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Ejecta emplacement of the martian Bamburg

Peter J. Mougjnis-Mark

Department of Geological Sciences, University. Providence, Rhode Island 02912

Abstract- Six exterior deposits surround the martian impact crater Bamburg (55 km in diameter). T he sequence of ejecta emplacement , although more complex. conforms to the same depositional history that has prod uced the ej ecta deposits a round martia n rampart craters smaller than 30 km in diameter. D uring ejecta e mplacement, secondary crater fo rmation preceeded the deposition of highly mobile su rface flows, which in tum were overrun by more viscous fl ows that are characlerized by longi tudinal grooves and transverse ridges. Numerous areas of flat terrain upon the ej ecta deposits, and the identification of I veed channels on th e wall s of Ba mburg, may indicate that either late in the cratering event, or after fin al ejecta emplacement, sedi ment-laden melt water percolated out of the vol atile- rich ejecta and the c rater ri m. The number of secondary craters associated wilh Bamburg is less tban one third the commensurate value for lunar and mercurian craters of equ iv alent size. T he maximum areal density of these marli,m seconda ry craters is observed at less than hajJ the range of those associated with the comparable me rcurian c rater Marc h. The deficiency of Bamburg secondary craters is attributed either to pref­ erential d structi on of ejecta blocks sufficiently large to form secondary craters or the subsequent burial of such craters o nce formed .

INTRODUCTION

Bamburg crater, approximately 55 km in diameter, lies to the ea t of and is centered at 40o N, 3°W. From 9 images, the crater was interpreted to lie On lhe boundary between plains material to the north and lower plateau material to the (U nderwood and Trask, 1978). Viking photography (Fig. I) ill ustrates that this plains material can be subdivided into remnant smooth plains material to the east and fractured plains in the west (Guest e! al., 1977) . Bamburg lies approximately 80 km north of the martian highland boundary de­ scribed by Scott (1978). Because of the high resolution (40 meters per picture element) images acquired by the Viking orbiters of the crater and its surroundings, Bamburg affords an excellent opportunity for the analysis of the depositional processes and resultant morphologicalfeatures associated with the formation ora complex martian impact crater. Secondary craters and a variety of ejecta units can be identified that are absent from martian craters smaller than 35 km in diameter (Carr et a!., 1977 ; Mouginis-Mark and Head, 1979) . These ejecta materials are described here in detail in an attempt to identify similarities between Bamburg and smaller martian 2651 2652 P . .J. Mouginis-Mark

Fig. I. Regional sell ing of Bamburg Crater. To the nOrth and west li es the fractured plains male ri al of Guest e f £II. (1977). Smooth plains material occurs in the eastern part of the area illustrated . The highland boundary described by Scott (1978) approximately corresponds to the southeastern third of the image . Rectangle shows the location of Fig. 2. Viking orbiter frames 673/855-64 . crat rs. The secondary crater distribution is compared to the lunar and mercurian examples cited by Gault et al . (1975) to contrast cratering events in the martian environment with those in the vacuum conditions of M rcury and the .

DESCRIPTION OF THE MORPHOLOGICAL UNITS

The type of exterior deposits surrounding fresh impact craters on is gra­ dational with crater size (Mouginis-Mark, 1979a). Single continuous ejecta facies, apparently emplaced by a . urface-ftow process (Carr et al ., 1977), typically are seen around craters sm aller than 15 km in diameter. Craters 5- 30 km diameter may have two concentric deposit. . For diameters larger than 30 km, multiple, fluidized. lobate flows or complex ejecta blankets with large azimuthal variations for a given range predominate. Bamburg conforms to this "complex ejecta" clas­ sification (Type 5 craters, Mouginis-Mark, 1979a) and possesses several mor­ phological units analogous to deposits seen around martian rampart craters smaller than Bamburg, or fresh impact craters on the moon (Howard, 1974) and Mercury (Gault et £II., 1975; Cintala el al., 1977) . Figure 2 shows the high resolution Viking photography from which the mor­ phological map (Fig. 3) was produced. Four materials con titute the interior ~",,' '"i:i

""~ '"S­ '" ""~ "";os <8, ;;:. "":: i5.., ~ . ~

~:::, Q ~ ~.., tll :::, ~ 2' ;j

Fi.g. 2. Photomosaic of Bamburg C rater, showing the area for wh ic h the morphological map (Fig. 3) has been compiled. Also di splayed are the locations of lhc type localities of the five ejecta deposits illustrated in Fig. 4. Viking orbi ter frames 70A21-32 e'" and 72A 19-32. <..v "" ~

"ll '­ s:~ ri.2 . ~ z;;'

::,~ ~

25 km

(a)

Fig. 3. (a) Morphological map of the interi or and exterior deposits associ ated with Bamburg . See key (Fig. 3b) and text for descriptio ns. Ejecta emplacement of the martian impact crater Bamburg 2655 deposits and six materials were identified beyond the rim crest. A brief descrip­ tion of each uni t is given b low, together with the type localities for the ejecta deposits (Fig. 4).

INTERIOR DEPOSITS

Central peak material (Cp)

T he diameter of the central pe k material is approximately 10 km. The summit portion of this peak comprises a near-circular pit 6 km in diameter, breached on its northern wall , with a fla t floor 1 x 2 km in extent. Such features have been identified by and Hartnell (1977) and Hodge (1978) and are attributed by Wood et al. ( 1978) to explosive decompression of subsulface volatiles within the target duri ng crater formation . No . {ratification i evident within the peak ma­ terial, but a linear ridge can be extrapolated from the southern pit rim to outcrops on the northern pit rim and may represent a structural trend orientated 10° west of north.

Floor material (Fm)

Much of Bamburg's floor appears to be covered by eolian or other sedimentary material. The surface of this material is relatively flat but domed slightly toward the central peak . Gentle slopes extend from the walls of the peak to the crater fl oor whereas smooth deposits are interdigitated between the floor and the in­ nermost wall ma terial.

INTERIOR DEPOSITS EXTERIOR DEPOSITS

WALL FLOW SMOOTH TE R R AIN ~ Cd'_ I .~,I'" M ATERIAL (Wf) ~ MA T ERIAL (SI)

WA LL M AS S FLO W [I] MAT ERI AL (Wm) D2J M AT ERIA L (Mf)

- . FLOO R ROUGH RADIAL 0 MATERIAL (Fm) D.", MATER IAL (Rr)

CENTRAL PE AK SM OOT H RADIAL [II MATERIAL (Cp) D>, " MATERIAL (Sr)

PITTED TE RRAI N MATER IAL (PI)

• RIM Fig. 3. (b) ~ MA TERIAL (Rm) 2656 P. 1. M Ollginis-Murk

WaJl material (Wm)

Multiple occurrences of ridged material characterize the wall unit of Bamburg. In places, this wall material may be [5 km wide, corresponding to 0. 55 crater rad ii. As many as eight discrete ridges can be identified in any radial direction from the central peak, but few ridges continue for more than lOG of arc. Each ridge may re present the edge of a tilted terrace block (hat has been partially buried by subsequent material, Ilt there are no direct counterparts to the terraces and scallop of lunar and mercurian craters (Cin tala ef al., 1977). In between these wall ridges, deposition by creep and slumping ha produced flat inliners which occasionally extend to, and merge with . the fl oor material.

Wall How material (Wf)

A series of leveed channel · 2 - 4 km in length extends from the lim crest to the lower wall ridges of the southern wall of Bamburg. In detail, these channels are similar to the channels observed on the ails of the Tycho and (Strom and Fielder, 1971; Hul me and Fielder, 1977). No obvious source areas (pits or ponded material) are evident for any of these martian chan­ nels, however, so that an impact melt origin such as described by Hawke and Head (1 977) for the lunar examples appears inapplicable in the case of Bamburg. Impact melts associated with martian craters remain unidentified. and extrapo­ lation of terrestrial field data and theoretical models (Kieffer and Simonds, 1979) predict that melt sheets would be preferentially assimilated during cratering events in volatile-rich targets on Mars. If this is the case. then the best alternate explanation for the formation of the e channels appears to be that they are of flu vial origin. possibly associated wi th the outward percolation of melt water incorporated within the rim unit of the crater. The duration of this release of melt water is not cl ear, but the superpo ition ing of these channels upon the wall ridges indicates that they post-date the wall-fai lure stage of crater formation.

EXTERIOR DEPOSITS

Rim material (Rm)

Bamburg possesses hummocky rim mateIi al (hat resembles the equivalent unit around lunar craters (Howard. 1974) . In many places, th is hummocky facies is composed of a series of small ridges, akin to the ridges of the wall material. On the northern rim. there is evidence of radial scouring that is morphologically similar to triations on the southeastern ri m of the lu nar crater Aristarchus (Guest, 1973). Guest believes that the scouring on the rim of Aristarchus is associated with the stripping of the initial ejecta deposits by high velocity debris Ej ecta emplacemel1t of the martian impact cra ter Bamburg 2657 surges, po sibly during or di rectly after the overturning of the crater rim. Such an explanation may also be applicable to Bamburg, because the scour marks fade rapidly with increasing distance from the rim rest and blend with the surrounding flo w deposits that overlie the distal portions of the rim material.

Pitted terrain material (Pt)

Widely distributed around Bamburg to radial distances greater than fou r crater radii from the pri mary center, this u nit comprises a series of closely packed, small-scale depre sions and mounds, each several hundred meter in diameter (F ig. 4a). Because these features are close to the re olution of the Viking images, their de tailed morphology and mode of emplacement cannot be identified, but they appear to represent a discrete component of the ejecta inasmuch as similar topography is not observed at greater distances from Bamburg, Only faint bound­ aries of the pined terrain material can be seen as a consequence of subsequent ejecta emplacement. This is indicated by a fainl pattern of ridges and grooves orientated radial to Bamburg that have been superimposed upon the pitted terrain material by the overriding smooth radial material.

Smooth radial material (Sr)

Extending to more than 4.7 crater radii from the center of Bamburg, the mooth radial material (Fig. 4b) is the mo

Fig. 4. f ype localities for the five ejecta deposits surrounding Bamburg: A) Pitted terrain material; B) Smooth radial material; C) Rough radial material ; 0 ) M a~ s Row material; E) Smooth terrain material. Location of each area is jllustrated in Fig. 2.

attributed to the difference in crater size; Mouginis-Mark (1979b) demonstrated that craters larger than 30 km in diameter commonly have ejecta materials that travelled a proportionally greater distance than ejecta from 15- 30 km diameter craters excavated in the ame target material. In tum, ejecta materials around 15-30 km diameter craters are proportionally more extensive than ejecta sur­ rounding craters smaller than 15 km in diameter. EJecta emplacement of the martian impacr craieI' Bamburg 2659

Many circular depressions up to several kilometers in diameter occur within the smooth radial material. OnJy a few of these depressions have raised rims, but the majority are int rpreted to be parti ally infilled secondary craters. Small-scale, pre-existing topography also appears to have been affected by the passage of the material compri ing th is unit; obstacles a few hundred meters high have been traversed by the outward movement of the ejecta flows.

Rough radial material (Rr)

T he material of this unit extends to radial distances of 2.5 - 3.5 crater radii from the center of Bamburg. It is characterized by hummocky terrain, with superposed radial scour marks and elongate depressions ( "ig. 4c). Where pre-existing topog­ raphy was encountered by the outward moving ejecta (e.g., northeast of ­ burg), there is an increase in the size and frequency of depressions. few of these depres ions have raised rims, and there is ample evidence of partial infilling by subsequent deposits. This infi ll is best seen within the three primary craters to the south of Bamburg, which have had their proximal rim crests overridden by the rough radial ejecta so that their floors are partially buried. The rough radial material is interpreted to have a similar mode offormation as the inner continuous ejecta facies that surround many rampart craters 10- 30 km in diameter (Mouginis­ Mark, 1979a), due to their similar positions relative to their parent crater and the convex di stal edges that are a characteristic feature of both materials.

Mass How material (Mf)

Mass flo w material is typifi ed by hummocky topography with many low trans­ verse ridges spaced approximately 0. 5- 2.0 km apart (Fig. 4d). These ridges, which commonl y extend to the crater rim and blend with the slumped wall blocks of the rim material, may in part owe their origin to the failure and subsequent movement of the rim deposits. The distal edges of these flows, which may extend three crater radii fro m the primary center, end abruptly in convex slopes where the fl ows have overridden the earlier ejecta deposits . Few secondary craters are preserved wi thin this unit, the only examples observ d are larger than 2 km in diameter and lack prominent rims as the result of burial of their exterior deposits. Examples of wall pluc kin g also are apparent on the distal sides of several smaIl craters that occur withi n the mass flows. Whereas the proximal and side waIls of these craters have remained in tact, waIl material from the distal rim has been "rafted" along with the flows.

Smooth terrain material (St)

Abnormally smooth material (Fig. 4e) is superimposed upon the other ejecta units of Bamburg. A paucity of surface detail on this material can be identified, al­ 2660 P . J. M OII&inis-M ark though faint ridge radial to the primary crater can be observed at a few localities. The large area of sm oth terrain material east of Bamburg may be due to re ur­ faci ng of that area by channel deposits originating from the highlands to the southeast Scott, 1978). However, other examples of smooth terrain material appear to have a different, impact-related origin, because of their intimate a 'so­ cjation with the ejecta material of Bamburg. The ponding of sediment-l aden ma­ terials from ejecta excavated from water- or ice-rich ubstrate may have produced this material after final ejecta deposition by the upward percolation of entrapped melt water (Rehfuss et al., 1978; Mouginis-Mark, I 979c). However, no feeder tributaries or channels are observed around the perimeter of the smooth terrain material to suggest that it was formed by the collection of sediment in localized depressions. A primary. late-stage depositional process during the cratering event therefore appears to be more acceptable as a mechanism to produce the smooth terrain material. although il. emplacement mechanism re mains unresolved.

SECONDARY CRATER DISTRIBUTION

A total of 657 near-circular depressions larger than 1 km diameter were identified around Bamburg out to radial distances of 110 km from the primary crater center (Fig. 5). Although many of these depressions lack raised rims and the character­ istic herringbone pattern of lunar secondary craters (Guest and Murray, 1971;

Fig. S. Areal distribution of 657 depressions larger th an I km diameter interpreted to be secondary craters associated with the Bamburg impact. Also shown are the primary crater's rim crest and radial distance from the center of Bamburg. £jecla empia cemenl of Ihe mar/ian impaCl crilier B amburg 2661

Oberbeck and Morri on, 1973). they are inferred to be Bambu rg secondaries because of their spatial distribution centered around Bamburg. These morpho­ logical differences are consequently att ributed to the overriding of the martian secondary craters by the surface flow of ejecta duri ng the latter stages of the cratering event. Schultz and Gault (L 979) commented that the total visibl e secondary crater popul ation around Bamburg is notably deficient in comparison to lunar and mer­ curian examples at equivalent distances from the primary. T hi s analysis supports their observation, and compares the areal distribution of martian secondaries with the data of Gault el aL. (1975) for satellite craters around Ari tarchus (40 krn in diameter) on the moon and the 77 km diameter mercurian crater March CHoN. 176°W). Gault et aL. ( 1975) included in their counts secondary craters larger than 0.014 of the primary rim diameter. Thi arbitrary cut-off point conesponds to Aristarchus secondaries 0.56 km in diameter and 1.08 km diameter craters around March. In this analy, is. the density of all Bamburg secondary craters larger than 1 km in diameter was measured. The areal density of Bamburg secondary craters. normalized to the diameter of the parent crater, is presented in Fig. 6 with the equivalent distributions for Aristarchus and March.

120 N E -'" MARCH_ "b 10 0 (77km) "­ >­ ~ 80 lJ.J AR IS TARCHU S :J o ~ (40km) w 60 cr u... >- 4 0 cr BAMBURG

2 3 4 5 6 7

DISTA NCE FROM CE N TE R OF PRI MA RY (CRATER RADII)

Fig. 6. Distribution of secondary craters around Bamburg compared to the data of Gault el al. (1975) for the lunar crater A ristarchus and March on Mercury. Data demonstrate that many more secondary craters are observed around the lunar and mercurian craters than Bamburg. T he maximu m concentration of secondary craters is observed muc h closer to the primary rim c rest for B.~ mburg than for March, despite similar surface gravities for the two planets , suggesting that atmospheric ueceleration may have influ­ enced the distribution of the martian ejecta. 2662 P . J. M ouginis-M ark

Fig. 7 . . tereo pair () f the north of Bamburg, illustrating the area discussed in lext and mapped in Fig. 8. Viking orbiter frames 37A45 and 37A46 (left), 70A27 (right).

The distribution of Bamburg secondary craters differs from that of March and Aristarchus in two respect :

3 2 I. The maximum density (44.7 craters/1 0 km ) of preserved secondary craters for Bamburg is approximately one third the number of secondaries around the other two craters. This may be an observational effect, however, si nce many of the observed craters di play evidence of subsequent overriding by ejecta flows, suggesting that additional craters may have been totally buried and remain undetected. Alternatively, fewer secondary craters may actually have been created, perhaps as a consequence of pre-impact target charac­ teristics preventing the production of sufficiently large ejecta blocks to form satellite craters (Head , 1976a; Schultz and Mendell, 1978). 2. Maximum areal density for Bamburg secondary craters occurs at a distance of 1.3- 1.7 primary radii from the center of the parent crater, much closer to the rim crest than for March (2 .5 -3.0) and Aristarchus (3.0- 3.5) . Previous attempts to model ejecta trajectories on Mars (Blackburn, 1977; Tauber et al., 1978; Schultz and Gault, 1979) and the role of atmospheric drag on Ejecta ClI1pillCefl]C I11 of rhe //I onian impact crarer Bambll rg 2663

ejecta (Sheerwood, 1967: Wilson, 1972; Settle, 1979) all qualitively predict the bserved reduction in range of ejecta particle' and the ob erved con­ centration of martian secondary craters closer to the primary than compa­ rable features produced under the similar gravitational field but vacuum environment of Mercury. The extent of this atmospheric deceleration of ejecta may be related to the ejecta particle size distribution (Seebaugh, 1976; Schultz and Gault, 1979), which in turn should be influenced by the target lithology.

EJECTA EMPLACEMENT

Contrasting emplacement sequences have been inferred for lunar and martian impact crater ejecta. On the moon, the ballistic transport and deposition of ejecta appears to be the dominant process for sub-kilometer sized craters (Oberbeck, 1975). For craters larger than 1 km diameter, the ejecta have sufficient velocity to crater pre-existing terrain and generate a mixture of primary and locally derived material that moves a short distance laterally away from the crater (Oberbeck, 1975; Oberbeck ef nl., 1975). The generation of ground surges and the surface flow of lunar ejecta have been deduced from detailed mapping of large craters and basins (Howard, 1972; Guest. 1973; Head. 1976b). On Mars. ejecta emplacement is dominated by apparently similar surface flow processes (Carr el (II., 1977), probably as a con equence of ejecta fluidization by volatiles originally within the target material (Mouginis-Mark, 1979a). Martian ejecta mobility has been predicted to be related to ejecta viscosity (Gault and , 1978), and is influenced by the target material, the latitude and altitude of the crater. and the size of the cratering event (Mouginis-Mark, 1979a). Multiple phases of deposition have been proposed for the emplacement of ejecta around martian craters larger than approximately 30 k.m in diameter (Mouginis-Mark and Head, 1979). Image resolution of much of Bamburg's ejecta blanket is insufficiently clear to identify this emplacement sequence, but a ke y locality for this purpose exists around the crater chain extending northward from the crater. A stereo photo-pair of this area is illustrated in ig. 7 and a morphological sketch map is provided in Fig. 8. Contained within the chain are approximately 40 individual craters, sep­ arated from a sequence of flow lobes (fla-fld and fza-f2c in Fig. 8) within the smooth radial material by longitudinal ridges along tbe side of the chain. In total the chain is 60 km long and extends 100 km from the northern rim of Bamburg. Very few secondary crater ' within the chain, or beneath the exterior flows, posse s raised rims. The majority of these craters have been partially overridden and buried by late arriving ejecta flows. The few examples of secondary crater rims that exist are on the ioward facing walls of the craters close to the center of the chain (Rr in Fig. 8), and these appear to have been preserved by the deflection of the flows by the other chain members. Several longitudinal ridges 2664 P . J . !vI ougini.I-Mark parall el much of the length of the chain. T hese are interpreted to be the remnants of secondary ejecta deposits, the majority of which have been removed by the passage of the ejecta flows, Furth r eviden e for the production of the crater hain as a discrete feature prior to the arri val of the firs t ejecta flows can also be identi fied at several local­ ities:

1. The string of craters to the east of the chain (B e in F ig. 8) have een

uniformerly blanketed by the f2c fl ow lobe. 2. The chain has effectively spli t the seque nce of fl ows comprising the smooth radial material into two unrelated groups, with li tHe correlation between the

bou ndaries of the f l lobe sequen e to the west and the eastern, f2 , series. 3. At the points Br in Fig. 8, the proximal walls of large secondary craters have been breached by the ejecta flows, resulting in partial infi lli ng of the crater floor. At the point Sf, the distal wall of the secondary crater has also been removed, allowing a small lobate flo w to emerge fro m thi s area and cover part of the already emplaced Cb deposit.

Pitted terrain mat rial is difficult to place in the emplacement chronology of th is area, primarily because the small-scale topography cannot be adequately resolved in the available Viki ng image . Northwest of Bamburg, the superposition relationships are easier to identify. Long it ud inal ridges parallel to the fl ow lines wi thin the smooth radial ejecta fl ow exist upon tbe pitted terrain, impl ying a pene ontemporaneous emplacement ti me for the pitted terrain and secondary craters. Pitted terrain material may be a close analogue to the formation of sec­ ondary craters, and might be the product of mall-scale secondary cratering by the fragmented "clumps" of fine ejecta postulated by Schultz and Mendenhall ( 1979) . T he juxta position of the mass flow material and the rough radi al material illus­ trated in F ig . 8 makes their times of emplacement quite similar. South and east of the crater chain, the mass flows appear to override the rough radial material, but in many places one unit blends into the other with no obvio us break in continuity. Both ejecta materials override the smooth radial material. with well defined convex slopes marking their distal edges. No good local it ies exist close to the crater chain that offer the evidence needed to con fi dently place the smooth terrain material into a un ique position within the depositional ,.equence. EJ ewhere on the ejecta material of Bamburg, the absence of secondary crater and the ridges characterist ic of the smooth and rough radial materials would indicate that the deposition of the smooth terrain material is a late-stage phenomenon. T he in terfingering of the unit edges at the low boundaries of the smooth and rough radial materials argues against a surface-flow emplace­ ment mechanism for the smooth terrain material. Nor is the infilling of local depre sions by the percolation of sediment-laden melt water an acceptable mode of formation because of the absence of feeder channels on the perimeter of each deposit. Consequently, it is postulated that the smooth terrain material represents J::.jecta emplacement of the martian ill7pact Cra IeI' B amburg 2665 the accumul ati n of fine ejecta that is directly emplaced in the observed localities after the emplacement of the surface flow materials.

CONCLUSIONS

High resolution Viking images of Bamburg permit the identification of ejecta facies not previously recognized arountl martian im pact craters. Several conclu­ sions can b drawn that relate to the emplacement seque nce of rhe ejecta and the gross characteristics of the target material:

I. Ejecta emplacement was a multi-phased process, initiated by the formation of secondary craters and the pitted terrain material. Successively less ex­

, , r~~~; <: 1 L ONG ITUDI NAL - ..O? 0 :', R I DGES I I ~" f I 1a , _/ I _-f2b I SEC ON DARY (S ) ' : ~ ;. D.< FLOW LOBE f \ I \ - PIT TED I - , TERRAIN \ , II ,, , I I flc ' \ , ROUGH RADIAL : - .,,~~ 0 - I TERRAIN , I D \/ \ \ \ II , D. _ . ·i:: MASS FLOW

~ 'b .0 0 f lo- fld J SMOOTH f - f R A DIA L FLOWS 20 2c

0 Rr - CR AT ERS W ITH RAISED 0 RI MS

\ tid' ­ - D 0 Br BREACHED RIMS 0

Be BURIED CRATER 0 10 - I CLUSTE R

Fig. 8. Morphological sketch map of the crater chain north of Bamburg. irection of ejecta flow was from south to north. Mapped from Viking orbiter frames 70A25-30. 2666 P . .!. M oItRini.I -M ({ I' k.

Len ive deposit. of mooth radial. rough radial and mas flow materials were then emplaced. The smooth. discontinuolls deposits of the smooth terrain material represent the final ejecta material to be deposited 2. Surface-flow emplacement of the ~mooLh radial and rough radial materials were similar to the depositional prOl.eS

Acknowledgments- J . W. Heau and 1. L Whitford-Slllrk providcd ll ' cful comment during the prep­ arati on of the manuscript. Helpful reviews were given by G. E McGill and an anonymous reviewer. T he photographic ab il ities of David Haas were also most helpfU l for the produc tion of the figures . This work was supported by NASA grant\ NGR 40-002-088 an d GR 40-00 2- 11 6.

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