the d a t a is under development. At the moment, the only conclusion t h a t can be reached is t h a t meteoritic impact can not offer all the answers to the origin of lunar craters. Either the craters are predominantly volcanic, or some endogenie control on the size of an impact crater exists. ACKNOWLEDGMENTS Help in the calculations from R. R. Green and critical comments from D. F. Winter, J. C. Noyes, J. M. Saari, and R. W. Shorthill are gratefully acknowledged.
REFERENCES
ARTHUR, D. W. G., AONIEP~¢¥, A. P, HORVA~, R. A., WOOD, C. A., AND CtIAPM^X. C. R. (1963). The system of lunar craters, Quadrant I. Commun. Lunar Planet. Lab., Univ. of Arizana 2, text pp. 71-78, catalog pp. 1--60. ARTHIJR, D. W. G., AGNmRAY, A. P., HOaV~VH, R. A., WOOD, C. A., AND CHAPMAN, C. R. (1964). The system of lunar craters, Quadrant II. Cornmun. Lunar Planet. Lab. Univ. o/ Arizona 3, text pp. 1-2, catalog pp. 1~9.
A~rr~ua, D. W. G, AONIZRAY,A. P., P~LZCO~U,R. H., WOOD, C. A., .~SD WELLZR, T. (1965). The systems of lunar craters, Quadrant III. Commun. Lunar Planet. Lab. Univ. o/ Arizona 3,
text pp. 61-62, catalog pp. 1-146. Aavaua, D. W. G., PZLLIOOFU,R. It, ^~n WOOD, C. A. (1966). The system of lunar craters,
LARGE
LUNAR
CRATERS
211
KozrRgV, N. A. (1962). Spectroscopic proof for Quadrant IV. Commun. Lunar Planet. Lab. existence of volcanic processes on the Moon. Univ. o/Arizona 5, text p I, catalog pp. 1-208. In "The Moon" (Z. Kopal, and Z. K. MikB^LvwIs, R. B. (1963). "The Measure of the Moon," 488 pp. Univ. of Chicago Press, Chicago, hailov, eds.), pp. 263-271. Academic Press, New York. Ilhnois. FIELDER, G. (1961). Selected lunar observations L~oN^avI, P. (1966). Osserv~ioni Geomorfologiche made at the Pic du Midi observatory in 1956 sui Crateri Lunari e Marziani. Atti Accad. Naz. and 1959. J. Brit. Astron. Assoc. 71, 207-209. Lincei 40, 763-769. FIELnsR, G. (1963). Nature of the lunar maria. MCCALL, G. J. H. (1965). The caldera analogy Nature 198, 1256-1260. in selenology. In "Geological Problems in FIELDER, G. (196,5a) Distribution of craters on the Lunar Research," Ann. N.Y. Acad. 8ci. 123, lunar surface. Monthly Notices Roy. Astron. 843-475. Soc. 129, 351--361. Mooa~, P. A. (1953). Lunar summit craters. J. FXELVER, G. (1965b). "Lunar Geology," 184 pp. Brit. Astron. Assoc. 64, 34-39. Lutterworth Press, London. O'K~FE, J. A., AND CAMERON, W. S. (1962). GAULT, D. E., QUAIl)E, W. L, ^,xD OaZRRzeK, U. R Evidence from the Moon's surface features for (1966). Interpreting Ranger photographs from the production of lunar granites. Icarus 1, 271impact cratermg studies. In "The Nature of 285. the Lunar Surface," Proceechngs of the 1965 Ro•cA, L. B. (1966a). An introduction to the IAU-NASA Symposmm, pp 125-140. Johns geology of the Moon Proc. Geol. Assoc. London Hopkins Press, Baltimore, MaD'land. 77, 101-126. GmVAR~Y, J. J. (1962). Dimensional Correlation of RoNca, L. B. (1966b). Meteoritic impact and Lunar Maria and Terrestrial Ocean Basins. volcanism. Icarus 5, 515-520. Nature 196, 975-976. SALmSWY, J. W., ^~a RONCa, L. B. (1966). The GREEN, J. (1962). The geosciences applied to origin of continents. Nature 210, 669--670. lunar exploration. In "The Moon" (Z. Kopal, and Z. K. Mlkhailov, eds.), pp. 169--257. SaLlSSVSv, J. W., SMALLEY, V. G., AND RONC.',, L. B. (1965). Origin of linear elements of Mare Academic Press, New York. Humorum. Nature 210, 38,5-388. H^aV.~AN~;, W. K. (1964). On the distribution of SHOE.~AK~R, E. M. (1962). Interpretation of lunar lunar crater diameters. Commun. Lunar Planet. craters. In "Physics an Astronomy of the Lab. Univ. o~ Arizona 2, 194-203. Moon" (Z. Kopal, ed.), pp. 283-359. Academic IC~vrEa~a,v, G. N. (1967). Types, ages, and Press, New York. origins of lunar ring structures: statistical and W^RNZR, B. (1962). Some problems of lunar comparative geological approach. Icarus 6, 360orogeny. J. Brit. Astron. Assoc. 72, 281-285. 380.