Young thrust-fault scarps in the highlands: evidence for an initially totally molten moon

ICARUS 6 ~ , 421--441

(1985)

Young Thrust-Fault Scarps in the Highlands: Evidence for an Initially Totally Molten Moon ALAN B. BINDER l AND HANNS-CHRISTIAN GUNGA Erde-Mond Forschergruppe, Institut far Mineralogy, Universitdit Miinster, 4400 Miinster, West Germany Received February 20, 1985; revised June 29, 1985 Thermoelastic stress calculations show that if only the outer few hundred kilometers of the Moon was initially molten and if it bad a cool interior, i.e., the magma ocean model of the Moon, the highlands should not have any young, compressional tectonic features. In contrast, if the Moon was initially totally molten, the highlands should have 10-km- scale, ~<0.5- to 1 × 109-year-old thrust faults. Observations using the Apollo panoramic imagery show that young thrust faults do exist in the highlands. Extrapolation of the data suggests that some 2000 thrust-fault scarps, whose average length is 9 km, are in the highlands. The fault scarps generally occur in series or complexes of four or five scarps. The average length of these complexes is 50 km; the largest observed complex is 120 km long. Extrapolation of the data suggests that there are about 400 such complexes. The ages of the scarps range from 60 -+ 30 to 680 - 250 my, with a possible bias of up to plus a factor of 2 or minus a factor of 4. These scarps are by far the youngest endogenic features on the Moon. The selenographical, size, age, morphological, and azimuth frequency distributions of the scarps can be explained by the effects of the kilobar-level thermoelastic stresses, the 100-bar-level tidal and rotational stresses, and influence by preexisting structures. These results show that the Moon has recently entered an epoch of late stage, global tectonism and favor the concept that the Moon was initially totally molten. © 1985AcademicPress, Inc.

1.0. INTRODUCTION

The fraction of the Moon which was molten at the beginning of its evolution must be known if we are to understand lunar petrologic and tectonic development. It is generally believed that the Moon initially had a cool, unmelted interior and a magma ocean which was a few hundred kilometers deep. Thermoelastic stress calculations indicate that under these initial conditions the current global stresses in the lunar crust are less than about 1 kbar (Solomon and Chaiken, 1976; Solomon and Head, 1979) and therefore that the highlands crust should be free from any global, post-Imbrian, compressional tectonic features. Alternatively, some investigators have suggested that the Moon was initially totally molten (Runcorn, 1977; Binder and Lange, 1 Current address: NASA Johnson Space Center, SN-4, Houston, Tex. 77058.

1980). Thermoelastic stress calculations (Binder and Lange, 1980) show that under this initial condition the Moon should have young thrust-fault scarps in the highlands (Binder, 1982). Using lunar orbiter images, Schultz (1972) noted that young scarps exist in the highlands. More recently, a preliminary study of the Apollo high-resolution imagery indicated that these scarps are thrust-fault scarps and that they have the characteristics predicted on the basis of the initially totally molten lunar model (Binder, 1982). As an extension of that work, we present here the results obtained from an extensive study of these scarps. 2.0. PHOTOGRAPHIC DATA BASE

The high-resolution photographic data base used consists mainly of third generation copies of all of the Apollo 15 and 16, rectified, panoramic imagery with solar illumination angles (a) between 0 to 70°. How-

421 0019-1035/85 $3.00 Copyright © 1985 by Academic Press, Inc. All rights of reproduction in any form reserved.

422

BINDER AND GUNGA

1°4 79

b

6

3 1-

•

---] '[

L , r

I

O@ 10 20 3LO z.lO 50 0 t0 2'(? 3% /,0 50

Ilium,nation Angle (deg) FIG. I, Detectability of highland scarps as a function of the solar illumination angle. Histograms a and b give the number of pictures in which individual scarps and scarp complexes are observed vs illumination angle, respectively.

ever, as shown in Fig. 1, scarps could only be seen on pictures with 5 ° ~< ~ ~< 45 ° . The areas investigated using the Apollo 15 and 16 imagery with the latter range of a c o v e r 4.4% of the highlands and are shown in Fig. 2. Also, selected imagery was used to study four scarps noted during a review of the Apollo 17 panoramic data. 3.0. T H E O R E T I C A L AND E X P E R I M E N T A l , CONSIDERATIONS

3.1. Post-lmbrian Global Stresses Thermoelastic global stresses. Thermoelastic stress calculations made for both the magma ocean model (Solomon and Chaiken, 1976; Solomon and Head, 1979) and the initially totally molten model (Binder and Lange, 1980) show that the Moon entered a phase of tangential, compressional stress buildup in the crust about 3.5 × 10 9 years ago. Solomon and co-workers (1976, 1979) argue on the basis of the m a g m a o c e a n model that these stresses are currently <~1 kbar and that the magma ocean was about 300 km deep. Since this stress level is less than the ~> 1 kbar of stress needed to cause thrust faulting, it follows that the lunar highlands, which are free from any additional stresses caused by the

mare basalt loads (Solomon and Head, 1979), should not have any young, compressional tectonic features caused by the global, thermoelastic stresses and should be aseismic. If the M o o n were totally molten, the thermoelastic compressional stresses in the outer crust would now be theoretically at the several-kilobar level (3.5 kbar in the exemplary model used for the calculations given in this paper, Fig. 3) (Binder and Lange, 1980). Since such stress levels are well a b o v e those needed to cause thrust faulting and c o m p a c t i o n of the brecciated outer crust (Sect. 3.2), it follows that the stresses have been partially relieved by these processes. Thus, the Moon should have 10-km-scale, ~<0.5- to 1 × 109-year-old thrust faults in the highlands and highstress (1- to ~>3-kbar) m o o n q u a k e s should be occurring on these thrust faults (Binder, 1982). T h e s e conclusions are model dependent; m a g m a o c e a n models with deep (>300-km) melted zones and/or hot interiors also currently have kilobar-level stresses in the outer crust (Solomon and Chaiken, 1976). Thus, the thermoelastic stress characteristics of deep m a g m a ocean models and/or hot interior m a g m a ocean models are indistinguishable from those of the totally molten model. H o w e v e r , theoretical studies of accretionai heating, which is generally accepted as the cause of the melting of the outer part of the M o o n in the m a g m a ocean model, show that it is hardly capable o f producing even a shallow m a g m a ocealt (Ransford and Kaula, 1979: Wood, 1982). Thus, if there was a m a g m a ocean, it was probably shallow (<300 km deep) and the conclusions reached by Solomon and coworkers are probably valid, ff so, there should be a reasonable distinction between the current stress levels in the outer crust of the Moon if it had a m a g m a ocean or if it was totally molten, and the presence or absence of young, highland thrust faults should help us to distinguish between these two models.

FIG. 2. Areas investigated using the Apollo 15 and 16 panoramic imagery with illumination angles between 5 and 45°. The filled circles give the locations of the scarp complexes and individual scarps observed in these areas.

424

BINDER AND GUNGA SH

~

10

2o

032z+i

0

2

Z,

6

8

10

S~ress (kbar)

FIG. 3. Tectonic parameters in the outer 20 km of the crust. The filled square labeled SH is the maximum compressional stress in the magma ocean model of the Moon (Solomon and Head, 1979). Curves 0, I, 2, and 3 give the stress as a function of depth at the present and at 1, 2, and 3 by ago, respectively, in a typical initially totally molten Moon model (Binder and Lange, 1980). The heavy straight line and the two lighter lines give the average, maximum, and minimum stresses, respectively, needed to initiate thrust faulting in the lunar crust according to Eq. (7).

Tidal

and

rotational

stress

effects.

Global, but latitutde- and longitude-dependent, stresses also form as the selenoid (a triaxial ellipsoid form by the combined effects of the Earth's gravity field and the locked rotation of the Moon) relaxes toward a sphere as the Moon moves farther from the Earth (Melosh, 1980). Model calculations show that the tital and rotational stresses formed in the crust since the beginning of the phase of compressionai, thermoelastic stress buildup (about 3.5 × 109 years ago) have maximum compressional and tensional values of about 100 bar at the suband anti-Earth points and at the poles, respectively (Binder and Brandt, 1985). Even near the sub- and anti-Earth points, where these stresses are compressionat, they are too small to have helped the thermoelastic stresses cause any significant thrust faulting in a magma ocean Moon. In the case of a totally molten Moon, the tidal and rotational stresses are insignificant in comparison to the several-kilobar-level thermoelastic stresses as a cause of faulting. However, the differences between the

greatest (o-0 and least ((r2) principal stresses due to the tidal and rotational effects in the areas studied (Fig. 2) range from about 40 bar at 0°N, 0°E and 0°N, 180°E to about 150 bar at 0°N, 90°E (Binder and Brandt, 1985). Thus, when these stresses are added to the isotropic thermoelastic stresses, the resulting stress fields are latitude and longitude dependent. Hence, the weak tidal and rotational stresses may have i n f l u e n c e d the pattern of the highland scarps, even though they could have hardly helped cause the faulting itself. In order to evaluate the possible influence of the tidal and rotational stresses on the faulting, we consider the degree of anisotropy (X) of the combined stress fields, where X = (o4 - o-2)/o-l.

(I) Figure 4 shows the variations of X with time and longitude, in the equatorial region studied, for the exemplary stress models used (Binder and Brandt, 1985). First, the degree of anisotropy of the global stress fields is greatest at the limbs (90 °) and is nearly zero at the sub- and anti-Earth points (0 and 180°). Second, the degree of anisotropy of the fields was greatest at the beginning of the thrust-fault epoch (probably ~<0.5 to 1 x 109 years ago, but possibly <2 x l09 years ago) (Binder, 1982) and has decreased toward zero during the epoch. Thus, the

02 01 O0

0

30

60 90 120 150 180 Longitude (deg.)

FIG. 4. The degree of anisotropy (X) of the tangential stresses in the crust as functions of time and longitude in the equatorial regions according to the respresentatire stress models used in this paper. Curves 0.0, 0.5. 1.0, 1.5, and 2.0 give X as a function of longitude at the present and at 0.5, 1.0, 1.5, and 2.0 by ago, respectively.

YOUNG LUNAR THRUST-FAULT SCARPS faulting may be age and longitude dependent. Additional stress effects. Although the thermoelastic, tidal, and rotational effects are the only sources of global-scale stresses in the highland crust since the Imbrian, it is possible that young faulting has been controlled by local effects. However, as is shown below, the distribution and characteristics of the scarps are those expected if the faulting was primarily due to the global stress fields. Thus, local effects have not strongly influenced the faulting. 3.2. T H R U S T - F A U L T D Y N A M I C S

Fault dynamics theory has been presented in at least two forms, that by Coulomb and Mohr (Clark, 1966) and that by Anderson (1951). Comparison of these different formulations shows that they are identical in their definition of the stresses needed to cause faulting. We use the more straightforward, Anderson formulation in the following. The compressional, tangential stress (o'c0 needed to produce thrust faulting is given by

o-ct >- Kpgz + S,

(2)

where O is the density of the rock (2.9 g/ cm3), g is the gravity (162.3 cm/sec2), z is the depth to the fault surface, S is the crushing strength of the rock, and K is a function of the coefficient of friction (F), defined by K = (k/I + F 2 + F)/(N/1 + F 2 - F).

(3)

Also, the angle (0) between the greatest principal stress vector and the fault plane, i.e., the dip angle of the thrust fault, is given by 0 = ½arctan (I/F).

(4)

As shown in Section 5.1, indirect measurements of the dips of lunar thrust faults and Eq. (4) indicate that the average value of F is 1.11 + 0.04 with a 18 (root-mean-square

425

deviation) of 0.18. Using these results and Eq. (3), the average value of K is 6.8 --- 0.4, with 8 = 1.6. Since the/5 of K is relatively small, we can neglect the variations in K and just use its average value in evaluating Eq. (2), which becomes o-ct -> 6.8pgz + S

(5)

O'ct --- 0.32z (kbar/km) + S.

(6)

or

The crushing strength (S) of firm rock under lunar conditions is 4 --- 3 kbar (Binder, 1982). Due to the brecciation of the rocks in the outer few kilometers of the crust, S might be - 0 there. However, because of this brecciation, the rocks have considerable void space and the stresses building up initially only compact the brecciated rock. Only when it has been fully compacted do the ensuing stresses form thrust faults (see Sect. 3.3). Thus, S must be replaced in Eq. (6) by an effective S which is equal to the amount of " s t r e s s " (in reality, linear shortening) used up during compaction. Given the densities of lunar breccias (Talwani et al., 1973), the void spaces constitute up to 30% of their volume. Assuming for demonstration purposes that the brecciated zone has only 3% void space and that 102 to 103 individual cracks, etc., per unit volume make up the void space, then the amount of linear shortening of the crust needed to compact the material is 0.4 to 0.1%, respectively. This means that a 0.1 to 0.4% thermal contraction of the lunar radius, or 2 to 8 km, would be required to compact the material of the brecciated zone before thrust faulting could begin there. This amount of contraction is the equivalent of 1.5 to 7 kbar of compressional stress. Even though it is not possible to accurately quantify the amount of shortening needed for compaction, the example indicates that the equivalent stress needed to form thrust faults in the brecciated zone is of the same order as the 4 -+ 3-kbar crush-

426

BINDER AND GUNGA

ing strength of firm lunar rock (Binder, 1982). So, for simplicity, we take S as being equal to 4 -+ 3 kbar throughout the crust, and Eq. (6) becomes

ate faults and their dip angles are proportionally related (Binder, 1982), i.e., 0 = kto.

(9)

If these two concepts are correct, then 0, Z, F, and K can be determined via Eq. (3), (4), Figure 3 gives O-ct as defined by Eq. (7) (8), and (9), and measurements of to. In orand the thermoelastic, compressional der to help determine if these concepts are stresses in the lunar crust according to the correct, and because arcuate thrust faulting magma ocean model (Solomon and Head, has not been previously investigated, we 1979) and the totally molten model (Binder have studied thrust faulting in isotropic and Lange, 1980). From Fig. 3, there stress fields in the laboratory. should be no young thrust faults in the crust The experiments were carried out using a in the magma ocean model, while thrust circular, 1-m-diameter " s a n d b o x " whose faulting should be occurring in the outer - 6 bottom was covered with a thick rubber km of the crust in the totally molten model. bladder which formed a segment of a Following the arguments given earlier spherical surface when filled with water. (Binder, 1982), the epoch of young thrust Moist, sifted sand was deposited in a unifaulting may have begun as early as 2 × 10 ~ formly thick (10- to 15-cm) layer on the exyears ago, but significant thrust faulting tended bladder and then the water was let probably began about ~<0.5 to 1 × 109 years out. As the bladder collapsed, an isotropic, ago. Since the magnitude of the stresses has tangential, compressional stress field was steadily increased with time (Fig. 3), the produced in the sand and caused faulting. level of thrust-fault activity should also Upon drying, the sand became somewhat have increased with time. Also, because cemented since it contained a small amount the current maximum depth of faulting is of natural goethite. Because of this cement- 6 km, the resulting fault scarps should ing, the faults could be easily dissected to have dimensions on the 10-km scale. determine their geometry. The experimental results obtained varify two major points concerning the develop3.3. Arcuate Thrust-Fault Theory and ment of thrust faults. First, if the material is Experiments not reasonably well packed, no thrust faults Since the preliminary observations of the form. The entire shortening of the segment lunar thrust faults showed that their scarps is taken up by compaction. Thus, as indiare often arcuate (Binder, 1982), it was pro- cated in Section 3.2, thrust faults do not posed that the fault surfaces are segments .form in loose or brecciated material until of right-angle cones whose polar equation is the equivalent of" very large stresses are reached, even though the crushing strength z =Zrtan0, (8) o f the material is essentially zero. Second, arcuate thrust faults do form in where r is the radius, Z is the maximum depth of the fault, and z is the depth to any isotropic, tangential, compressional stress point on the fault surface (see Fig. 10a of fields and these laboratory arcuate fault Binder, 1982). According to Jacobs et al. scarps have the same characteristics as (1959), conical fault surfaces are expected those on the Moon (Figs. 5, 6a, and 6d). The experimental arcuate thrust faults to form in an isotropic stress field. So, conical faults should form in areas of the lunar have a limited range of angular extent (Tacrust where X - 0 (Fig. 4). It was also sug- ble I); tO varies only from 35 to 49 ° and has gested on the basis of the empirical obser- an average value of 40.4 _+ 0.9 °. Further, 0 vations that the half angles (to) of the arcu- does seem to vary linearly with to over the ~rct -> 0.32z (kbar/km) + 4 -+ 3 (kbar).

(7)

YOUNG LUNAR THRUST-FAULT SCARPS

FIG. 5. Arcuate thrust faults developed in laboratory experiments. Note that faults A and B have reversed directions of faulting (see Fig. 6b for a lunar comparison). Also, compare these laboratory arcuate faults with the lunar arcuate faults in Figs. 6a and d and 7b. The ruler in the picture is 22 cm long.

small range of observed values. Substituting the constant of proportionality, as defined by our experiments (0/~b in Table I), into Eq. (9) gives 2 ~,. 0 = (0.63 --- 0.02)tO = ~-

(10)

We assume that Eq. (10) is also valid for the Moon. The experiments also show that the arcuate fault surfaces approximate a segment of a right-angle cone. However, the dip angle decreases slightly with depth. Thus, the observed maximum depth of the fault is less than that calculated from Eq. (8). If this holds for lunar arcuate thrust faults is, of course, not known. 4.0.

HIGHLAND

THRUST-FAULT

SCARPS

Young, 10-kin-scale scarps do exist in the highlands (Mattingly et al., 1972; Schultz,

427

1972; Masursky et al., 1978). Although Schultz (1972) noted that the scarps were expressions of very young thrust faults, these earlier workers failed to recognize the origin or significance of the scarps. For example, in describing such scarps the Apollo 16 astronauts noted that "the scarps have the appearance of 'flow fronts,' yet lack evidence of source or of surface patterns," and that " a perplexing phenomenon was that when tracing an apparent west-facing scarp it would suddenly become an eastfacing scarp" (Mattingly et at., 1972). Masursky et al. (1978) noted that "small scarps of this kind--unrelated to any apparent source material or to any detectable tectonic control--are widely scattered in the highlands; their origin remains enigmatic." However, on the basis of the characteristics of highland thrust-fault scarps as predicted using the thermoelastic stress models (as discussed here in Sect. 3), Binder (1982) identified these features as being young thrust-fault scarps caused by the global thermoelastic stresses. Their identification as thrust-fault scarps is based on several criteria. First, the mor-

TABLE EXPERIMENTAL

ARCUATE

I THRUST-FAULT

DATA

Fault No.

R (cm)

tO (deg)

0 (deg)

O/t~

0 (deg)

Zc (cm)

Zo (cml

Zo/Zc

1-1 1-2 I-3 1-4 2-1 2-2 2-3 2-4 2-5

14.0 6.7 8.4 7.6 7.9 7.8 6.2 8.3 7.3

42 38 42 35 42 40 49 36 40

29 21 28 22 26 25 25 26 25

0.70 0.56 0.65 0.61 0.62 0.66 0.51 0.72 0.62

26 21 -19 21 22 20 23 22

7.8 2.6 4.4 3.0 3.9 3.6 2,9 4,0 3,4

>4.6 >1.8 ->1.4 >1.7 >2.0 >2.6 >2.1 >2.1

>0.59 >0.69 ->0.47 >0.44 >0.56 >0.90 >0.52 >0.62

Average o8

----

40.4 0.9 2.7

25.1 0.6 1.7

0.63 0.02 0.04

21.7 0.5 1.3

----

----

>0.60 ---

N o t e . R is the radius of the arcuate scarp; tO is the half angle of the arcuate scarp; 0 is the dip angle m e a s u r e d at the lip of the fault; ~ is the average dip angle of the fault surface which is slightly concave upward; Zc is the calculated m a x i m u m depth of the fault using R, 0, and Eq. (12); Z0 is the o b s e r v e d m a x i m u m depth of the fault and is a m i n i m u m value since excavation of the fault near its m a x i m u m depth is not possible due to the small a m o u n t of d i s p l a c e m e n t there; o- is the standard deviation of the mean; and eS is the root-mean-square deviation of the data.

428

BINDER AND GUNGA

FIG. 6. (a) Morozov scarp. Note the morphology of this arcuate scarp and the 250-m crater A which is cut by the fault surface. It is clear from the deformation of this crater that the scarp is a thrust-fault scarp. The length of the scarp is 14.8 km. The scarp is located at 7.0°N lal, 130.0°E long. (b) Aratus A

YOUNG LUNAR THRUST-FAULT SCARPS phology and geometry of the scarps are consistent with those of thrust faults. The morphology o f craters cut by the faults shows that the hanging walls have moved up relative to the footwalls (Fig. 6a), and there are often reversals in the direction o f m o v e m e n t of different segments of the scarps (Fig. 6b), a characteristic also seen in the laboratory experiments (Fig. 5). Second, these scarps are so young (<700 my old, Sect. 6.5) that they cannot be lava flows or ejecta blanket fronts of basin-forming impacts (as discussed in Sect. 4.4, the scarps are generally in complexes which are up to 120 km long and thus, if they were formed from ejecta, they would have to be associated with basin impact-sized e v e n t s - - a l l of which are very much older than the scarps). T h e y are not young debris flow fronts since many of them are on fiat, light plains units or climb hills. Third, the scarps are of tectonic origin since they show clear evidence of tectonic control in their orientations, their distributions as functions of age and longitude, and their morphologies. The observed thrust-fault scarps are listed in Table II and their characteristics are discussed below.

4.1. General Morphology The thrust faults fall into three general morphological classes: (1) linear (Fig. 6c), (2) arcuate (Figs. 6a and d), and (3) irregular (scarps 3, 4, and 9 in Fig. 7a). The linear thrust faults are expressions of anisotropic stress fields, while the arcuate thrust faults o c c u r in areas with isotropic stress fields (Sect. 3.3). Further, we suggest that the irregular scarps are also expressions of isotropic stress fields since these scarps generally have no preferred direction of thrusting

429

and they are generally associated with arcuate scarps. The scarps frequently consist of a series o f c o n n e c t e d subscarps (Fig. 6d). There are also scarps which have several connected, but branching subscarps, sometimes with additional disconnected subscarps (Fig. 6a). Some scarps consist of a series of closely spaced, but disconnected subscarps (Fig. 6c). All of these different types of scarps are distinct geometric features whose characteristic scale is 10 km. The scarps generally o c c u r in series of up to 10, but generally 4 or 5 scarps. The distance between the scarps in these series is roughly equal to the size of the scarps (Figs. 7a and b). We call these series of scarps " s c a r p c o m p l e x e s . "

4.2. Scarp Frequency A total o f 71 scarps have been found using the Apollo panoramic imagery; 9 are single features and 62 are members of 15 scarp complexes (Table II). The 62 scarps and 12 scarp complexes on the Apollo 15 and 16 imagery serve as the statistical basis for the following analysis. The usable Apollo 15 land 16 imagery covers 4.4% of the highlands (Sect. 2). Assuming that all of the scarps in the areas photographed at oc - 2 0 ° (at the maxima of the histograms in Fig. 1) were detected, we believe that the data given in Fig. 1 indicate that approximately 30 more scarps, which were not detected due to nonoptimum lighting conditions, are in the areas photographed with 5° ~< ~ ~< 45 °. Correcting the data for incompleteness and extrapolating from the 4.4% of the highlands studied to 100%, we estimate that about 2000 scarps are in the highlands, that about 300 of them are single fea-

scarps 9 and 10 (also see Fig. 7a). Note the reversals of the directions of the thrust faulting, both between the scarps (main directions indicated by the large arrows) and within scarp 10 at A, B, and C (minor reversals indicated by small arrows). Scarp 10 is 9.3 km long. The scarps are located at 21.8°N lat, 3.4°E long, and 21.5°N lat, 3.2°E long, respectively. (c) St. John scarp. This scarp is typical of those with a linear morphology. The scarp is 8.9 km long. The scarp is located at 7.2°N lat, 149.7°E long. (d) Mandel'shtam scarp 3 (also see Fig. 7b). This scarp is typical of those with an arcuate morphology. The scarp is 13.3 km long. The scarp is located at 6.6°N lat, 161°E long.

430

BINDER AND GUNGA T A B L E II--Continued

T A B L E II HIGHLAND

THRUST-FAUI

]

SCARPS

Scarp Complex

Scarp

Type"

(lat. l o n g ) Scarp Complex

Scarp

Type"

No

(lat, l o n g )

ol

~ubscarp~

I

( 7 , 5 ° S , 10.0°W) Palisa T

I

I

2

I

Ikm}

Mendeleev

II I1

:'

(8.1°S, 9 . 9 ° W I Hipparchus J

1

I,

17.8°S. 3 . 8 " E ) Aratus A

-

I.

6 6 St. J o h n

(22,3~N, 4.4"E ~

1

',

( 7 . 2 ° N . 149.7°E)

85

Henderson ! 7 . 5 ° N . 152.9°E1

. . . . . . I

I

2

2.~

2

l

t)

6 ,4

4

I

Iq

10.4

6

A I

l0 7

142 ~.9

7

I

l,

4 ~

8

I.

,,I 6 I) 9

9

1

1

l(I

A,

12

Mgdler A

47

I

-

I

A

Is

A

12

Ansgarius-Behaim (14.1°S, 79.8°E1

I2

I.

12

4

1 I

? 4

7

,,\

19

X

I

2

~4 q.8

10

104 ~4 12.4 92

I0

I

Bowditch (24.3°S.

22~ 64 89 16.8 92 92 122

I

I 101.8°E)

.

-

I

I

S

~

6

Kova'lskiy (21.0°S. 102.5°[ -)

~2

I. -

.

I

I

I

2

I

l.

.

48

.

.

I,

1,

14 6

1 ~,~ II.1

3

I.

2

7.1

I

I,

9

~;q

-

1 .

.

45 .

.

.

I 2

I I. 1.

16 4

8.0 14.2 ti4

4 5

[ L

~ I

0.7

6

-

I. .

.

.

8.2 24

.

.

I

I

2

~ 7

2

&

9

¢~.8

I

4

A .

.

.

.

6 t

~3 .

I

A

2 4 > 6 v

A A I ,X '~ .•

II 20 13 18 14 18

g.0 1~.4 I t . ~, 8.0 12 ; 9.9 %9

]

I

2

I ~

1 _ +

I 2 Aitken NI! { 14,6°S, 176,2 E /

__

2

.

3

Sharonov ( 9 . 1 ° N , 172.4°E) Aitken 116.2°S. 1 7 4 . 4 E

-.

.

I 2

Mandel'shtam ( 6 . 2 ° N . 161,2°El

194 197

I

.

(9,7~N, 157.0°E~

12O

I

tkm)

L .

Mills

(9. V'S, 29.8°E} 2

Length

I ength

19. I ° N , 141.6°E) Lalande A

No. of subscarps

-

24

A

7

7(,

I

9

I~1,7

I.

.43

I

1

9

7.t~

2

I,

14

12.4

[

]7

197

13.~

De Vries (19.0°S, 1 8 2 . 0 ° E )

9 (I

I

I

7

2

1

8

9. ~

"8

4

1

2

Kondratyuk

I

1

t

21 2(Lt~

114.5°S, 1 1 6 A ° E ) l,angemak

I

I

4

23~

( 12.T~S. 1 2 0 . 0 ° E ) Fermi

I

I

4

..... ,~

" 1. = l i n e a r , A

(20. I ' S . 122.4°i:A l.titke ( ]7.6'S,

I 123.3q~Jl

"

I

1siolkovsky ~ 2 0 , & S , 125,6°E}

Morozov

ilregtllar.

tures, and that the remainder are in about 400 scarp complexes.

-

,_9

L

4~ ,)7

I

I

I

2 :~

I

I

A

I

I¢, I

2I

'~ 29

~48

17.0°N, 130.0°El Walerman 124.WS, 131.4"i%

arcuate, and I

I I

I

I

2

I

7

2, ..., ~"

4.3. Morphology Frequency Distribution About 60% of the scarps and 70% of the complexes are basically linear structures formed by anisotropic stresses or, in a few cases, influenced by preexisting structures (Table I1). About 20% of the scarps and 10% of the complexes are arcuate. The remaining 20% of the scarps and 20% of the complexes are irregular. Thus, 30 to 40% of

YOUNG LUNAR THRUST-FAULT SCARPS a o

10

431

I

t/

g

:p130

0

/-%---.o

7 15~-50

8 >70

0

~

10

v 6

o /.

o (280~-G01

0

-'r-

1 i.~ "It "ll

.y 0

160--30

oe

o

0

o

0

2 >tO

C)

OA:,° \ oo

h

o

©

0

O o

180±~-~)

0

,g~

0

"

'~ ,~._-,0,X O ~

lg0._s0

;~,,

10 km

FIG. 7. (a) A r a t u s A scarp complex. T h e age (in my) of each of the 10 scarps of this c o m p l e x is given next to the scarp n u m b e r . L o w quality ages are given in parentheses. The c o m p l e x is centered at 22.3°N lat, 4.4°E long. (b) M a n d e l ' s h t a m scarp complex. Otherwise, same as a. The c o m p l e x is centered at 6.2°N lat, 161.2°E long.

432

BINDER AND GUNGA 13 12 11 10 9

8 7

\

6 5 N

z, 3 2

q

1 0

I 2

I

I

I--J

6 8 Length

l

10 12 (ki n)

~

|_ 18 2 0 2 2 2 4 3--_L

1L %

l

These results show that the highland scarps have a characteristic size which is in excellent agreement with the theoretical result that the scarps should be on the 10-km scale (Sect. 3.2; Binder, 1982). The lengths of the complexes range from 20 to 120 km and have an average of 51 +- 5 km. The 50-km scale of the scarp complexes is so large that they are clearly major tectonic features of the highlands. This is well demonstrated by the 80- to 85-km-long Aratus A and Mandel'shtam complexes (Figs. 7a and b) or the 120-km-long Ansgarius-Behaim complex. 5.0.

FIG.

8. Frequency

distribution

PHYSICAl.

of the lengths of the

scarps.

the areas studied have, or had, essentially isotropic stress fields. The morphology of about 20% of the scarps and complexes seems to be controlled by nearby topographic or structural features: The Aratus A linear complex is parallel to the Apennine front which is only I00 km to the N W , and the greatest principal stress vectors of the main linear elements of the complex are within 1° of being radial to the center of the Imbrium basin which is 750 km to the N48°W of the complex. The Tsiolkovsky scarps and about half of the Mendeleev scarps are parallel to the adjacent rims of the larger craters in which they lie. The remainder of the Mendeleev scarps have the same trend as a nearby, prominent crater chain which has been interpreted as a series of diatremes formed on a deep tissue (Mailer and Binder, 1983). However, 80% of the scarps and complexes do not show any obvious effects of local tectonic control and so it appears that the statistical studies are not seriously biased by these local effects.

4.4. Size Frequency Distribution From Table II and Fig. 8, the lengths of the scarps range from 0.7 to 22.3 km, average 9.0 -+ 0.4 km, and have a maximum in their frequency distribution at ~ 8 km.

DATA

FROM

THE

ARCUATE

FA U LTS

The data for 25 arcuate scarps found in the areas studied, as well as those for the arcuate c o m p l e x - - M a n d e l ' s h t a m - - a r e given in Table III. Of these features, the

TABLE ARCUATE

Scarp

Lalande A, la Lanlande A, Ib M~.dler A. 1 Aratus A, 5 Ansgarius-Behaim. 4 Ansgarius-Behaim, 7a Ansgarius-Behaim, 7b Bowditch, 2 Morozov, la Morozov, Ib Morozov, Ic Henderson, 2

Mandel'shtam (complex) Mandel'shtam. 2a Mandel'shtam 2b Mandel'shtam 2c Mandel'shtam 3a MandeFshtam 3b Mandel'shtam 3c Mandel'shtam 4 Mandel'shtam S Mandel'shtam 6 Mander shtam, 7 Aitken, 1 Aitken. 3 De Vries. I Avg. ~r

111

FAULT

DATA

R (kml

tO (deg)

0 tdeg)

t.I 1.6 ~.8 4.0 2,1 f.t 7.3 6.4 t.2 2.4 10,5 5,0 59 2.5 19 1.9 6.1 2.4 7.9 1).9 9.0 22 t9 81

3s 42 30 46 4q 29 29 311 34 28 ~2 ~6 45 "~6 t8 3X 27 48 35 4(1 34 30 32 29 27 29

22 26 19 29 27 18 18 19 22

341) 0.8 L9

21.4 O.S 2.~

I 8

2.4

Z (kml 12 0.S 1.3 2.2

2(1

I.t [.s 24 22 13 08 18

22

2 1

22 24 21 17 ~(I 22 23 21 19 2(I 18 I7 18

Io 119 117 I 8 14 a.2 I1 4 3. ~ o.g 1.4 2.7

Ig

(I.t~ 118

1.04 I).77 1~2 0.6~ 073 1~4 I.t4 1.28 107 1.41 I Ig I Ol I Ol 1189

I.II I.ql 0.~8 1.02 08~ I I0 I 26 121) 1~4 147 I 34

III O.(H 1118

N o t e . 0 was derived using Eq. ( 10); P was derived using Eq. ( I I I; and /7 was derived using Eq. 112).

YOUNG LUNAR THRUST-FAULT SCARPS 6

433

a

6 -b

5

5

4

4

3

3 N 2

2 1

1

0 2Z,

00.5/h 07

28

32

36

40

44

48

I

0.9

1.3

11

1.5

1.7

F

FIG. 9. (a) Frequency distribution of the half angles (+) of the arcuate scarps. The dashed line is a smoothed curve which passes through the ~nn errors of the data. (b) Frequency distribution of the coefficient of friction IF). The dashed line is a Gaussian curve which passes through the ~ errors of the data.

M o r o z o v scarp and the Mandel'shtam complex are the best examples (Figs. 6a and 7b). Mandel'shtam is worthy of special mention since six of its seven scarps, most of which are arcuate or have arcuate subscarps, form a 83-kin-long arcuate structure whose angular extent is nearly 90 ° .

5.2. Depth of Faulting The maximum depth of faulting (Z) on the proposed conical faults, as derived from Eqs. (8) and (10), is given by

5.1. Half Angle, Dip Angle, and Coefficient of Friction The half angle (tO) of the arcuate scarps varies from 27 to 48 ° , has an average value of 34.0 +- 0.8 °, and has a root-mean-square deviation (8) of 3.9 ° (Table III). The frequency distribution of to is strongly skewed toward smaller values (Fig. 9a). A smooth curve drawn within the ~ errors of the data suggests that they have a skewed Gaussian distribution; if so, then the skewing of the data must have a physical basis. Since by Eq. (4) and (10) tO = 0.79 arctan ( l / F )

data in Table III and Eq. (10) and (11), the average value of the dip angle (0) is 21.4 +0.5 ° with 8 = 2.5 °, and the average value of F is 1.11 --- 0.04 with 8 = 0.18.

Z = tan 0 = R tan(0.63to),

(12)

where R is the radius of the scarp. The maximum values of Z are all less than the estimated current maximum depth of faulting of about 6 km (Table III and Fig. 10). Also, e x c e p t for the paucity of faults with Z less than about 800 m, the number of faults with a maximum depth of faulting Z drops off essentially linearly with depth. This dep e n d e n c y is expected since the difference between the stress in the crust and the mini-

(11)

a skewed distribution of tO would result if the coefficient of friction (F) has a Gaussian distribution. As is shown in Fig. 9b, the frequency distribution of F is Gaussian within the ~nn errors of the data (Table III). We interpret this result as supporting the concept that the dip angles of the faults and the coefficient of internal friction of the rocks can be determined indirectly from measurements of the half angles of the arcuate scarps (Sect. 3.3). On the basis of these conclusions, the

7 6 5 4 3 N 2 1 0

]

i

0

I

L

I

1 2 Depth (km)

L

i

3

I

4

FIG. 10. Frequency distribution of the maximum depths of faulting of the arcuate thrust faults.

434

BINDER AND GUNGA

A

Bowditch 2 ._ ) \\

//

Aratus A 3

Palisa T 1

tl~ tt2 %\\%!44,d

/////1 b ~tl,

,t2

i2t

,t1

The m a x i m u m and minimum age data are given for three representative scarps in Fig. 11. Plots A and B are typical for the majority of the dated scarps, with A yielding a m o r e well-defined age than B. In these cases the scarp age (T) is defined as T-

~a~L,l

L L thuA

107 10~ Age (yr I

i

~ ~IL~I___

109

FIG. I I. Representative plots of the m a x i m u m and m i n i m u m crater age data used to determine the ages of the thrust-fault scarps. The m a x i m u m and m i n i m u m ages are represented by left- and right-facing arrowheads, respectively (see the text for further details).

m u m stress needed for thrust faulting also d e c r e a s e s essentially linearly with depth (Fig. 3), and it is likely that the probability that faulting will o c c u r is proportional to this stress difference. The paucity of faults with Z < 800 m may be due to two effects. First, faults with Z < 800 m have scarps which are typically less than 2 km long and therefore are so small that it is difficult to judge if they are arcuate or not. Hence, the lack of faults with Z < 800 m m a y just be a sampling problem. Second, as deduced from Sections 3.2 and 3.3, the strongly brecciated nature of the outer several 100 m of the crust may prevent the formation of faults which are so small that they would be limited in depth to this region. 6.0. SCARP AGE DATA 6.1. M e t h o d

The ages of the scarps were determined as follows: A m a x i m u m age for a scarp was determined from the ages of the craters which are partially o v e r r u n - - o r cut by the fault. Its m i n i m u m age was determined from the ages of craters which are on the scarp front where slumping and landsliding caused by the m o v e m e n t of the fault would destroy all older craters each time it was active.

(t~ + t2)/2,

(13)

where t~ and t2 are the limiting minimum and m a x i m u m ages as indicated in the figore.

Plot C in Fig. 11 is representative of only a few scarps. In these cases the limiting m a x i m u m age(s) determined from lhe crater(s) partially overrun or cut by the scarp is y o u n g e r than the minimum age(s) as determined from the crater(s) on the scarp front. Since the craters located on the front are younger than as determined by the T r a s k method (Sect. 6.4), we assume that the age of the scarp is equal to the age of the youngest crater partially overrun or cut by the scarp, i.e., T = t2,

(14)

where t2 is the limiting m a x i m u m age indicated in the figure. 6.2. Crater A g e C o m p u t a t i o n s

The crater ages were c o m p u t e d following the Trask method (Trask, 1971) in which the craters are classified according to their state of degradation (class 1, totally degraded, to class 6, fresh) and using the calibration data of M o o r e et al. (1980). The age of a crater (t, in units of 106 years) is computed from its degradation class and its dia m e t e r (D, in meters) using t = t010 °'7 tog D

(15)

as derived f r o m Fig. 7 of Moore et al. (1980), where to is a constant for the degradation class of the crater (Table IV). 6.3. I n t e r n a l Error C o m p u t a t i o n s

The internal errors of the ages were calculated on the basis of the following considerations: (1) We found that the craters are classi-

YOUNG LUNAR THRUST-FAULT SCARPS T A B L E IV DEGRADATION AGE CLASS CONSTANTS Degradation class

Class constant

6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

0.74 1.05 1.6 2.4 3.8 6.9 12 17 21 29 36 46 55

fled with a _+½ degradation class uncertainty. So, the tl and t2 ages in Eq. (13) have errors dh and dt2 calculated from Eq. (15) using a ½ class error. (2) T a s defined by Eq. (13) has a (t2 - tO~ 2 error c o m p o n e n t . (3) We assume that the errors propagate like normal errors. Thus, in the limiting case for Eq. (13), where tl = t2, dh 4: O, and dt2 4: O, the error in T (dT) is given by a T = ½ %/dt 2 + dt~.

(16)

Also, in the limiting case for Eq. (13), where t2 > ti and dtl = dt2 = O, d T i s defined by consideration (2) above as d T = (t2 - h)/2.

(17)

It follows that in the general case (A and B in Fig. 11), d T is given by dT=

½"X/dtZl + dt~ + ( t 2 - t0 2. (18)

(4) In case C (Fig. 11), where the age is given by Eq. (14), d T = dtz.

(19)

6.4. B i a s e s

The scarp ages are subject to a number of biases and are therefore a p p a r e n t - - r a t h e r

435

than t r u e - - a g e s . The possible sources of biases are as follows. (1) The Trask method (Trask, 1971) was developed for mare craters which are on level surfaces. H o w e v e r , the degradation rates increase with increasing slope and depend on the strength of the surface material (Schultz et al., 1977), so the age of a crater depends on the slope and character of the local surface, as well as its diameter and degradation class. The effect of slope is not considered in the calibration data of Moore et al. (1980). H o w e v e r , the calibration data were obtained using craters on the ejecta blankets of highland craters and are therefore valid for surfaces with small slopes, rather than for fiat surfaces. Thus these data can be used without serious bias for large parts o f the highlands discussed in this paper. Nevertheless, a significant fraction o f the scarps studied are on surfaces with moderate slopes; thus, if the age data are biased by this effect, the true ages are younger than calculated. (2) Since craters degrade faster on steeper slopes, the ages determined for the craters on the relatively steep slopes of the fault scarp fronts are definitely biased toward older apparent ages compared to the craters which are cut or partially overrun by the faults and which are on relatively level surfaces. Thus, the minimum tl ages used in Eq. (13) are biased toward older ages c o m p a r e d to the maximum t2 ages; so the true ages of the scarps are y o u n g e r than calculated. (3) About two-thirds of the craters used to define the minimum tl ages and the maximum t2 ages have diameters between 10 and 40 m. Since the resolution of the panoramic imagery is about 2 m, most of these craters are not too well resolved. This effect softens the apparent morphology of the craters and makes them look older than they really are. Thus, the true ages of the scarps are again y o u n g e r than calculated. So, the possible biases which affect our data all result in apparent ages which are older than the true ages. The magnitude of

436

BINDER AND GUNGA TABLE

TABLE

V

THRUST-FAUI.T AGE DATA Scarp complex, scarp, subscarp

Age (my)

P a l i s a T, I

Aratus A Aratus Aratus Aralus Aratus Aratus

A, 3

A, A, A, A,

4 5 6 7

Mddler A" M/idler A. I M/idler A, 2a Mfidler A , 2 b

Ansgarius-Behaim" Ansgarius-Behaim. Ansgarius-Behaim. Ansgarius-Behaim. Ansgarius-Behaim, Ansgarius-Behaim, Ansgarius-Behaim, Ansgarius-Behaim,

Bowdit<'h Bowdilch, I Bowdi,tch, 2

Koval'sk~v" Koval"skiy, I Koval'skiy, 2 Koval'skiy, 3 Kondratyuk. I Fermi. |

Lt~tke IAi,tke. 1 1.0tke. 2

Tsiolkousky Tsiolkovsky, 1 Tsiolkovsky, 2 Tsiolkovsky, 3 Morozov, I

Waterman Waterman, Waterman,

1 2

Mendeleev Mendeleev, I Mende~eev. 3 St. J o h n , 1

ttenderson Henderson, 2 Henderson, 3 Henderson, 4

Mills Mills, 2

Mandel'shtam Mandel'shtam,

I

1 3 4 6 8 9 10

210 +- 4(1 160 + 30 2 8 0 ± 160 150 ± 50 16(1 ± 311 190 -+ 150 160 + 511 61) :± 30, 1511 + 30. 4 6 0 + ll}11 6(I :~: 3(1 150 + 30 460 ± I(X) 80 ± 50. 240 + 511 2611 + 50 190 + 150 2411 ± 511 140 + 80 250 + 230 120 + 100 80 + 50 ~311 ~ 80 3511 + 170 330 ± 80 240 ± 60, 6211 + 28t1 620 + 2811 2 1 0 + 110 220 ± I ~ I 680 + 25(1 310 + 1811 1511 -+ 31t 3 4 0 .! 150 + 311 6 0 + 4(1 60 + 411 9 0 + 70 160 + 1511 140 ± 50 270 + th) 270 ~: 90 220 + 90 150 + 30 150 ± 3(1 350 + 320 3110 + 1111 210 ± 61) 290 + 1211 2 0 0 + 50 530 ± 330 410 + 270 4 1 0 ~- 2 7 0 180 ± 50 170 Jr 70

V--Continued Age (myJ

Scarp complex, scarp, subscarp Mandel'sh,tam Mande['shtam MandeFshlam Mandel'shtam Mandel'sh,tam Mandel'shtam Sharonov, I

Aitken Ai,tken, 2

Aitken NE Ai'tken N E. I Ailken NE, 2 Aitken NE, 3

l)e Vrics De V r i e s , I De V r i e s , 2 De V r i e s , 3

2 3 4 5 6 7

180 ± 611 180 ± 511 100 + 7 0 1911 ± 511 181t + 511 19(J + 71t 1711 + 40 39(1 + 18(1 2 9 O ± 24O 170 + 5(1 250 ± 250 220 ± gO 150 + 611 2411 + 10(1 2 3 0 _+ 190 240 ± I @1 4 0 0 + 28t)

" Complex wilh multiple ages. Note. C o m p l e x e s a r e g i v e n in italics; s c a r p s a r e g i v e n in n o r m a l t y p e ; h i g h q u a l i t y a g e s a r e g i v e n in n o r m a l t y p e ; l o w q u a l i t y a g e s a r e g i v e n in b o l d f a c e .

the total bias is u n k n o w n . H o w e v e r , Moore et al. (1980) suggest that the ages derived using their calibration data have a bias of up to plus or minus a factor of 3. Considering this value and the fact that all of the biases lead to overestimations of the scarp ages, we suggest that they may have biases of up to plus a f a c t o r o f 2 or minus a f a c t o r o f 4. 6.5. General Results Table V gives the ages determined for the observed scarp complexes, scarps, and, in two cases, individual subscarps. The ages whose uncertainties are <50% (normal type) are used as the basis for the statistical studies discussed here. Those ages with errors > 5 0 % (boldface) are not considered further in this study, with the exception of those ages which are < 100 my. These ages are so young that even a >50% error is small in absolute terms, and so these ages are statistically significant. Scarp ages. With the exception of one pair of subscarps discussed below, all the subscarps of each scarp have ages which

YOUNG LUNAR THRUST-FAULT SCARPS Morozov

tl,t 2

o

150+-1-.0my (

b

( "-.

my

//all x t2

K

d

107

108

< 290 my

109

Age (yr.) FIG. 12. Plots of the m a x i m u m and minimum crater age data used to determine the ages of the Morozov subscarps and the scarp itself. Otherwise, same as Fig. I 1.

are consistent with a single age for the entire scarp. As an example, the age data for the subscarps of the Morozov scarp are given in Fig. 12. The limiting t~ and t2 ages are generally consistent with a uniform age and, even though the computed ages indicate that the different subscarps might have different ages, the uncertainties are always larger than the possible age differences. Thus, we conclude that the subscarps of each scarp have the same age and compute the scarp age from the combined data from all the subscarps. Scarp complex ages. The ages of the scarp complexes are of two types. First, the data for the majority of the complexes show that all of the scarps of a complex formed at the same time. The most impressive examples of this type are the large complexes Aratus A and Mandel'shtam (Figs. 7a and b). The age data for Mandel'shtam are shown in Fig. 13, which demonstrates how consistent the limiting tl and tz ages determined individually for each scarp are; the entire complex has an age of 180 -+ 50 my. The only possible exception is scarp 4 whose low quality age of 100 +_ 70 my suggests, but does not require, that this scarp is younger than all the others in this complex. The age of this type of complex was computed using Eq. (13), the oldest limiting

437

h age, and the youngest limiting t2 age taken from all the data for all of the scarps in the complex; i.e., the entire complex was treated as a single scarp. Though the uniformity of the scarp ages within a complex of this type might mean that the faulting activity in all the scarps ended simultaneously after a long period of development, this is statistically unlikely. We believe that the uniformity of the scarp ages means that the period of development of the entire complex was very short in comparison to its age. Second, three of the complexes (M~idler A, Ansgarius-Behaim, and Koval'skiy) consist of scarps and, in the case of Madler A, subscarps with distinctly different ages. The data for these three complexes (Table V) indicate that thrust-fault activity produced scarps, intermittently (?), over periods of up to 400 -+ 100 my. The age differences between the successive scarps or subscarps within each of these complexes vary from 90 -+ 40 to 380 - 290 my and

MQndeUshtom ~ // l/f/// 2-

~ 170±70

. "-L. ~JJ~ 180+-60 )//#/rib (<((( t~,t2 180-'50 \ \\\\ \\ \"J/////--/~ / ////// /_,'INN\\\\

)

3 -- )

,

>

5 )

\

<1oo: o t~,,t~ 19o-'so

6-

/

\ \ %\\%\Xlv / / / / /

///.'/.z~4 F \ \ \ x \ \ .~/180±50

~>b

.- , ~ , \

,t2 190"70 \ \ \ \~] V/ / J I

7 ,

/// / 4 Y\ -.x.

,

,I,,,A

,

,,I,,,d

107 108 Age (yr.)

,

,,h,,d

109

FIG. 13. Plots of the m a x i m u m and minimum crater age data used to determined the ages of the seven Mandel'shtam scarps and the Mandel'shtam scarp complex. Otherwise, same as Fig. II.

438

BINDER AND GUNGA 10 9 8 7 6

6.6. Secondary Age Ejfects Size-age dependency. F r o m Fig. 3, the

It__ ! I !

maximum depth of faulting should have increased essentially linearly with time from 0 to about 6 km during the faulting epoch. II follows that the lengths of the faults should have also increased essentially linearly with time, which is the case (Fig. 15).

-1

L

0

FIG.

0

120

2/,0 360 480 Age (my)

500

720

14. Frequency distribution of the ages of the

scarps.

average 230 _+ 50 my. Thus, some of the complexes developed over very long periods of time.

Age of the highland thrust-fault epoch. Figure 14 gives the age frequency distribution for the scarps. Excluding the paucity of ages less than 120 my (which we believe is due to the biases which lead to overestimations of the scarp ages, Sect. 6.4), this figure shows that the development of the scarps began about 700 my ago and that the level of activity has increased with time. These results are in excellent agreement with the theoretical findings (Binder, 1982: Sect. 3.2) that the highland thrust-fault epoch probably began ~<0.5 to 1 × 109 years ago and that the level of activity should have increased with time as the thermoelastic stresses increased (Fig. 3). H o w e v e r , before we accept the above results, we must consider the possibilities that crater erosional and depositional effects destroyed scarps which were older than 700 my and caused the apparent increase in the n u m b e r of scarps with time. If these were the cases, then the scarps should show strongly increasing degrees of degradation with increasing age, with the oldest scarps being nearly completely destroyed. H o w e v e r , our observations show that neither of these are the case. Thus, we believe that the above stated results are valid.

Age-morphology-longitude dependencies. The histograms given in Fig. 16 show that as a class, the irregular scarps tend to be slightly younger than the arcuate scarps. which in turn tend to be younger than the linear scarps. The average ages of the scarps in these morphology classes are 170 -+ 30, 200 -+ 20, and 270 _+ 20 my, respectively. While the mean ages of the irregular and arcuate scarps do not differ by a statistically significant amount (hence, we consider them as a single group in the following), the average age of the linear scarps is clearly greater than those of the first two groups, collectively (190 _+ 20 my), or as separate classes. Since linear scarps are formed by anisotropic stress fields, while both irregular and arcuate scarps formed in essentially isotropic stress fields (Sect. 4.1 ), the age differences between the linear and nonlinear scarps support the theoretical 20

"~

+

10

==

0

I 0

I

200 400 Age ( m y )

I 600

FIG. 15. Average lengths of all the scarps with ages between 0 and 200 my, between 200 and 400 my, and >400 my as a ['unction of age.

YOUNG LUNAR THRUST-FAULT SCARPS 3

the direction of faulting of the scarps. Note

Irregular

[-~

I

I

I

I

I

Arcuate

4

1 I

I

Linear

4 3 2 1

o

0

120

240

360 480 Age [my I)

600

that the rose diagrams discussed here are for the directions of the principal stresses, not the strike directions of the scarps. 7.1. Theoretical Considerations

3 2 o

439

720

FIG. 16. Frequency distributions of the ages of the irregular, arcuate, and linear scarp groups.

I f only the isotropic, thermoelastic stresses caused the faulting, and preexisting structures did not influence it, then the highland fault scarps would show no preferred orientations. H o w e v e r , as is indicated by the age data (Sect. 6.6), the stresses due to the tidal and rotational effects have also affected the faulting, and so the global stress fields have not been completely isotropic. The combined fields due to the thermoelastic stresses and the tidal and rotational stresses have their greatest principal stresses oriented e a s t - w e s t in the equatorial region studied. Thus, if there are no additional controlling effects, the direction of thrusting should be e a s t - w e s t .

result that the degree of anisotropy of the global stress fields has steadily d e c r e a s e d toward zero during the thrust-fault e p o c h 7.2. Stress Pattern (Fig. 4 and Sect. 3.1.). The azimuth f r e q u e n c y distribution of H o w e v e r , Fig. 4 not only shows that X the principal stresses is neither randon nor d e c r e a s e d during the faulting epoch, but e a s t - w e s t oriented (Fig. 18). Considering also that X is strongly longitude dependent. the X/n counting uncertainties, Fig. 18 indiF r o m this figure, the linear scarps should cates that there are two major stress vector also be m o r e frequent near the limbs than directions, N63 ° + 2°W and N65 ° -+ 2°E. n e a r the sub- and anti-Earth areas. This T h e s e directions are about 10 ° greater theoretical conclusion is weakly supported t h a n - - b u t a p p e a r to be related t o - - t h e maby the data s h o w n in Fig. 17, in which the j o r strike directions of the lunar lineaments p e r c e n t a g e o f linear scarps, with respect to (N54°W and N54°E) as defined by Strom all scarps, in 45 ° longitude segments are (1964). F o r c o n v e n i e n c e , we define the plotted against longitude. E v e n though the quantity A as the sum of the angles between uncertainties are large, the limited data 100 tend to show that linear scarps are rela8O tively m o r e a b u n d a n t near 90 ° than near 0 and 180 °. Also, the four points in Fig. 17 do 60 % tend to fit a c u r v e w h o s e f o r m is that of X as 40 a function of longitude (Fig. 4). 20

7.0. AZIMUTH FREQUENCY DISTRIBUTIONS OF THE GREATEST PRINCIPAL STRESSES We present in the following the results of a study of the azimuth f r e q u e n c y distributions o f the directions o f the greatest principal stresses of the fields as determined from

0

I

o

30

I

I

I

I

I

60 g0 120 150 180 Longitude (deg)

FIO. 17. Percentage of linear scarps with respect to all scarps within 45° segments of longitude as a function of longitude. The curve through the points is from Fig. 4 and is shown for comparison.

440

BINDER AND GUNGA N54W 6,~

N63W ±2 N35W / ~ ..... _+2 ",, "~'---. b,

-'1 . / ~

~

.6SE S

~\ / /

N54E G

*-2

,/

....

O ~ q-- -~5

/

""'

FIG. 18. Rose diagram of the directions of the greatest principal stresses of the thrust faults. The scale at the bottom of the diagram gives the number of stress vectors per unit length in the diagram. The major strike directions of the lineaments at N54°W and N54°E are indicated by arrows and the letter G (see the text for further details).

the two main stress axes m e a s u r e d from the E - W axis (Fig. 18). A/2 is therefore a measure of the deviation of the o b s e r v e d major stress vectors f r o m the theoretically defined E - W axis of the global stress field (Sect. 7.1). In these terms, the o b s e r v e d stress vectors have A/2 = 26 -+ 2 °, while the strikes of the lunar lineaments have A/2 = 36 ° . We interpret these observations to m e a n that the preexisting structures of the ancient lunar lineaments have s o m e h o w modified the global stresses so that the directions of thrust faulting tend to follow the lineament strike directions. The fact that A/2 for the stress axes is 10 + 2 ° smaller than that of the strikes of the lineaments may mean that the modification of the principal stress directions is not perfect and thus the new directions are intermediate between their theoretical E - W direction and those of the lineament strikes. If so, then both in the areas near the sub- and antiEarth points and late in the faulting epoch, where and when the global stress fields were nearly isotropic (X -~ 0 in Fig. 4), the relative influence of the lineament system should be strongest and the A/2 of the stress vectors should be close to the 36 ° value of the lineaments. C o n v e r s e l y , both in the areas near the limb and early in the epoch, where and when the E - W anisotropy of the fields was greatest (X ~ 0 in Fig. 4), ~/2 of the stress vectors should be relatively small. This is what the limited data show.

Rose diagrams for the scarps within _+45° of the sub- and anti-Earth points and for the scarps which are younger than 200 my old both have A/2 = 32 -+ 2 ° , while the rose diagrams for the scarps within _+45° of the limb and for the scarps which are older than 200 my have A/2 = 25 --+ 4 ° and 25 _+ 2 ° , respectively. The data (Fig. 18) also suggest that there is a principal stress v e c t o r which is essentially E - W (N84 ° _+ l°W) and which is p r o b a b l y the unmodified E - W primary global field. Finally, there is a N35 ° _+ 2°W stress v e c t o r which m a y be related to a similar s e c o n d a r y strike direction of the lineaments (Strom, 1964). 8. SEISMOLOGICAL EVIDENCE

The stress model for a totally molten Moon predicts that high-stress (1 to ~ 3 kbar) m o o n q u a k e s o c c u r as the young, highland thrust faults form. As discussed by Binder and Oberst (1985), an analysis of the 28 o b s e r v e d shallow m o o n q u a k e s suggests that 3 of them have minimum stress drops which are in the kilobar range. Thus, the possible o c c u r r e n c e of kilobar-range stress drop, shallow m o o n q u a k e s is consistent with the c o n c e p t that the highland scarps are caused by kilobar-levei thermoelastic stresses. 9. SUMMARY AND CONCLUSIONS

Thermoelastic stress calculations show that if only the outer few hundred kilometers of the M o o n were initially molten and if it had a cool interior, as p r o p o s e d for the m a g m a o c e a n model of the Moon (Solomon and Chaiken, 1976; Solomon and Head, 1979), the highlands would not have any young, compressional tectonic features and should be aseismic. If the Moon were initially totally molten (Runcorn, 1977; Binder and Lange, 1980), the thermoelastic stress calculations show that there should be 10-kin-scale, ~<0.5- to 1 x 109-year-old thrust faults in the highlands and that highstress (l- to ~>3-kbar) m o o n q u a k e s should be occurring on these faults (Binder, 1982). O b s e r v a t i o n s using the Apollo panoramic

YOUNG LUNAR THRUST-FAULT SCARPS

imagery substantiate preliminary findings that thrust faults do exist in the highlands (Binder, 1982), and seismological studies suggest that kilobar-level stress drop moonquakes are occurring in the highlands (Binder and Oberst, 1985). Extrapolation of the data suggests that about 2000 thrust-fault scarps, whose average length is 9 km, are in the highlands. The fault scarps generally occur in series or complexes of 4 or 5 scarps. The average length of these complexes is 50 km; the largest observed complex is 120 km long. Extrapolation of the data suggests that there are about 400 such complexes. The ages of the scarps range from 60 --- 30 to 680 --- 250 my, with an absolute uncertainty of plus a factor of 2 or minus a factor of 4. Thus, these scarps are by far the youngest endogenic features on the Moon. The selenographical, size, age, morphological, and azimuth frequency distributions of the scarps can be explained by the combined effects of the kilobar-level isotropic thermoelastic stresses, the 100-bar level anisotropic tidal and rotational stresses, and influence by preexisting lunar structures. These results show that the Moon has recently entered an epoch of late stage, global tectonism and favor the concept that the Moon was initially totally molten. ACKNOWLEDGMENTS We thank Diplom Geolog W. Buser for his assistance in the experimental studies of the arcuate thrust faults, the USGS Branch of Astrogeology at Flagstaff, Arizona, for providing us with the Apollo 15 and 16 panoramic imagery, and Dr. B. Lucchitta for providing us with contact negatives of selected imagery from the Apollo 17 panoramic data. This work was supported by the Deutsche Forschungsgemeinschaft. REFERENCES ANDERSON, E. M. (1951). The Dynamics o f Faulting. Oliver & Boyd, Edinburgh. BINDER, A. B. (1982). Post-Imbrian global tectonism: Evidence for an initially totally molten Moon. Moon Planets 26, 117-133. BINDER, A. B., AND H.-J. BRANDT (1985). Lunar Stress and Tectonic History. 1. Global Thermoelastic, Tidal, and Synchronous Rotational Stresses. In preparation. BINDER, A. B., AND M. A. LANGE (1980). On the

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thermal history, thermal state, and related tectonism of a moon of fission origin. J. Geophys. Res. 85, 3194-3208. BINDER, A. B., AND J. OBERST (1985). High stress shallow moonquakes: Evidence for an initially totally molten Moon. Earth Planet. Sci. Lett., 74, 149-154. CLARK, S. P., JR. (1966). Handbook of Physical Constants. Geol. Soc. Amer. Mern. 97. JACOBS, J. A., R. D. RUSSEL, AND T. J. WILSON (1959). Introduction to Geophysics. McGraw-Hill, New York. MASURSKY, H., G. W. COLTEN, AND F. EL-BAZ (1978). Apollo over the Moon: A View from Orbit. NASA, Washington, D.C. MATTINGLY, T. K., F. EL-BAZ, AND R. A. LAIDLEY (1972). In Apollo 16 Preliminary Science Report. NASA, Washington, D.C. MELOSH, H. J. (1980). Tectonic patterns on a tidally distorted planet. Icarus 43, 334-337. MOORE, H. J., J. M. BOYCE, AND D. A. HAHN (1980). Small impact craters in the lunar regolith--Their morphology, relative ages, and rates of formation. Moon Planets 23, 231-252. MOLLER, A., AND A. B. BINDER (1983). Linear crater chains: Indication of a volcanic origin. Moon Planets 28, 87-107. RANSFORD, G. A., AND W. M. KAULA (1979). A comparison of accretional models. Lunar Planet. Sci. X, pp. 998-1000. RUNCORN, S. K. (1977). Early melting of the Moon. Proc. Lunar Sci. Conf. 8th, 463-469. SCHULTZ, P. H. (1972). Moon Morphology. Univ. of Texas Press, Austin. SCHULTZ, P. H., R. GREELEY, AND D. GAULT (1977). Interpreting statistics of small lunar craters. Proc. Lunar Sci. Conf. 8th, 3539 -3564. SOLOMON, S. C., AND J. CHAIKEN (1976). Thermal expansion and thermal stress in the Moon and terrestrial planets: Clues to early thermal history. Proc. Lunar Sci. Conf. 7th, 3229-3243. SOLOMON, S. C., AND J. W. HEAD (1979). Vertical movement in the mare basins: Relation to mare implacement, basis tectonics, and lunar thermal history. J. Geophys. Res. 84, 1667-1682. STROM, R. G. (1964). Analysis of lunar lineaments. 1. Tectonic maps of the Moon. Comm. Lunar Planet. Lab. 2, 205-216. TALWANI, M., G. THOMPSON, B. DENT, H.-G. KAHLE, AND S. BUCK (1973). Traverse gravimeter experiment. In Apollo 17 Preliminary Science Report. NASA, Washington, D.C. TRASK, N. J. (1971). Geological Comparison o f Lunar Materials in the Lunar Equatorial Belt, Including Apollo 11 and Apollo 12 Landing Sites. U.S. Geol. Survey Prof. Paper 750D, D138. WOOD, J. A. (1982). The lunar magma ocean, thirteen years after Apollo 11. In Pristine Highlands Rocks and the Early History o f the Moon, pp. 87-89. Lunar and Planetary Institute, Houston.