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The terrestrial cratering record
ICARUS 3~, 2 3 0 - 2 4 2
(1979)
The Terrestrial Cratering Record II. The Crater Production Rate 1 R. A. F. GRIEVE
AND M.
R. DENCE
Earth Physics Branch, Department of Energy, Mines and Resources, Ottawa K I A OY3 Canada
Received August 11, 1978; revised October 18, 1978 The terrestrial cratering record for the Phanerozoic has a size-frequency distribution of NaD -2.°5 for D > 22.6 km and NaD -°.2~ for D < 11.3 km. This shallowing of the distribution
slope at D > 22.6 km reflects the removal of small terrestrial craters by erosion. The number of large craters on the North American and East European cratons provide estimated terrestrial crater production rates for D > 20 km of 0.36 -4- 0.1 and 0.33 ~ 0.2 X 10-14 km-2 year-1, respectively. These rates are in good agreement with previous estimates and astronomical observations on Apollo bodies. Comparisons with the lunar rate, taking account of the effects of variations in impact velocity, surface gravity, and gravitational cross section, indicate that the lunar and terrestrial rates overlap, if the cratering flux has been constant during the last 3.4 by. If the early (pre 4.0 by) high-flux rate did not decay to a constant value until 3.0 to 2.5 by then the rates differ by a factor of 2 and the Phanerozoic can be interpreted as a period of higher than normal cratering. INTRODUCTION
tainty. However, they can be checked against each other through the use of impact energy-scaling laws (Shoemaker, 1977 ; Wetherill, 1979) and for consistency between the planets (0pik, 1960; Shoemaker et al., 1963; N e u k u m et al., 1975), provided provisions are made for interplanetary variations in mean impact velocity, surface gravity, and gravRational cross section (Hartmann, 1977). This contribution reviews the crater production rate on the E a r t h as estimated from the data presented in P a r t I and compares it with t h a t calculated from astronomical observations and from other planets. Although the ages of individual craters and the acquisition age of potential counting surfaces are known with a higher degree of precision on E a r t h t h a n on a n y other planet, there are other factors which militate against the determination of a precise terrestrial cratering rate. All are a function of
The desire to establish a relative chronology for the surface evolution of the terrestrial planets has heightened interest in crater production rates as a remote-sensing dating technique (McGill, 1977). Production rates can be derived from crater counts per unit area, provided the age of the counting surface can be estimated and allowances made for crater degradation by repeated impact and endogenic processes ( H a r t m a n n , 1965, 1977; Soderblom et aI., 1974). T h e y can also be estimated from astronomical data and theoretical considerations of the expected orbital history of particular interplanetary bodies and the probability of collision with a particular planet (Shoemaker, 1977; Wetherill, 1975). Both methods have high levels of uncer1Contribution from the Earth Physics Branch No. 747. 230
0019-1035/79/050230-13502.00/0 Copyright O 1979 by Academic Press, Inc. All rights of rel~roduction in a n y f o r m reserved.
THE TERRESTRIAL CRATER PRODUCTION RATE the high level of endogenic activity, which results in a poor preservation record and associated difficulties in the recognition of terrestrial i m p a c t craters. I n general, potential counting surfaces are young relative to the age of the E a r t h and preserve only a partial cratering record over the time period they h a v e been available for crater acquisition. T h e r e can be appreciable differences, therefore, between the retention rate of recognized craters a n d the crater production rate, particularly for the smaller craters. THE DATA For the purpose of this discussion all terrestrial structures with shock m e t a m o r p h i c effects (French a n d Short, 1968) are classed as being of i m p a c t origin, irrespective of whether or not they h a v e physical or chemical evidence of the bolide. Of the over 80 terrestrial structures > 1 0 0 m in diameter with meteoritic f r a g m e n t s or evidence of shock m e t a m o r p h i s m listed in P a r t I of this work, only 3 h a v e radiometric ages in the P r e c a m b r i a n . Two, S u d b u r y and Vredefort, are very large, a p p r o x i m a t e l y 140 k m in diameter. T h e third, Janisji~rvi, is only 14 k m b u t lies close to the present outcrop of the Paleozoic cratonic cover of the S c a n d i n a v i a n Shield. I t was p r o b a b l y covered b y it and only exhumed in relatively recent geologic time. I t is a p p a r e n t , therefore, t h a t the E a r t h retains only rare r e m n a n t s of its P r e c a m b r i a n cratering record, the record being restricted to conditions of exceptional preservation because of size or protection b y p o s t c r a t e r sedim e n t a r y cover. T h u s in determining the terrestrial crater production rate, the d a t a base has been limited to the Phanerozoic cratering record (Table I). However, even within this relatively short time period of 600 m y the preserved population is not complete. A plot of log d i a m e t e r - l o g c u m u l a t i v e frequency of the total earth population of Phanerozoic craters > 1 k m in d i a m e t e r
231
TABLE I WORLD POPULATION OF PHANEROZOICCRATERS > 1 km IN DIAMETER
Diameter (km)
N
1.0-1.4
1.4-2.0 2.0-2.8 2.8-4.0 4.0-5.7 5.7-8.0 8.0-11.3 11.3-16.0 16.0-22.6 22.6-32.0 32.0-45.2 45.2-64.0 64.0-90.5 90.5-128.0
1
4 6 6 9 4 10 10 4 9 4 3 2 1
(cumulative)
km -* (Land area 14.88 × 10~km2)
73 72 68 62 56 47 43 33 23 19 10 6 3 1
4.91 (× 10-0 4.84 4.57 4.17 3.76 3.16 2.89 2.22 1.55 1.28 0.67 0.40 0.20 0.06
Nc
N # I O -6
N¢ = 18,283 D-2.°5 for D > 22.6 km. Nc = 80 D-°.~ for D < 11.3 kin. shows a m a r k e d shallowing in slope at diameters of less t h a n a p p r o x i m a t e l y 22.6 k m (Fig. 1). T h e distribution of Phanerozoic craters has been a p p r o x i m a t e d b y two leastsquares linear segments (Fig. 1, T a b l e I ) : Nc = 18,283 D -2.°5
for D > 22.6 kin,
Nc = 80 D -°.u
for D < 11.3 km,
where Nc is the cumulative n u m b e r and D the diameter of the a p p a r e n t crater rim. T h e flattening of the slope is believed to reflect the shorter preservation life combined with the lower probability of recognition of small relative to large i m p a c t structures. T h e change in slope at a p p r o x i m a t e l y 20 k m in diameter is in keeping with the survey of variations in the degree of crater preservation with age a n d size presented in P a r t I of this work, which indicated that, in general, an u n p r o t e c t e d terrestrial crater < 2 0 k m has a recognizable life time of < 6 0 0 my. Therefore, we consider the slope for D > 22.6 k m to represent the true size distribution of terrestrial craters. T h e lower slope for D < 11.3 k m represents a modified
232
GRIEVE AND DENCE
1
1
I-
l~"--<]o~.~__T_ NaD-0.24 .....
Nc
Phanerozoic Impact Craters
10
~~!1~ \
I
I 2
L
I 4
I
I 8
Diamet Kmer, I
I 16
I
I 52
I
I 64
128
FIG. 1. Log cumulative number-log diameter plot of world population of currently known Phanerozoic impact structures > 1 km in diameter. Bars indicate la confidence interval, assuming a Poisson distribution.
distribution, in which the acquisition of relatively small craters during the Phanerozoic is balanced by their removal through terrestrial geologic processes. The removal of craters <20 km in diameter by endogenic processes even from surfaces of Phanerozoic age, surfaces only one-seventh to one-eighth the age of the planet, compounds the problem of determining statistically meaningful terrestrial crater counts. The population of craters upon any potential counting surface is small, because of a relatively short acquisition time, and the sample within that population with the highest probability of reflecting the crater production rate is further limited to the larger but much less numerous craters.
THE CRATERING RATE
The selection of representative counting surfaces is central to determining a crater production rate. The ideal surface should be of large areal extent; have a single age of origin, preferably as old as possible; and have undergone a minimal and uniform level of subsequent modifying geologic activity. An additional factor to be considered is the level of crater recognition. On the other planets this generally equates with the availability of high-resolution imagery. However, crater recognition on the Earth is less dependent on photographic coverage and more dependent on the extent of reported geologic investigation and the awareness of local workers to the existence of terrestrial impact structures.
THE TERRESTRIAL CRATER PRODUCTION RATE
233
T h e use of this size distribution law can be further justified from the observed size distribution of craters in the size range from a few kilometers to approximately 100 km on the other planets. Martian craters approximate a N = D -~ power law (Neukum and Wise, 1976), and distributions varying from N ¢c D-~.8 (Baldwin, 1971) to N ¢¢ D -2 (Hartmann and Wood, 1971) are reasonable averages for the larger lunar craters (Neukum et al., 1975). An additional, but not totally independent argument for the validity of a power law around N ¢c D -2 can be made from a consideration of the size distribution of interplanetary bodies capable of forming large terrestrial craters. The distribution of the estimated sizes of the Apollo objects (Wetherill, 1976) is shown in Fig. 2. Their size distribution is N = D -1"8 for D > 1 km, which corresponds to a mass distribution of M -°'~8, if the bodies are assumed to be spherical and have constant density. This is similar to the mass distribution of M -°-6 determined for asteroids in this size range (Millman, 1973). If there are no systematic variations in velocity with size, then the application of the energy scaling law of E 1/3"4 derived for large terrestrial craters (Dence et al., 1977) indicates that the Apollo bodies will produce a terrestrial crater population with a
As noted in Part I (Tables I and II) the distribution of recognized terrestrial impact structures is localized, with approximately 70% of the known impact structures occurring in less than 10% of the Earth's land surface. The areas with high levels of crater recognition are the North American craton, with its exposed Precambrian Shield and surrounding platform sediments, and the European craton, an area with a similar geologic history in Europe and the western USSR. These, therefore, have been taken as our counting areas. We believe that their overall geologic stability and large areal extent offset the details of variations in age and geologic history within these areas. Their relatively large area also serves to minimize biases in the size distribution of the sample, which might occur if smaller areas with more uniform geologic history but fewer craters were chosen. In analyzing the size-frequency relationships of the cratering record in these areas a N ¢: D -~ size-frequency distribution has been adopted as a standard. The - 2 power law, based on the total E ar t h population of Phanerozoic craters with D > 22.6 km (Fig. 1, Table I), is thus considered to most closely approximate the expected size distribution of any subset of the terrestrial cratering record.
20
10 Nc Apollo
5
Bodies
\
I
J
I
I
I 0.5
I
I
I
i
1 2 Diorneter, Km
i
I 4
I~k 8
FIG. 2. Log cumulative number-log diameter plot of Apollobodies. Data from Wetherill (1976). Bars indicate l r confidence interval.
234
G R I E V E AND D E N C E
Hedreacratan ---..=
/
..,
o~
'I °°
/
'~: o25
28e o2.9
,oo°
FIG. 3. Location of currently known impact structures > 1 km in diameter in North America. 1, Haughton Dome; 2, Nicholson Lake; 3, Pilot Lake; 4, Steen River; 5, New Quebec; 6, Lac Couture; 7, Lac La Moinerie; 8, Carswell; 9, Gow Lake; 10, Deep Bay; 11, Clearwater (East and West); 12, Mistastin; 13, Lake St. Martin; 14, West Hawk Lake; 15, Ile Rouleau; 16, Manicouagan; 17, Red Wing; 18, Slate Islands; 19, Sudbury; 20, Wanapitei; 21, Brent; 22, Holleford; 23, Charlevoix; 24, Conception Bay; 25, Manson; 26, Kentland; 27, Serpent Mound; 28, Decaturville ; 29, Crooked Creek ; 30, Barringer ; 31, Wells Creek ; 32, Flynn Creek ; 33, Middelsboro ; 34, Sierra Madera.
THE TERRESTRIAL CRATER PRODUCTION RATE size d i s t r i b u t i o n of N ~ D -I'8. T h i s is in g o o d a g r e e m e n t w i t h N ~" D -2, d e r i v e d from the observed terrestrial craters >22.6 k m in d i a m e t e r . (a) N o r t h A m e r i c a n
Craton
T h e N o r t h A m e r i c a n c r a t o n ( K a y , 1947) h a s a n a r e a of a p p r o x i m a t e l y 12.5 X 106 k m 2 a n d c o n t a i n s 33 r e c o g n i z e d P h a n e r o z o i c i m p a c t s t r u c t u r e s > 1 k m in d i a m e t e r (Fig. 3). T h e s i z e - f r e q u e n c y d i s t r i b u t i o n of t h e N o r t h A m e r i c a n s u b s e t of t h e t e r r e s t r i a l d a t a is s h o w n in F i g . 4 a n d l i s t e d in T a b l e I I . F i g u r e 4 i n d i c a t e s t h a t for D > 22.6 k m t h e N o r t h A m e r i c a n d a t a a r e in g o o d a c c o r d w i t h a N ¢¢ D -2 d i s t r i b u tion. B y c o n t r a s t , s m a l l e r a r e a s s u c h as Q u e b e c - L a b r a d o r of t h e C a n a d i a n Shield, 1.5 )< 106 k m ~, o r t h e e a s t c e n t r a l U n i t e d S t a t e s , 0.7 X 106 k m 2 ( S h o e m a k e r , 1977), h a v e d i s t r i b u t i o n s of D -~'5 a n d D -~'°, res p e c t i v e l y ( G r i e v e a n d D e n c e , 1978). T h i s m a y b e d u e to a d e f i c i e n c y of s m a l l c r a t e r s o r t h e i n c l u s i o n of one o r m o r e e x c e p t i o n a l l y l a r g e s t r u c t u r e s in a r e l a t i v e l y s m a l l a r e a . F o r e x a m p l e , t h e N o r t h A m e r i c a n size dis-
235
t r i b u t i o n d a t a s u g g e s t t h a t o n l y one i m p a c t e v e n t t h e size of M a n i c o u a g a n , 70 k m in diameter, should occur within the entire c r a t o n since t h e e a r l y P h a n e r o z o i c . I t s i n c l u s i o n in a n a r e a of 1.5 X 106 k m 2 cons e q u e n t l y d i s t o r t s t h e d i s t r i b u t i o n for t h e Q u e b e c - L a b r a d o r area. I t r e s u l t s in a s h a l l o w e r slope to t h e d i s t r i b u t i o n a n d in a h i g h e s t i m a t e for t h e c r a t e r p r o d u c t i o n r a t e for t h i s a r e a if t h e o c c u r r e n c e of M a n i c o u a g a n (No. 16 in F i g . 3) is u s e d in c o m b i n a t i o n w i t h t h e s t a n d a r d N ~ D -2 dist r i b u t i o n ( G r i e v e a n d D e n c e , 1978). The craton has not had a uniformly stable geologic h i s t o r y , w i t h t h e f o r m a t i o n ages of rocks within this area ranging from Archean to R e c e n t . H o w e v e r , w i t h t h e e x c e p t i o n of S u d b u r y all t h e i m p a c t s t r u c t u r e s a r e P h a n e r o z o i c in age. T h e r e is a b u n d a n t e v i d e n c e t h a t m o s t of t h e P r e c a m b r i a n S h i e l d of C a n a d a was c o v e r e d b y a n u p p e r O r d o v i c i a n Sea ( S t o c k w e l l et al., 1969). Alt h o u g h O r d o v i c i a n s e d i m e n t a t i o n s e r v e d to protect some small structures such as H o l l e f o r d (2 k i n ; 550 :t: 100 m y ) a n d B r e n t (3.8 k m , 450 :t: 30 m y ) , it is a p p a r e n t t h a t
TABLE II PHANEROZOIC IMPACT CRATERS ON NORTH AMERICAN ANn E o - E u R o P A CRATONSa
North Americab
Diameter (km) 1.0-1.4
1.4-2.0 2.0-2.8 2.8-4.0 4.0-5.7 5.7-8.0 8.0-11.3 11.3-16.0 16.0-22.6 22.6-32.0 32.0-45.2 45.2-64.0 64.0-90.5
Eo-europac
N
N~
N~/IO -6 k m -2
1 0 2 3 3 4 5 4 2 4 3 1 1
33 32 32 30 27 24 20 15 11 9 5 2 1
2.64 2.56 2.56 2.40 2.16 1.92 1.60 1.20 0.88 0.72 0.40 0.16 O. 08
N
N~
No/IO -6 k m -2
0 1 2 0 6 0 2 4 1 2 0 1 1
20 20 19 17 17 11 11 9 5 4 2 2 1
4.44 4.44 4.22 3.78 3.78 2.44 2.44 2.00 1.11 0.89 0.44 0.44 O. 22
a Distribution based on D > 22.6 km. N~/lO -6 km -2 ffi 584 D -'.° (North America); N~/IO -s k m - ' 48 D -1"~ (Eo-europa). b Area: 12.5 )< 106 km 2. Area: 4.5 )< 10e km 2.
=
236
GRIEVE AND DENCE
\\ \\\
5.0
\\2O NeD' \\ T \\
~0
_o
£
1.o
E= E
0.5 Phonerozoic Impoct Structures {..)
o =
o E o - e u r o p e o n Croton = N. Americon Croton
0.1
0.051
I
i 2
I
I 4
I
I I I i 8 16 Diameter, D, Km
i :52
I J. I 64
I
i 128
FIG. 4. Log cumulative n u m b e r / 1 0 -e k m - L l o g diameter plot of Phanerozoic impact structures > 1 k m in diameter on N o r t h American and Eo-european eratons. Bars indicate l a confidence interval.
the bulk of the N o r t h American craton has existed as an emergent counting surface only since the Ordovician. T h e Ordovician cover has still not been completely rem o v e d and was p r o b a b l y widespread over the P r e c a m b r i a n Shield even 200-300 m y ago, as judged from outliers of downdropped Ordovician s t r a t a within a n u m b e r of C a n a d i a n i m p a c t structures. We, therefore, consider the presently exposed Prec a m b r i a n and i m m e d i a t e l y adjacent areas of Paleozoic p l a t f o r m sediments, approxim a t e l y one-half of the area of the N o r t h American craton, to h a v e been available for crater acquisition since the Ordovician, i.e., for 450 my. This area includes most of the k n o w n large i m p a c t structures in N o r t h America. T h e remainder of the craton has had a more varied history of erosion a n d sedimentation. T h e Mississippi lowland region of the central United States is
a n o t h e r area with a high concentration of i m p a c t structures (Fig. 3). I n general, the structures in this area are relatively small and the ages of the bedrock s t r a t a range f r o m C a m b r i a n to Recent, with a n a v e r a g e formational age of 235 m y (Shoemaker et al., 1963). T h e oldest of these structures is F l y n n Creek at 360 ± 20 my, a n d m a n y have ages around 300 m y (Table I I , P a r t I, this work). We h a v e t a k e n this region as being representative of the rest of the N o r t h American craton a n d as having acquired craters over the last 300 my. T h u s the d a t a in T a b l e I I for craters with D :> 22.6 km, extrapolated to D = 20 k m with the N ¢¢ D -2 distribution (Fig. 4), and a n assigned age of 450 m y for half the craton and 300 m y for the remainder, give an estimated production rate for craters with D > 20 k m of 0.36 ± 0.1 X 10 -14 k m -2 y e a r -1. T h e u n c e r t a i n t y in the rate car-
THE TERRESTRIAL CRATER PRODUCTION RATE responds to an uncertainty of 150 my in the ages assigned to the counting surfaces within the craton. (b) European Craton
T h e counting surface is the ancient craton of Eo-europa (Khain, 1977), which has an area of approximately 4.5 X 108 k m 2 (Fig. 5). I t corresponds roughly to the N o r t h e r n E u r o p e a n Plain and is bounded by the orogenic fold belts of the Scandinavian Caledonides in the west and north, the Urals in the east, and the Carpathians and Caucasus in the south. T w e n t y Phanerozoic impact structures with D > 1 k m are cur-
237
rently recognized within this area, and their locations and size-frequency distribution are indicated in Figs. 5 and 4, respectively. T h e E u r o p e a n data show more scatter a b o u t the standard D -z distribution t h a n the N o r t h American d a t a (Fig. 4). This is probably the result of a smaller sample. At diameters >22.6 km, a distribution slope approaching the standard - 2 is maintained only over two counting intervals: 22.6 < D > 32.0 k m and 45.2 < D > 64 km (Fig. 4). A least-squares fit to all the data for D > 22.6 k m has a slope of - 1 . 3 . This relatively shallow slope may be due to a lack of recognized structures with
FIG. 5. Location of currently known impact structures ) 1 km in diameter on Eo-european craton. 1, Lappaj~ixvi; 2, Dellen; 3, Siljan; 4, S~i~ksjfxvi;5, Janisj~rvi; 6, Mishina Gora; 7, Kj ardla; 8, Mien; 9, Puchezh-Katunki; 10, Karla; 11, Vepriaj ; 12, Misarai; 13, Logoisk; 14, Kaluga; 15, Kursk; 16, Obolon; 17, Rotmistrovka; 18, Ilintsy; 19, Bolytsh; 20, Zeleny Gai; 21, Kamensk.
238
GRIEVE AND DENCE
D > 22.6 k m within the area. However, it is more likely to result from the occurrence of the very large structure, PuchezhK a t u n k i with a diameter of 80 km, in a relatively small counting area. This suggestion is based on the argument advanced for only one structure the size of Manicouagan, a structure similar in diameter to Puchezh-Katunki, occurring on the N o r t h American craton, an area approximately twice as large as that of the Eo-europa craton. T h e age of the surface rocks is again variable, with a general younging southward and eastward from exposed Procambrian overlain b y Paleozoic and, in turn, Mesozoic platform sediments (Nalivkin, 1960). However, the surface geology is relatively complicated with inliers of Precambrian (the Ukrainian Shield) and Paleozoic rocks occurring within the Mesozoic. The impact structures are fairly evenly divided between the Mesozoic and Paleozoic and older surfaces. As with N o r t h America, an acquisition age of 450 my has been taken for the northern part of the Eo-europa craton centered on the Baltic Shield. The oldest large structure in the southern, mainly Mesozoic, portion of the craton is Kaluga at 360 ± 10 my, and again an acquisition age of 300 my is considered appropriate for this area. If Puchezh-Katunki (No. 9 in Fig. 5) is regarded as a statistical sport for this relatively small area, the crater production rate is controlled b y the number of craters in the 22.6- to 64-km-diameter interval. Taking the number of structures in this interval (Table II) and using a N ¢¢ D -~ distribution, the crater production rate for Eo-europa is estimated at 0.33 -4- 0.2 X 10 -14 k m -2 year -1 for D > 20 km. The larger uncertainty given to this estimate is a reflection of the more complicated geology of E u r o p e a n USSR and our lower level of familiarity with it compared to N o r t h America.
This rate is essentially identical to t h a t derived from the N o r t h American craton. However, because of the large uncertainty attached, it should not be t a k e n as confirmation of the numerical accuracy of the N o r t h American production rate. T h e combined production rate for the N o r t h American and E u r o p e a n counting surfaces, weighted according to their relative areas, is 0.35-+-0.13 X 10-14 k m -2 year -1 for craters with D > 20 km. However, both the individual rates and the combined rate should be regarded only as estimates, which if anything are conservative because of the liberal age estimates assigned to the counting surfaces. COMPARISON WITH OTHER RATES
(a) Terrestrial Previous estimates of the terrestrial cratering rate have been made b y Shoemaker e t a l . (1963), H a r t m a n n (1965), and Dence (1972). These rates, standardized to D > 20 km, are listed in Table I I I and are in generally good correspondence with the rates estimated in this work. However, it should be noted t h a t these previous estimates are not totally independent of the presently estimated rate for the N o r t h American craton. T h e y were derived at least in part from subsets of the N o r t h American data, as it stood at the time of publication of the earlier estimates. Also given in Table I I I is a terrestrial cratering rate calculated b y Shoemaker (1977) from an impact rate of 0.7 ± 0.35 X 10-14 k m -2 year -I for Apollo bodies greater than an absolute visual magnitude 18. Assuming a mean geometric albedo of 0.2 and a density of 3.3 g cm -a, he has translated this, through an energy-scaling law and allowing a 40% increase in diameter due to postexcavation slumping, to a crater production rate of 1.2 ± 0.6 X 10-14 k m -2 year -1 for D > 10 k m (Shoemaker, 1977). This rate is slightly less t h a n t h a t estimated here. If the scaling law D = 1.96 X 10 -5
239
T H E T E R R E S T R I A L CRATER PRODUCTION RATE TABLE I I I ESTIMATED TERRESTRIAL CRATER PRODUCTION RATES, D ~ 20 k m
Rate, × 10-14 km-2 year-1
Data source
0.36 -4- O. 1 0.33 :i: 0.2 0.3
N. American craton Eo-europa eraton Best estimate, N. American and astronomical observations Central U.S.A. Canadian Shield Quebec-Labrador Observations on Apollo bodies Apollo bodies, using scaling law of Dence et al. (1977)
0.55 ± 0.28 0.1 0.5 0.3 ± 0.15 0.55 ± 0.28
(E) ~/8.4 for D /> 2.4 k m (where D is the a p p a r e n t rim diameter in kilometers and E is impact energy in joules), which directly includes the effects of late-stage modification (Dence et al., 1977) is applied, an Apollo body of magnitude 18 (p = 3.3 g cm -8, D = 0.7 km) impacting the earth with a r m s impact velocity of 24.6 k m sec -~ (Shoemaker, 1977) will produce a slightly larger, 17.7 km-diameter, crater t h a n t h a t calculated b y the scaling laws used b y Shoemaker (1977). A crater of this size for an Apollo b o d y of magnitude 18, in conjunction with the estimated impact rate of Apollos given b y Shoemaker (1977), now results in a terrestrial crater production rate of 0.55 ± 0.28 X 10-14 k m -2 year -1 for D > 20 km, which is slightly higher than the observed terrestrial rate. However, the predicted cratering rate b y Apollo bodies is probably biased toward high values (Wetherill, personal communication). Although the effect of observational selection is accounted for in estimating the total n u m b e r of bodies, the values derived for their impact probability and velocity are based on observed orbits (Shoemaker, 1977, Table I). High values for the probability of impact m a y result, since the Apollo bodies most likely to be discovered are those with orbits which make frequent close encounters with the Earth.
Reference This work This work Hartmann (1965) Shoemaker et al. (1963) Dence (1972) Dence (1972) Shoemaker (1977) This work
Similarly, high-velocity objects are more likely to be discovered, as they produce more obvious trails on photographic plates. Higher-velocity bodies will produce larger craters for a given mass. Therefore, a cratering rate based on high-velocity bodies will be biased toward a greater number of craters with diameters larger t h a n a given diameter. (b) L u n a r
T h e Moon is the only other terrestrial planet for which the ages of the cratercounting surfaces are known with some degree of certainty. In comparing the lunar and terrestrial rates account must be taken of differences in impact velocity, the effect of surface gravity on energy-scaling laws, and differences in gravitational cross section. H a r t m a n n (1977) has tabulated such correction factors for the comparison of the crater production rate on all the terrestrial planets. There are differences in the gravity scaling relationships and the mean impact velocities used in H a r t m a n n (1977) and those adopted in this work. However, these differences are minor considering the uncertainties attached to the estimated rates, and they do not affect the basic conclusions reached here. In comparing the lunar and terrestrial rates, the correction factors have been ap-
240
GRIEVE AND DENCE
plied through the size of crater formed b y a body of the same mass impacting either planet. As a standard we have adopted an Apollo body of magnitude 18. The rms impact velocity of Apollo bodies on the Moon is 21.7 k m sec -1 (Shoemaker, 1977). This lower impact velocity is the result of the lower escape velocity on the Moon and means that, for a given mass, impact craters might be expected to be smaller on the Moon (Frey, 1977). However, this is offset by the effect of the lower lunar surface gravity on crater dimensions. An energy-scaling relationship for lunar craters >14.4 km in diameter, that is, craters which have undergone modification from simple bowl shapes b y slumping (Pike, 1974), is developed in Dence (1979). The scaling law D = 2.42 X 10 -~ (E) 1/3"4,where D is the diameter in kilometers and E is impact energy in joules, differs from the terrestrial equivalent (Dence et al., 1977) b y a gravitational factor g0.11s. This factor takes account of both the increase in the a m o u n t of material ejected and the reduction in the a m o u n t of collapse during modification for an impact event under the reduced gravity of the Moon relative to the Earth. I t is less t h a n the g0.~ factor used by H a r t m a n n (1977) and is also slightly smaller than the experimental value of gO.165 for impacts into quartz sand (Gault and Wedekind, 1977) used by Shoemaker (1977). When this scaling law is applied, a magnitude 18 Apollo body impacting the Moon at 21.7 km sec -1 will produce a 20.3 km-diameter crater. This increase in crater diameter of 14.6vflv for an object of the same mass over the previously calculated equivalent impact on E a r t h accounts for the effects of differences in impact velocity and surface gravity. The final factor is the difference in gravitational cross section. Its effect varies with approach velocity, diminishing at higher velocities. For the impact velocities used here the approach velocity of an Apollo
body is approximately 22 k m sec -1. For this velocity and with the relationship given by Wetherill (1974) used, the E a r t h will collect 1.24 times as m a n y Apollo objects of the same mass per unit area as the Moon. A compilation of crater counts with D > 4 km on the lunar frontside maria (Hartmann, personal communication) indicates a lunar crater production rate due to Apollo bodies greater than magnitude 18 (i.e., lunar craters >20.3 km in diameter) of 0.30 :t: 0.03 X 10-14 km -2 year -1, assuming an average mare age of 3.38 X 109 years and a size-frequency distribution of N ~ D -1.8 for mare craters. If the difference in the gravitational cross section is considered, this rate recast into an equivalent terrestrial rate is 0.37 -4- 0.04 X 10-14 km -2 year -I. F r o m the data for the N o r t h American craton (Table II), the observed terrestrial crater production rate due to bodies of the same mass (terrestrial craters larger than 17.7 k m diameter) is 0.45 ~ 0.1 X 10-14 k m -2 year -1. This overlap in the estimated crater production rates for the E a r t h and Moon can be interpreted as indicating t h a t the cratering rate in the E a r t h - M o o n system has remained constant during the last 3.4 by. However, crater counts on individual mare surfaces of differing ages suggest t h a t the lunar crater production rate was still decaying at 3.4 b y (Neukum et al., 1975) from peak values which occurred during the early b o m b a r d m e n t of the Moon prior to 4.0 by (Wetherill, 1975). If the lunar data are interpreted as indicating that the cratering rate did not reach a constant value until 3.0 to 2.5 by, then the data of H a r t m a n n (personal communication) indicate t h a t the lunar rate at 3.0 to 2.5 by was approximately a factor of 2 lower than the estimated terrestrial crater production rate during the Phanerozoic. Inasmuch as the terrestrial rate is apparently in good agreement with estimates of the present population of Apollos (Shoemaker, 1977),
THE TERRESTRIAL CRATER PRODUCTION RATE this raises t h e p o s s i b i l i t y t h a t t h e c r a t e r production rate in the E a r t h - M o o n system has n o t b e e n c o n s t a n t o v e r t h e l a s t 3.0 to 2.5 by. T h i s i m p l i e s t h a t t h e P h a n e r o z o i c has b e e n a period of r e l a t i v e l y high c r a t e r p r o d u c t i o n , a n d i n t e g r a t i o n o v e r such a r e l a t i v e l y s h o r t t i m e s p a n is insufficient to a v e r a g e o u t periodic f l u c t u a t i o n s i n a n otherwise c o n s t a n t c r a t e r i n g rate.
ACKNOWLEDGMENTS We would like to thank W. K. Hartmann for kindly providing his most recent unpublished compilations of lunar crater counts. Reviews of this contribution and Paper I by S. J. Weidenschilling, G. W. Wetherill, and an anonymous reviewer are gratefully acknowledged. This paper constitutes Contribution No. 30 of the Basaltic Volcanism Study Project, which is organized and administered by the Lunar and Planetary Institute, operated by the Universities Space Research Association under Contract NSR 09-051-001 with the National Aeronautics and Space Administration.
REFERENCES
BALDWIN, R. (1971). On the history of lunar impact cratering: The absolute time-scale and the origin of planetismals. Icarus 14, 36-52. DENCE, M. R. (1972). The nature and significance of terrestrial impact structures. 24th Int. Geol. Congr., Sect. 15, 77-89. DENCE, M. R. (1979). An energy-scaling relationship for lunar impact craters. Geophys. Res. Left., in press. DENCE, M. R., GRIEVE, R. A. F., AND ROBERTSON, P. B. (1977). Terrestrial impact structures: Principal characteristics and energy considerations. In Impact and Explosion Cratering (D. J. Roddy, R. O. Pepin, and R. B. Merrill, Eds.), pp. 247-276. Pergamon, Elmsford, N. Y. FRENCH, B. M., AND SHORT, N. M. (1968). Shock Metamorphism of Natural Materials. Mono, Baltimore. FREY, H. (1977). Origin of the Earth's ocean basins. Icarus 32, 235-250. GAULT, D. E., AND WEDEKIND, J. A. (1977). Experimental hypervelocity impact into quartz sand-II, Effects of gravitational acceleration. In
241
Impact and Explosion Cratering (D. J. Roddy, R. O. Pepin, and R. B. Merrill, Eds.), pp. 12311244. Pergamon, Elmsford, N. Y. GRIEVE, R. A. F., AND DENCE, M. R. (1978). The terrestrial cratering record. AbEt. with Prgms., Cordilleran Sec. Geol. Soc. Amer. Ann. Meeting, 108. HARTMANN, W. K. (1965). Terrestrial and lunar flux of large meteorites in the last two billion years. Icarus 4, 157-165. HARTMANN, W. K. (1977). Relative crater production rates on planets. Icarus 31, 260-276. HARTMANN,W. K., AND WOOD, C. A. (1971). Moon: Origin and evolution of multiringed basins. Moon 3, 3-78. KAY, M. (1947). Geosynclinal nomenclature and the craton. Bull. Amer. Assoc. Petrol. Geol. 31, 12891293. KHAIN, V. E. (1977). The new international tectonic map of Europe. In Europe from Crust Core (D. V. Ager and M. Brooks, Eds.), pp. 19-40. Wiley, New York. McGILL, G. E. (1977). Craters as "fossils": The remote dating of planetary surface materials. Bull. Geol. Soc. Amer. 88, 1102-1110. MILLMAN, P. M. (1973). The observational evidence for mass distribution in the meteorite complex. Moon 8, 228-240. NALIVKIN, D. V. (1973). The Geology of the U.S.S.R. Pergamon, Elmsford, N. Y. NEUKUM, G., AND WISE, D. U. (1976). Mars: A standard crater curve and possible new time scale. Science 194, 1381-1387. NEUKUM, G., KONIG, B., AND FECHTIG, H. (1975). Cratering in the Earth-Moon system: Consequences for age determination by crater counting. Proc. 6th Lunar Sci. Conf., 2597-2620. 0PIK, E. J. (1960). The lunar surface as an impact counter. Mon. Not. Roy. Astron. Soc. 120, 404-411. PIKE, R. J. (1974). Depth/diameter relations of fresh lunar craters from spacecraft data. Geophys. Res. Lett. 1, 291-294. SHOEMAKER, E. M. (1977). Astronomically observable crater-forming projectiles. In Impact and Explosion Cratering (D. J. Roddy, R. O. Pepin, and R. B. Merrill, Eds.), pp. 617-628. Pergamon, Elmsford, N. Y. SHOEMAKER, n. i . , HACKMANN~R., ANDEGGELTON~ R. (1963). Interplanetary correlation of geologic time. Advan. Astron. Sci. 8, 70-89. STOCKWELL,C. H., McGLYNN, J. C., EMSLIE, R. F., SANFORD, R. V., NORRIS, A. W., DONALDSON,J.
242
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A_., FAHRIG, W. F., ANY CURRIE, K. L. (1969). The Geology of the Canadian Shield. In Geology and Economic Minerats of Canada (R. J. W. Douglas, Ed.), Geol. Surv. Canada, Ottawa, Canada. SOD~.RBLO~, L. A., CONDIT, C. D., WEST, R. A., HERMAN, B. M., AND KREIDLER, T. J. (1974). Martian planetwide crater distributions: Implications for geologic history and surface processes. Icarus 22, 239-263. WETHERILL,G. W. (1974). Solar system sources of
meteorites and large meteroids. Ann. Rev. Earth Planet. Sci. S, 303-331. WETHERILLjG. W. (1975). Late heavy bombardment of the Moon and terrestrial planets. Proc. 6th Lunar Sci. Conf. 1539-1561. WETHERILL,G. W. (1976). Where do the meteorites come from? A re-evaluation of the Earth-crossing Apollo objects as sources of chondritic meteorites. Geochim. Cosmochim. Acta 40, 1297-1318. WETHERILL, G. W. (1979). Steady state population of Apollo-Amor bodies. Icarus 37, 96-112.
(1979)
The Terrestrial Cratering Record II. The Crater Production Rate 1 R. A. F. GRIEVE
AND M.
R. DENCE
Earth Physics Branch, Department of Energy, Mines and Resources, Ottawa K I A OY3 Canada
Received August 11, 1978; revised October 18, 1978 The terrestrial cratering record for the Phanerozoic has a size-frequency distribution of NaD -2.°5 for D > 22.6 km and NaD -°.2~ for D < 11.3 km. This shallowing of the distribution
slope at D > 22.6 km reflects the removal of small terrestrial craters by erosion. The number of large craters on the North American and East European cratons provide estimated terrestrial crater production rates for D > 20 km of 0.36 -4- 0.1 and 0.33 ~ 0.2 X 10-14 km-2 year-1, respectively. These rates are in good agreement with previous estimates and astronomical observations on Apollo bodies. Comparisons with the lunar rate, taking account of the effects of variations in impact velocity, surface gravity, and gravitational cross section, indicate that the lunar and terrestrial rates overlap, if the cratering flux has been constant during the last 3.4 by. If the early (pre 4.0 by) high-flux rate did not decay to a constant value until 3.0 to 2.5 by then the rates differ by a factor of 2 and the Phanerozoic can be interpreted as a period of higher than normal cratering. INTRODUCTION
tainty. However, they can be checked against each other through the use of impact energy-scaling laws (Shoemaker, 1977 ; Wetherill, 1979) and for consistency between the planets (0pik, 1960; Shoemaker et al., 1963; N e u k u m et al., 1975), provided provisions are made for interplanetary variations in mean impact velocity, surface gravity, and gravRational cross section (Hartmann, 1977). This contribution reviews the crater production rate on the E a r t h as estimated from the data presented in P a r t I and compares it with t h a t calculated from astronomical observations and from other planets. Although the ages of individual craters and the acquisition age of potential counting surfaces are known with a higher degree of precision on E a r t h t h a n on a n y other planet, there are other factors which militate against the determination of a precise terrestrial cratering rate. All are a function of
The desire to establish a relative chronology for the surface evolution of the terrestrial planets has heightened interest in crater production rates as a remote-sensing dating technique (McGill, 1977). Production rates can be derived from crater counts per unit area, provided the age of the counting surface can be estimated and allowances made for crater degradation by repeated impact and endogenic processes ( H a r t m a n n , 1965, 1977; Soderblom et aI., 1974). T h e y can also be estimated from astronomical data and theoretical considerations of the expected orbital history of particular interplanetary bodies and the probability of collision with a particular planet (Shoemaker, 1977; Wetherill, 1975). Both methods have high levels of uncer1Contribution from the Earth Physics Branch No. 747. 230
0019-1035/79/050230-13502.00/0 Copyright O 1979 by Academic Press, Inc. All rights of rel~roduction in a n y f o r m reserved.
THE TERRESTRIAL CRATER PRODUCTION RATE the high level of endogenic activity, which results in a poor preservation record and associated difficulties in the recognition of terrestrial i m p a c t craters. I n general, potential counting surfaces are young relative to the age of the E a r t h and preserve only a partial cratering record over the time period they h a v e been available for crater acquisition. T h e r e can be appreciable differences, therefore, between the retention rate of recognized craters a n d the crater production rate, particularly for the smaller craters. THE DATA For the purpose of this discussion all terrestrial structures with shock m e t a m o r p h i c effects (French a n d Short, 1968) are classed as being of i m p a c t origin, irrespective of whether or not they h a v e physical or chemical evidence of the bolide. Of the over 80 terrestrial structures > 1 0 0 m in diameter with meteoritic f r a g m e n t s or evidence of shock m e t a m o r p h i s m listed in P a r t I of this work, only 3 h a v e radiometric ages in the P r e c a m b r i a n . Two, S u d b u r y and Vredefort, are very large, a p p r o x i m a t e l y 140 k m in diameter. T h e third, Janisji~rvi, is only 14 k m b u t lies close to the present outcrop of the Paleozoic cratonic cover of the S c a n d i n a v i a n Shield. I t was p r o b a b l y covered b y it and only exhumed in relatively recent geologic time. I t is a p p a r e n t , therefore, t h a t the E a r t h retains only rare r e m n a n t s of its P r e c a m b r i a n cratering record, the record being restricted to conditions of exceptional preservation because of size or protection b y p o s t c r a t e r sedim e n t a r y cover. T h u s in determining the terrestrial crater production rate, the d a t a base has been limited to the Phanerozoic cratering record (Table I). However, even within this relatively short time period of 600 m y the preserved population is not complete. A plot of log d i a m e t e r - l o g c u m u l a t i v e frequency of the total earth population of Phanerozoic craters > 1 k m in d i a m e t e r
231
TABLE I WORLD POPULATION OF PHANEROZOICCRATERS > 1 km IN DIAMETER
Diameter (km)
N
1.0-1.4
1.4-2.0 2.0-2.8 2.8-4.0 4.0-5.7 5.7-8.0 8.0-11.3 11.3-16.0 16.0-22.6 22.6-32.0 32.0-45.2 45.2-64.0 64.0-90.5 90.5-128.0
1
4 6 6 9 4 10 10 4 9 4 3 2 1
(cumulative)
km -* (Land area 14.88 × 10~km2)
73 72 68 62 56 47 43 33 23 19 10 6 3 1
4.91 (× 10-0 4.84 4.57 4.17 3.76 3.16 2.89 2.22 1.55 1.28 0.67 0.40 0.20 0.06
Nc
N # I O -6
N¢ = 18,283 D-2.°5 for D > 22.6 km. Nc = 80 D-°.~ for D < 11.3 kin. shows a m a r k e d shallowing in slope at diameters of less t h a n a p p r o x i m a t e l y 22.6 k m (Fig. 1). T h e distribution of Phanerozoic craters has been a p p r o x i m a t e d b y two leastsquares linear segments (Fig. 1, T a b l e I ) : Nc = 18,283 D -2.°5
for D > 22.6 kin,
Nc = 80 D -°.u
for D < 11.3 km,
where Nc is the cumulative n u m b e r and D the diameter of the a p p a r e n t crater rim. T h e flattening of the slope is believed to reflect the shorter preservation life combined with the lower probability of recognition of small relative to large i m p a c t structures. T h e change in slope at a p p r o x i m a t e l y 20 k m in diameter is in keeping with the survey of variations in the degree of crater preservation with age a n d size presented in P a r t I of this work, which indicated that, in general, an u n p r o t e c t e d terrestrial crater < 2 0 k m has a recognizable life time of < 6 0 0 my. Therefore, we consider the slope for D > 22.6 k m to represent the true size distribution of terrestrial craters. T h e lower slope for D < 11.3 k m represents a modified
232
GRIEVE AND DENCE
1
1
I-
l~"--<]o~.~__T_ NaD-0.24 .....
Nc
Phanerozoic Impact Craters
10
~~!1~ \
I
I 2
L
I 4
I
I 8
Diamet Kmer, I
I 16
I
I 52
I
I 64
128
FIG. 1. Log cumulative number-log diameter plot of world population of currently known Phanerozoic impact structures > 1 km in diameter. Bars indicate la confidence interval, assuming a Poisson distribution.
distribution, in which the acquisition of relatively small craters during the Phanerozoic is balanced by their removal through terrestrial geologic processes. The removal of craters <20 km in diameter by endogenic processes even from surfaces of Phanerozoic age, surfaces only one-seventh to one-eighth the age of the planet, compounds the problem of determining statistically meaningful terrestrial crater counts. The population of craters upon any potential counting surface is small, because of a relatively short acquisition time, and the sample within that population with the highest probability of reflecting the crater production rate is further limited to the larger but much less numerous craters.
THE CRATERING RATE
The selection of representative counting surfaces is central to determining a crater production rate. The ideal surface should be of large areal extent; have a single age of origin, preferably as old as possible; and have undergone a minimal and uniform level of subsequent modifying geologic activity. An additional factor to be considered is the level of crater recognition. On the other planets this generally equates with the availability of high-resolution imagery. However, crater recognition on the Earth is less dependent on photographic coverage and more dependent on the extent of reported geologic investigation and the awareness of local workers to the existence of terrestrial impact structures.
THE TERRESTRIAL CRATER PRODUCTION RATE
233
T h e use of this size distribution law can be further justified from the observed size distribution of craters in the size range from a few kilometers to approximately 100 km on the other planets. Martian craters approximate a N = D -~ power law (Neukum and Wise, 1976), and distributions varying from N ¢c D-~.8 (Baldwin, 1971) to N ¢¢ D -2 (Hartmann and Wood, 1971) are reasonable averages for the larger lunar craters (Neukum et al., 1975). An additional, but not totally independent argument for the validity of a power law around N ¢c D -2 can be made from a consideration of the size distribution of interplanetary bodies capable of forming large terrestrial craters. The distribution of the estimated sizes of the Apollo objects (Wetherill, 1976) is shown in Fig. 2. Their size distribution is N = D -1"8 for D > 1 km, which corresponds to a mass distribution of M -°'~8, if the bodies are assumed to be spherical and have constant density. This is similar to the mass distribution of M -°-6 determined for asteroids in this size range (Millman, 1973). If there are no systematic variations in velocity with size, then the application of the energy scaling law of E 1/3"4 derived for large terrestrial craters (Dence et al., 1977) indicates that the Apollo bodies will produce a terrestrial crater population with a
As noted in Part I (Tables I and II) the distribution of recognized terrestrial impact structures is localized, with approximately 70% of the known impact structures occurring in less than 10% of the Earth's land surface. The areas with high levels of crater recognition are the North American craton, with its exposed Precambrian Shield and surrounding platform sediments, and the European craton, an area with a similar geologic history in Europe and the western USSR. These, therefore, have been taken as our counting areas. We believe that their overall geologic stability and large areal extent offset the details of variations in age and geologic history within these areas. Their relatively large area also serves to minimize biases in the size distribution of the sample, which might occur if smaller areas with more uniform geologic history but fewer craters were chosen. In analyzing the size-frequency relationships of the cratering record in these areas a N ¢: D -~ size-frequency distribution has been adopted as a standard. The - 2 power law, based on the total E ar t h population of Phanerozoic craters with D > 22.6 km (Fig. 1, Table I), is thus considered to most closely approximate the expected size distribution of any subset of the terrestrial cratering record.
20
10 Nc Apollo
5
Bodies
\
I
J
I
I
I 0.5
I
I
I
i
1 2 Diorneter, Km
i
I 4
I~k 8
FIG. 2. Log cumulative number-log diameter plot of Apollobodies. Data from Wetherill (1976). Bars indicate l r confidence interval.
234
G R I E V E AND D E N C E
Hedreacratan ---..=
/
..,
o~
'I °°
/
'~: o25
28e o2.9
,oo°
FIG. 3. Location of currently known impact structures > 1 km in diameter in North America. 1, Haughton Dome; 2, Nicholson Lake; 3, Pilot Lake; 4, Steen River; 5, New Quebec; 6, Lac Couture; 7, Lac La Moinerie; 8, Carswell; 9, Gow Lake; 10, Deep Bay; 11, Clearwater (East and West); 12, Mistastin; 13, Lake St. Martin; 14, West Hawk Lake; 15, Ile Rouleau; 16, Manicouagan; 17, Red Wing; 18, Slate Islands; 19, Sudbury; 20, Wanapitei; 21, Brent; 22, Holleford; 23, Charlevoix; 24, Conception Bay; 25, Manson; 26, Kentland; 27, Serpent Mound; 28, Decaturville ; 29, Crooked Creek ; 30, Barringer ; 31, Wells Creek ; 32, Flynn Creek ; 33, Middelsboro ; 34, Sierra Madera.
THE TERRESTRIAL CRATER PRODUCTION RATE size d i s t r i b u t i o n of N ~ D -I'8. T h i s is in g o o d a g r e e m e n t w i t h N ~" D -2, d e r i v e d from the observed terrestrial craters >22.6 k m in d i a m e t e r . (a) N o r t h A m e r i c a n
Craton
T h e N o r t h A m e r i c a n c r a t o n ( K a y , 1947) h a s a n a r e a of a p p r o x i m a t e l y 12.5 X 106 k m 2 a n d c o n t a i n s 33 r e c o g n i z e d P h a n e r o z o i c i m p a c t s t r u c t u r e s > 1 k m in d i a m e t e r (Fig. 3). T h e s i z e - f r e q u e n c y d i s t r i b u t i o n of t h e N o r t h A m e r i c a n s u b s e t of t h e t e r r e s t r i a l d a t a is s h o w n in F i g . 4 a n d l i s t e d in T a b l e I I . F i g u r e 4 i n d i c a t e s t h a t for D > 22.6 k m t h e N o r t h A m e r i c a n d a t a a r e in g o o d a c c o r d w i t h a N ¢¢ D -2 d i s t r i b u tion. B y c o n t r a s t , s m a l l e r a r e a s s u c h as Q u e b e c - L a b r a d o r of t h e C a n a d i a n Shield, 1.5 )< 106 k m ~, o r t h e e a s t c e n t r a l U n i t e d S t a t e s , 0.7 X 106 k m 2 ( S h o e m a k e r , 1977), h a v e d i s t r i b u t i o n s of D -~'5 a n d D -~'°, res p e c t i v e l y ( G r i e v e a n d D e n c e , 1978). T h i s m a y b e d u e to a d e f i c i e n c y of s m a l l c r a t e r s o r t h e i n c l u s i o n of one o r m o r e e x c e p t i o n a l l y l a r g e s t r u c t u r e s in a r e l a t i v e l y s m a l l a r e a . F o r e x a m p l e , t h e N o r t h A m e r i c a n size dis-
235
t r i b u t i o n d a t a s u g g e s t t h a t o n l y one i m p a c t e v e n t t h e size of M a n i c o u a g a n , 70 k m in diameter, should occur within the entire c r a t o n since t h e e a r l y P h a n e r o z o i c . I t s i n c l u s i o n in a n a r e a of 1.5 X 106 k m 2 cons e q u e n t l y d i s t o r t s t h e d i s t r i b u t i o n for t h e Q u e b e c - L a b r a d o r area. I t r e s u l t s in a s h a l l o w e r slope to t h e d i s t r i b u t i o n a n d in a h i g h e s t i m a t e for t h e c r a t e r p r o d u c t i o n r a t e for t h i s a r e a if t h e o c c u r r e n c e of M a n i c o u a g a n (No. 16 in F i g . 3) is u s e d in c o m b i n a t i o n w i t h t h e s t a n d a r d N ~ D -2 dist r i b u t i o n ( G r i e v e a n d D e n c e , 1978). The craton has not had a uniformly stable geologic h i s t o r y , w i t h t h e f o r m a t i o n ages of rocks within this area ranging from Archean to R e c e n t . H o w e v e r , w i t h t h e e x c e p t i o n of S u d b u r y all t h e i m p a c t s t r u c t u r e s a r e P h a n e r o z o i c in age. T h e r e is a b u n d a n t e v i d e n c e t h a t m o s t of t h e P r e c a m b r i a n S h i e l d of C a n a d a was c o v e r e d b y a n u p p e r O r d o v i c i a n Sea ( S t o c k w e l l et al., 1969). Alt h o u g h O r d o v i c i a n s e d i m e n t a t i o n s e r v e d to protect some small structures such as H o l l e f o r d (2 k i n ; 550 :t: 100 m y ) a n d B r e n t (3.8 k m , 450 :t: 30 m y ) , it is a p p a r e n t t h a t
TABLE II PHANEROZOIC IMPACT CRATERS ON NORTH AMERICAN ANn E o - E u R o P A CRATONSa
North Americab
Diameter (km) 1.0-1.4
1.4-2.0 2.0-2.8 2.8-4.0 4.0-5.7 5.7-8.0 8.0-11.3 11.3-16.0 16.0-22.6 22.6-32.0 32.0-45.2 45.2-64.0 64.0-90.5
Eo-europac
N
N~
N~/IO -6 k m -2
1 0 2 3 3 4 5 4 2 4 3 1 1
33 32 32 30 27 24 20 15 11 9 5 2 1
2.64 2.56 2.56 2.40 2.16 1.92 1.60 1.20 0.88 0.72 0.40 0.16 O. 08
N
N~
No/IO -6 k m -2
0 1 2 0 6 0 2 4 1 2 0 1 1
20 20 19 17 17 11 11 9 5 4 2 2 1
4.44 4.44 4.22 3.78 3.78 2.44 2.44 2.00 1.11 0.89 0.44 0.44 O. 22
a Distribution based on D > 22.6 km. N~/lO -6 km -2 ffi 584 D -'.° (North America); N~/IO -s k m - ' 48 D -1"~ (Eo-europa). b Area: 12.5 )< 106 km 2. Area: 4.5 )< 10e km 2.
=
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GRIEVE AND DENCE
\\ \\\
5.0
\\2O NeD' \\ T \\
~0
_o
£
1.o
E= E
0.5 Phonerozoic Impoct Structures {..)
o =
o E o - e u r o p e o n Croton = N. Americon Croton
0.1
0.051
I
i 2
I
I 4
I
I I I i 8 16 Diameter, D, Km
i :52
I J. I 64
I
i 128
FIG. 4. Log cumulative n u m b e r / 1 0 -e k m - L l o g diameter plot of Phanerozoic impact structures > 1 k m in diameter on N o r t h American and Eo-european eratons. Bars indicate l a confidence interval.
the bulk of the N o r t h American craton has existed as an emergent counting surface only since the Ordovician. T h e Ordovician cover has still not been completely rem o v e d and was p r o b a b l y widespread over the P r e c a m b r i a n Shield even 200-300 m y ago, as judged from outliers of downdropped Ordovician s t r a t a within a n u m b e r of C a n a d i a n i m p a c t structures. We, therefore, consider the presently exposed Prec a m b r i a n and i m m e d i a t e l y adjacent areas of Paleozoic p l a t f o r m sediments, approxim a t e l y one-half of the area of the N o r t h American craton, to h a v e been available for crater acquisition since the Ordovician, i.e., for 450 my. This area includes most of the k n o w n large i m p a c t structures in N o r t h America. T h e remainder of the craton has had a more varied history of erosion a n d sedimentation. T h e Mississippi lowland region of the central United States is
a n o t h e r area with a high concentration of i m p a c t structures (Fig. 3). I n general, the structures in this area are relatively small and the ages of the bedrock s t r a t a range f r o m C a m b r i a n to Recent, with a n a v e r a g e formational age of 235 m y (Shoemaker et al., 1963). T h e oldest of these structures is F l y n n Creek at 360 ± 20 my, a n d m a n y have ages around 300 m y (Table I I , P a r t I, this work). We h a v e t a k e n this region as being representative of the rest of the N o r t h American craton a n d as having acquired craters over the last 300 my. T h u s the d a t a in T a b l e I I for craters with D :> 22.6 km, extrapolated to D = 20 k m with the N ¢¢ D -2 distribution (Fig. 4), and a n assigned age of 450 m y for half the craton and 300 m y for the remainder, give an estimated production rate for craters with D > 20 k m of 0.36 ± 0.1 X 10 -14 k m -2 y e a r -1. T h e u n c e r t a i n t y in the rate car-
THE TERRESTRIAL CRATER PRODUCTION RATE responds to an uncertainty of 150 my in the ages assigned to the counting surfaces within the craton. (b) European Craton
T h e counting surface is the ancient craton of Eo-europa (Khain, 1977), which has an area of approximately 4.5 X 108 k m 2 (Fig. 5). I t corresponds roughly to the N o r t h e r n E u r o p e a n Plain and is bounded by the orogenic fold belts of the Scandinavian Caledonides in the west and north, the Urals in the east, and the Carpathians and Caucasus in the south. T w e n t y Phanerozoic impact structures with D > 1 k m are cur-
237
rently recognized within this area, and their locations and size-frequency distribution are indicated in Figs. 5 and 4, respectively. T h e E u r o p e a n data show more scatter a b o u t the standard D -z distribution t h a n the N o r t h American d a t a (Fig. 4). This is probably the result of a smaller sample. At diameters >22.6 km, a distribution slope approaching the standard - 2 is maintained only over two counting intervals: 22.6 < D > 32.0 k m and 45.2 < D > 64 km (Fig. 4). A least-squares fit to all the data for D > 22.6 k m has a slope of - 1 . 3 . This relatively shallow slope may be due to a lack of recognized structures with
FIG. 5. Location of currently known impact structures ) 1 km in diameter on Eo-european craton. 1, Lappaj~ixvi; 2, Dellen; 3, Siljan; 4, S~i~ksjfxvi;5, Janisj~rvi; 6, Mishina Gora; 7, Kj ardla; 8, Mien; 9, Puchezh-Katunki; 10, Karla; 11, Vepriaj ; 12, Misarai; 13, Logoisk; 14, Kaluga; 15, Kursk; 16, Obolon; 17, Rotmistrovka; 18, Ilintsy; 19, Bolytsh; 20, Zeleny Gai; 21, Kamensk.
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D > 22.6 k m within the area. However, it is more likely to result from the occurrence of the very large structure, PuchezhK a t u n k i with a diameter of 80 km, in a relatively small counting area. This suggestion is based on the argument advanced for only one structure the size of Manicouagan, a structure similar in diameter to Puchezh-Katunki, occurring on the N o r t h American craton, an area approximately twice as large as that of the Eo-europa craton. T h e age of the surface rocks is again variable, with a general younging southward and eastward from exposed Procambrian overlain b y Paleozoic and, in turn, Mesozoic platform sediments (Nalivkin, 1960). However, the surface geology is relatively complicated with inliers of Precambrian (the Ukrainian Shield) and Paleozoic rocks occurring within the Mesozoic. The impact structures are fairly evenly divided between the Mesozoic and Paleozoic and older surfaces. As with N o r t h America, an acquisition age of 450 my has been taken for the northern part of the Eo-europa craton centered on the Baltic Shield. The oldest large structure in the southern, mainly Mesozoic, portion of the craton is Kaluga at 360 ± 10 my, and again an acquisition age of 300 my is considered appropriate for this area. If Puchezh-Katunki (No. 9 in Fig. 5) is regarded as a statistical sport for this relatively small area, the crater production rate is controlled b y the number of craters in the 22.6- to 64-km-diameter interval. Taking the number of structures in this interval (Table II) and using a N ¢¢ D -~ distribution, the crater production rate for Eo-europa is estimated at 0.33 -4- 0.2 X 10 -14 k m -2 year -1 for D > 20 km. The larger uncertainty given to this estimate is a reflection of the more complicated geology of E u r o p e a n USSR and our lower level of familiarity with it compared to N o r t h America.
This rate is essentially identical to t h a t derived from the N o r t h American craton. However, because of the large uncertainty attached, it should not be t a k e n as confirmation of the numerical accuracy of the N o r t h American production rate. T h e combined production rate for the N o r t h American and E u r o p e a n counting surfaces, weighted according to their relative areas, is 0.35-+-0.13 X 10-14 k m -2 year -1 for craters with D > 20 km. However, both the individual rates and the combined rate should be regarded only as estimates, which if anything are conservative because of the liberal age estimates assigned to the counting surfaces. COMPARISON WITH OTHER RATES
(a) Terrestrial Previous estimates of the terrestrial cratering rate have been made b y Shoemaker e t a l . (1963), H a r t m a n n (1965), and Dence (1972). These rates, standardized to D > 20 km, are listed in Table I I I and are in generally good correspondence with the rates estimated in this work. However, it should be noted t h a t these previous estimates are not totally independent of the presently estimated rate for the N o r t h American craton. T h e y were derived at least in part from subsets of the N o r t h American data, as it stood at the time of publication of the earlier estimates. Also given in Table I I I is a terrestrial cratering rate calculated b y Shoemaker (1977) from an impact rate of 0.7 ± 0.35 X 10-14 k m -2 year -I for Apollo bodies greater than an absolute visual magnitude 18. Assuming a mean geometric albedo of 0.2 and a density of 3.3 g cm -a, he has translated this, through an energy-scaling law and allowing a 40% increase in diameter due to postexcavation slumping, to a crater production rate of 1.2 ± 0.6 X 10-14 k m -2 year -1 for D > 10 k m (Shoemaker, 1977). This rate is slightly less t h a n t h a t estimated here. If the scaling law D = 1.96 X 10 -5
239
T H E T E R R E S T R I A L CRATER PRODUCTION RATE TABLE I I I ESTIMATED TERRESTRIAL CRATER PRODUCTION RATES, D ~ 20 k m
Rate, × 10-14 km-2 year-1
Data source
0.36 -4- O. 1 0.33 :i: 0.2 0.3
N. American craton Eo-europa eraton Best estimate, N. American and astronomical observations Central U.S.A. Canadian Shield Quebec-Labrador Observations on Apollo bodies Apollo bodies, using scaling law of Dence et al. (1977)
0.55 ± 0.28 0.1 0.5 0.3 ± 0.15 0.55 ± 0.28
(E) ~/8.4 for D /> 2.4 k m (where D is the a p p a r e n t rim diameter in kilometers and E is impact energy in joules), which directly includes the effects of late-stage modification (Dence et al., 1977) is applied, an Apollo body of magnitude 18 (p = 3.3 g cm -8, D = 0.7 km) impacting the earth with a r m s impact velocity of 24.6 k m sec -~ (Shoemaker, 1977) will produce a slightly larger, 17.7 km-diameter, crater t h a n t h a t calculated b y the scaling laws used b y Shoemaker (1977). A crater of this size for an Apollo b o d y of magnitude 18, in conjunction with the estimated impact rate of Apollos given b y Shoemaker (1977), now results in a terrestrial crater production rate of 0.55 ± 0.28 X 10-14 k m -2 year -1 for D > 20 km, which is slightly higher than the observed terrestrial rate. However, the predicted cratering rate b y Apollo bodies is probably biased toward high values (Wetherill, personal communication). Although the effect of observational selection is accounted for in estimating the total n u m b e r of bodies, the values derived for their impact probability and velocity are based on observed orbits (Shoemaker, 1977, Table I). High values for the probability of impact m a y result, since the Apollo bodies most likely to be discovered are those with orbits which make frequent close encounters with the Earth.
Reference This work This work Hartmann (1965) Shoemaker et al. (1963) Dence (1972) Dence (1972) Shoemaker (1977) This work
Similarly, high-velocity objects are more likely to be discovered, as they produce more obvious trails on photographic plates. Higher-velocity bodies will produce larger craters for a given mass. Therefore, a cratering rate based on high-velocity bodies will be biased toward a greater number of craters with diameters larger t h a n a given diameter. (b) L u n a r
T h e Moon is the only other terrestrial planet for which the ages of the cratercounting surfaces are known with some degree of certainty. In comparing the lunar and terrestrial rates account must be taken of differences in impact velocity, the effect of surface gravity on energy-scaling laws, and differences in gravitational cross section. H a r t m a n n (1977) has tabulated such correction factors for the comparison of the crater production rate on all the terrestrial planets. There are differences in the gravity scaling relationships and the mean impact velocities used in H a r t m a n n (1977) and those adopted in this work. However, these differences are minor considering the uncertainties attached to the estimated rates, and they do not affect the basic conclusions reached here. In comparing the lunar and terrestrial rates, the correction factors have been ap-
240
GRIEVE AND DENCE
plied through the size of crater formed b y a body of the same mass impacting either planet. As a standard we have adopted an Apollo body of magnitude 18. The rms impact velocity of Apollo bodies on the Moon is 21.7 k m sec -1 (Shoemaker, 1977). This lower impact velocity is the result of the lower escape velocity on the Moon and means that, for a given mass, impact craters might be expected to be smaller on the Moon (Frey, 1977). However, this is offset by the effect of the lower lunar surface gravity on crater dimensions. An energy-scaling relationship for lunar craters >14.4 km in diameter, that is, craters which have undergone modification from simple bowl shapes b y slumping (Pike, 1974), is developed in Dence (1979). The scaling law D = 2.42 X 10 -~ (E) 1/3"4,where D is the diameter in kilometers and E is impact energy in joules, differs from the terrestrial equivalent (Dence et al., 1977) b y a gravitational factor g0.11s. This factor takes account of both the increase in the a m o u n t of material ejected and the reduction in the a m o u n t of collapse during modification for an impact event under the reduced gravity of the Moon relative to the Earth. I t is less t h a n the g0.~ factor used by H a r t m a n n (1977) and is also slightly smaller than the experimental value of gO.165 for impacts into quartz sand (Gault and Wedekind, 1977) used by Shoemaker (1977). When this scaling law is applied, a magnitude 18 Apollo body impacting the Moon at 21.7 km sec -1 will produce a 20.3 km-diameter crater. This increase in crater diameter of 14.6vflv for an object of the same mass over the previously calculated equivalent impact on E a r t h accounts for the effects of differences in impact velocity and surface gravity. The final factor is the difference in gravitational cross section. Its effect varies with approach velocity, diminishing at higher velocities. For the impact velocities used here the approach velocity of an Apollo
body is approximately 22 k m sec -1. For this velocity and with the relationship given by Wetherill (1974) used, the E a r t h will collect 1.24 times as m a n y Apollo objects of the same mass per unit area as the Moon. A compilation of crater counts with D > 4 km on the lunar frontside maria (Hartmann, personal communication) indicates a lunar crater production rate due to Apollo bodies greater than magnitude 18 (i.e., lunar craters >20.3 km in diameter) of 0.30 :t: 0.03 X 10-14 km -2 year -1, assuming an average mare age of 3.38 X 109 years and a size-frequency distribution of N ~ D -1.8 for mare craters. If the difference in the gravitational cross section is considered, this rate recast into an equivalent terrestrial rate is 0.37 -4- 0.04 X 10-14 km -2 year -I. F r o m the data for the N o r t h American craton (Table II), the observed terrestrial crater production rate due to bodies of the same mass (terrestrial craters larger than 17.7 k m diameter) is 0.45 ~ 0.1 X 10-14 k m -2 year -1. This overlap in the estimated crater production rates for the E a r t h and Moon can be interpreted as indicating t h a t the cratering rate in the E a r t h - M o o n system has remained constant during the last 3.4 by. However, crater counts on individual mare surfaces of differing ages suggest t h a t the lunar crater production rate was still decaying at 3.4 b y (Neukum et al., 1975) from peak values which occurred during the early b o m b a r d m e n t of the Moon prior to 4.0 by (Wetherill, 1975). If the lunar data are interpreted as indicating that the cratering rate did not reach a constant value until 3.0 to 2.5 by, then the data of H a r t m a n n (personal communication) indicate t h a t the lunar rate at 3.0 to 2.5 by was approximately a factor of 2 lower than the estimated terrestrial crater production rate during the Phanerozoic. Inasmuch as the terrestrial rate is apparently in good agreement with estimates of the present population of Apollos (Shoemaker, 1977),
THE TERRESTRIAL CRATER PRODUCTION RATE this raises t h e p o s s i b i l i t y t h a t t h e c r a t e r production rate in the E a r t h - M o o n system has n o t b e e n c o n s t a n t o v e r t h e l a s t 3.0 to 2.5 by. T h i s i m p l i e s t h a t t h e P h a n e r o z o i c has b e e n a period of r e l a t i v e l y high c r a t e r p r o d u c t i o n , a n d i n t e g r a t i o n o v e r such a r e l a t i v e l y s h o r t t i m e s p a n is insufficient to a v e r a g e o u t periodic f l u c t u a t i o n s i n a n otherwise c o n s t a n t c r a t e r i n g rate.
ACKNOWLEDGMENTS We would like to thank W. K. Hartmann for kindly providing his most recent unpublished compilations of lunar crater counts. Reviews of this contribution and Paper I by S. J. Weidenschilling, G. W. Wetherill, and an anonymous reviewer are gratefully acknowledged. This paper constitutes Contribution No. 30 of the Basaltic Volcanism Study Project, which is organized and administered by the Lunar and Planetary Institute, operated by the Universities Space Research Association under Contract NSR 09-051-001 with the National Aeronautics and Space Administration.
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