A Geometric Analysis of Surface Deformation: Implications for the Tectonic Evolution of Ganymede

ICARUS 60, 200--210 (1984)

M. T. ZUBER AND E. M. PARMENTIER Department of Geological Sciences, Brown University, Providence, Rhode Island 02912

Received August 5, 1982: revised May 30, 1984

The visual nonalignment of the furrows and the circularity of impact craters are used to study surface deformation on Ganymede. The furrow system is examined to test the hypothesis that lateral motion has taken place between areas of dark terrain. Results show that while lateral motion cannot be ruled out, it may not be required to explain the geometry of the system. Initial nonconcentricity of the furrows or an early period of penetrative deformation shortly after furrow formation could also account for the present configuration. Centers of curvature of the furrows in Galileo and Marius Regiones are numerically determined and it is shown that if lateral movement did occur, it is not possible to determine the amount of displacement. The axial ratios of impact craters in the Uruk Sulcus region which separates Galileo and Marius Regiones are determined and show that large scale shear deformation has not occurred in that area since bright terrain was emplaced. Deformation of impact craters within Galileo Regio suggests that Ganymede's lithosphere has behaved rigidly throughout most of the satellite's evolution. The shapes and orientations of impact craters in dark terrain around wedges of bright terrain are used to place an upper limit on the amount of extension associated with bright terrain formation. ,, 1984 Academic Prcs~. Inc.

INTRODUCTION mation, although of importance in under- standing the mechanism of global rifting on The surface of Ganymede preserves the Ganymede, has yet to be determined. record of an active and diverse tectonic his- Evidence for shear deformation on Gany- tory. The major surface units consist of ap- mede is localized and small scale (Luc- proximately equal portions of dark, heavily chitta, 1980; Golombek and Allison, 1982; cratered polygons and bright, lightly cra- Parmentier et al., 1982). The most convinc- tered regions which penetrate and separate ing examples are several impact craters dark areas (Smith et al., 1979a,b). Funda- whose rims are offset by not more than a mental observations of the nature of defor- few kilometers. Lucchitta (1980) has cited mation within these units lead to basic con- the nonconcentricity of the Ganymede fur- clusions about the tectonic history of the row system as evidence for large lateral satellite. Deformation on Ganymede, at motion of dark terrain blocks. The exis- least since bright terrain formation, has tence of lateral displacements at this scale been primarily extensional. Compressional would place important constraints on the deformation has not been identified within global tectonic history of Ganymede. the dark terrain and is uncertain in bright Also of considerable importance would terrain. Parmentier et al. (1982) cite evi- be the recognition of smaller scale deforma- dence which suggests that bright terrain tion within individual terrain areas. Con- formed due to finite extension of the litho- straints on the style, degree, and timing of sphere, and Shoemaker et al. (1982) suggest deformation within isolated units has rele- that bright bands resemble normal fault pat- vance not only to the tectonics, but to the terns in terrestrial rift zones. The amount of physical properties of the lithosphere at the extension associated with bright terrain for- time of deformation. The manner in which 200 0019-1035/84 $3.[~) ('opyright ~ 1984 by Academic Press. Inc All righls of reproduction in any form reserved SURFACE DEFORMATION ON GANYMEDE 201

the near surface deforms throughout time the satellite's surface, as it predates essen- has implications for the rheological struc- tially all impact craters in the dark terrain ture of the lithosphere, the geothermal gra- (Smith et al., 1979b). dient, and possibly the source of stress. The pattern of furrows is most distinct in This study focuses on the identification Galileo Regio, shown in Fig. 1. Furrows in of various types of surface deformation on this region are approximately 10 km wide, Ganymede by a geometric study of the fur- spaced 50 km apart, and extend for hun- row system and an analysis of circularity of dreds of kilometers across the surface impact craters. First, we test the hypothe- (Smith et al., 1979b). A number of linear sis that the furrow system was initially con- bright bands along the southern border of centric and that the present configuration of Galileo resemble furrows in width, spacing, the furrows provides a measure of lateral and orientation. The system continues into motion of dark terrain. This is accom- adjacent Marius Regio, however furrows in plished by determining the present centers this area exhibit distinct morphological dif- of the furrow system in several dark terrain ferences compared to those in Galileo (Zu- blocks and observing the amount of defor- ber, 1982). The Marius furrows occur as mation in bright terrain regions which sepa- shorter segments spaced an average of 22 rate these blocks. Second, we place an up- km apart and 6 km in width. A faint second- per limit on the amount of extension ary trend in the strike of furrows can be associated with bright terrain formation by observed, where approximately nine per- using the deviation from circularity of im- cent of the Marius furrows trend at an angle pact craters to calculate the strain field greater than thirty degrees from the local around wedge-shaped regions of bright ter- mean orientation. These secondary furrows rain. Third, we attempt to identify penetra- are either contemporaneous or postdate tive deformation in Ganymede's litho- those of the main set; in no case do they sphere by examining the circularity of predate furrows of the main trend. There- impact craters in dark terrain. fore they must have formed concurrently or in a subsequent event to that which pro- FURROW CONCENTRICITY duced the main system. The reason for the differences in widths The Furrow System and spacings of furrows in adjacent areas is The furrow system is a regional array of unclear. From the theory of multiringed ba- subparallel, arcuate structures that traverse sin formation (McKinnon and Melosh, several areas of dark terrain on the satel- 1980; Melosh, 1982), ring spacing should in- lite's leading hemisphere. A furrow is char- crease with lithospheric thickness. If the acterized by a central depression flanked by furrow system was impact-produced, then raised rims with relief not exceeding a few the variation in furrow spacings may reflect hundred meters (Smith et al., 1979b). Fur- a difference in lithosphere thickness be- rows are locally discontinuous, but broad tween Marius and Galileo Regiones at the arcs can be traced up to hundreds of kilo- time of formation of the system. Differ- meters across individual dark areas. The ences in furrow geometry may instead be furrows have been interpreted as ring gra- related to inhomogeneous mechanical prop- ben formed as a consequence of a basin- erties in the Galileo and Marius areas. scale impact into Ganymede's lithosphere However, the regions are separated by a (Smith et al., 1979b; McKinnon and Me- relatively narrow band of bright terrain and losh, 1980), though evidence to substantiate a gradual transition in furrow widths and this hypothesis is inconclusive. Whatever spacings is not observed. It is enigmatic the origin, the formation of the furrow sys- that two adjacent areas of the lithosphere tem marks the earliest event preserved on should display such an abrupt change in ei- 202 ZUBER AND PARMENTIER

FIG. 1. Part of the Ganymede rimmed furrow system as seen in Galileo Regio. Furrows continue into Marius Regio, which lies to the west of this region. The bright terrain unit Uruk Sulcus, shown in the lower left of this photograph, separates the Galileo and Marius Regiones (Voyager 2 frame 0104J2- O01L ther mechanical properties or lithosphere therefore asymmetrical structures cannot thickness. be predicted. Asymmetries have also been noted in the The furrows in Galileo and Marius are morphology of the Valhalla ring system on not concentric, and it has been suggested Callisto in areas of high resolution Voyager that some degree of right lateral motion coverage (Hale et al., 1980; Remsberg, and/or clockwise rotation of Marius terrain 1981). These studies report an azimuthal blocks would restore the system to a circu- transition from graben structures to out- lar geometry (Passey and Shoemaker, 1982; ward-facing scarps as opposed to a simple Shoemaker et al., 1982). If the two systems change in graben dimensions. Because of were initially concentric, then the present mathematical intractibility, axial asymme- orientation of the furrows in the displaced try has not been incorporated into present dark terrain blocks provides evidence for theoretical models of basin formation, lateral motion between adjacent blocks. If SURFACE DEFORMATION ON GANYMEDE 203 lateral motion has taken place, then the off- since a longer furrow defines a greater arc, set of the respective centers of curvature it provides a better constraint on the center provides a measure of the displacement of curvature. which has occurred between the areas since The linear least-squares formulation rep- their formation. Inherent in this approach resented in Eq. (1) assumes a Gaussian dis- are two basic assumptions: (1) the furrow tribution of errors, which is that observed systems were initially concentric, and (2) on a plane surface. However, as noted in dark terrain areas acted as rigid plates since various studies of terrestrial plate tectonics the formation of the system, such that pen- (e.g., Minster et al., 1974), the distribution etrative deformation could not explain any of errors on a sphere is characterized by the present deviation from circularity. nonlinear Fisherian distribution. The nonlinear problem can be simplified by realiz- Method ing that the error density on the surface of a To determine the centers of curvature, unit sphere is proportional to exp(k cos 0) we employed a numerical scheme to per- where 0 is the angular error and k is a mea- form a linearized least-squares fit of the fur- sure of the precision (Fisher, 1953). If the rows to small circles about a center. For an precision is large (k >> l), such that errors assumed center of curvature, the deviation are confined to a small section of the sphere of each furrow from a corresponding small in the area of the global (absolute) mini- circle was determined using the standard mum, the error density reduces to a Gaus- least-squares formula sian distribution if k = 1/orE where o .2 is the variance of the distribution. This linear ap- ~2 = ~,i(Ri -- R )2 (1) proximation is valid if the normalized resid- where e is the residual, Ri is the radial dis- uals of the best-fit solution have a mean tance from the center to the ith point on a near zero and a variance close to one. Fig- furrow, and ~' is the mean radial distance ure 2 shows the cumulative distribution of of the furrow from the center. The center least-square residuals for the center of cur- which minimized the mean squared residual of the deviation from concentricity for all furrows in the system was taken to be the best fit. Over 300 furrows were digitized from the °°I Voyager images. Measured points on the furrows were approximately equally spaced at about 4-km intervals along strike. Be- cause of the large size of the data set, runs were made using various parts of the sam- ple and results were compared to ensure consistency. The furrows in Marius which possessed the secondary trend in orientation described above were not included in 0 1.0 2.0 the analysis. The furrows were intrinsically weighted FIG. 2. Solid line shows the cumulative distribution according to both length and distance from of normalized residuals (e/tr) for the center of curva- the center. Since a greater number of fur- ture of furrows in Galileo Regio. Dashed line repre- rows are present farther from the center, sents the theoretical Gaussian distribution. The agreement of the two curves at the 99% confidence level and since longer furrows contain more digi- justifies the use of the linearized least-squares proce- tized points, these features made a greater dure. See text for explanation, e = residual, tr = stan- contribution to the total residual. However, dard deviation. 204 ZUBER AND PARMENTIER

220 ° 200 ° 180 ° 160 ° 140 ° 120 ° vature of Galileo Regio compared to the 60O i i I i i r i i i 60 ° theoretical normal distribution function. N Marius Galileo Regio The general agreement of the two curves, Regio o~ ~'~.'~ which was verified by the X2 and Kolmo- gorov-Smirnov tests at the 99% confidence 40 ~ 40 ° limit, indicates a close approximation to Gaussian errors. For this reason lineariza- 20 ¢ 20 ° tion is valid for the data set. Errors in the Marius areas show similar distributions. A major difficulty with the nonlinear dis- 0 o j A. SMRg tribution is that a solution may not exist, and if it does, it may be nonunique. A good - 20 t S Marius -20 ° starting guess is generally necessary to as- Regio GR/ sure convergence to the correct result. - 40 ( .40 ° Multiple minima may still be encountered, SMR t in which case other criteria must be em- N~R I ployed to determine the most physically re- alistic solution (Draper and Smith, 1977). In -60 o I I I I I z I I = ~ 60 ° this analysis, two methods were employed 220 ° 200 ° 180 ° 160 ° 140 ° 120 ° to determine the best-fit center. The first FIG. 3. Centers of curvature of the furrow system in was a grid search to locate the minimum Galileo Regio (GR), North Marius Regio (NMR), and residual within a specified area. Subse- South Marius Regio (SMR), with corresponding quently, a random search method was used small circle fits. Multiple solutions were obtained for the centers of curvature of furrows in North and South to verify convergence to this solution. The Marius Regio. Subscripts refer to global (g) and local centers of the Galileo Regio furrow system (I) minima. Small circle fits to furrows in North and as initially estimated by Smith et al. (1979b) South Marius are about the local minima. The 95% and Shoemaker et al. (1982) were first cho- confidence contour is shown for the Galileo Regio sys- sen as the starting centers. Numerous other tem. starting points were then used in the attempt to identify other possible minima. The Smith and Shoemaker values proved to Depending on the starting estimate, the be appropriate starting guesses in the North and South Marius areas each yielded search for the Galileo Regio center, how- two different centers of curvature, shown ever unrealistic solutions were obtained in Fig. 3. To choose between solutions, a when these were used in the Marius search, visual match of the Marius furrows to small as will be shown later. circles about each of the centers was employed. The local (relative) minima for North and South Marius at 48°S, 148°W and Centers of the Furrow System 44°S, 131°W, respectively, exhibited much Centers of curvature of the furrow sys- better visual fits than the global minima. tem were found for three areas: Galileo Re- The multiple solutions obtained for this regio, and North and South Marius Regio. gion are a consequence of the short furrow Results are shown in Fig. 3. The Galileo lengths, which make it difficult to strictly Regio system yielded a single, well-defined define the center of curvature. Because the center at 39°S, 178°W. The initial estimate final distribution of residuals for each of the for the center of this region made by Smith Marius solutions was dominated by the et al. (1979b) at 30°S, 180°W lies within the global minimum, confidence contours could 95% confidence interval of the least- not be constructed about these centers. squares solution. The fit of small circles about the final cen- SURFACE DEFORMATION ON GANYMEDE 205 ters of all three regions is shown in Fig. 3. centers in the northwest and central sectors From the small circle fits, it is readily ap- fell close to or within the 95% confidence parent that furrows in Galileo Regio deviate ellipse of the Galileo Regio center, but the from the small circles about the best-fitting center of the furrows in the southeastern center. The deviation is greatest in the east- section of Galileo markedly deviated from ern Galileo area. This follows from the the best-fit center for the full system. This weighting factor employed in the least- requires either that the furrow system was squares formulation, whereby longer seg- initially noncircular or that deformation has ments were given a greater weight. The occurred within Galileo Regio. center of curvature in Galileo Regio is con- trolled by the longest furrows which are lo- CRATER CIRCULARITY cated farthest from the center. However, One test for the occurrence of deforma- since the longest arcs provide the best con- tion on a surface is the analysis of the straints on the center of curvature, this ap- present geometry of objects with known proach was deemed valid. initial shapes. Impact craters, which are It may be possible to use a number of ubiquitous on all terrain units on Gany- different weighting criteria to produce a mede, are possible strain markers. The somewhat "better" fit of the furrows. For shape of an impact crater can be described example, it would be equally valid to mini- in terms of the circularity index, which for a mize Z(~bi)2, where t/) i is the angular devia- circular or elliptical feature is the ratio of tion of the strike of the ith furrow from the minor/major axes (i.e., axial ratio). If mea- strike of the assumed small circle at that surable deformation has occurred, then ini- point. However, allowing longer furrow tially circular impact craters which predate arcs a greater weight in defining the "best" the episode of deformation should be modi- center reflects the fact that the longer arcs fied into ellipses whose axial ratios and ori- contain more information about the loca- entations characterize the strain field. tion of the center. Regardless of the criteria Axial ratios were determined for craters chosen and the "best" center thus deter- digitized from the Voyager images. In order mined, small circles that fit furrows in one to detect the smallest possible strains, cor- part of the system will not fit those in other rections were made for Voyager viewing parts. geometry. Approximately 10 to 50 rim As shown in Fig. 3, the separation of the points were digitized for a given crater, de- centers of curvature of the furrows between pending on its size. The crater area (A) was Galileo and the local minima in Marius is found from the equation for the area of an about 20 ° of surface arc. If an initially con- N-sided polygon, where N is the number of centric system is assumed, then the differ- rim points. The center of the crater was ence in the calculated centers suggests sig- taken to be the centroid of the area. All nificant lateral motion of dark blocks, and points on the crater were translated into a major shearing within the bright terrain local coordinate system whose origin was which separates these areas. If the shearing the centroid. The best-fit ellipse was de- postdated the formation of bright terrain, fined by the eccentricity and the orienta- then surface features in the bright units tion, ~b, of the major axis which minimized should show evidence of shear deforma- the mean square residual of the equation tion. 7rR z To define the circularity of furrows A(1 - eZ)1/2 {1 - e 2 cos2(0 - ~b)} - 1 = 0 within Galileo Regio, the area was broken into three sectors of twenty degree angular (2) width, and the centers of curvature of the for rim points (R, 0). The axial ratio was furrows in each area were determined. The determined from the eccentricity e = (a 2 - 206 ZUBER AND PARMENTIER

12 formation might concentrate in a particular transverse unit. Results are shown in Fig. 4. The aver- I0 N=27 8 age axial ratio of craters in longitudinal ter- 6 rain is 0.840 -+ 0.024 and that in transverse 4 terrain is 0.873 -+ 0.017. This result can be 2 compared to a similar study of lunar cra- 7r-l ters, since it is generally thought that the J longitudinal 6 N=21 lunar lithosphere has behaved rigidly 4 throughout its evolution. Ronca and Salis- 2 t bury (1966) measured the circularity of lu- 1.0 90 .80 ."tO .60 nar craters and identified two populations. b/o The majority of craters had a mean axial ratio of 0.8984 -+ 0.0076 and a much smaller FIG. 4. Histogram of crater axial ratios in Uruk Sul- cus (centered at 0°N, 160°W), divided into transverse subgroup had a mean of 0.8097 -+ 0.0089. and longitudinal groove bands. N is the number of Therefore, craters in Uruk Sulcus are less craters. The long-short dashed lines refer to the mean circular than most lunar craters. To check axial ratio in a given region. The dashed line is the whether the observed deviation from circu- lunar mean. larity of craters is due to lateral motion of dark terrain blocks, it is necessary to exam- b2)l/Z/a where a and b are the semimajor and ine the orientations of the major axes of the semiminor axes of the best-fit ellipse. To best-fit ellipses. assure a good fit, the normalized residual Shoemaker et al. (1982) suggest that Ma- was required to be less than the quantity (a rius Regio has been rotated counterclock- - b)/a. This selection criterion was satis- wise or translated to the left with respect to fied by every crater. Galileo Regio. This would require the major axes of deformed craters to be aligned NW- Shear Deformation SE if deformation occurred due to pure Since bright terrain is thought to have shear. If deformation occurred by simple formed in progressive stages (Golombek shear, the orientation of the craters would and Allison, 1981; Parmentier and Zuber, depend on the amount and sense of rotation 1982), at least some of the craters with- which accompanied the deformation. Fig- in bright terrain regions should be de- ure 5 shows the orientation of craters from formed if lateral motion occurred during or the combined Uruk Sulcus data set, which after its emplacement. As a test of this hypothesis, axial ratios were measured for 48 craters in Uruk Sulcus, an area of bright terrain which trends along the south and west borders of Galileo Regio. This region N . , = 8 is marked by a conspicuous pattern of grooves, which run both longitudinally (subparallel) and transverse (at high angles) to bright terrain borders. No craters in this area are offset along grooves, therefore sig- nificant lateral movement cannot be attrib- 20 40 60 80 100 120 140 160 180 uted to displacement along possible faults. Craters in this study were grouped ac- FIG. 5. Orientations of the major axes of the best-fit ellipses of craters in the combined Uruk Sulcus data cording to whether they occurred in longi- set. The peak near 80° is not in the direction expected tudinal or transverse groove bands, in an ff lateral motion of dark terrain blocks has occurred. attempt to determine whether possible de- See text for explanation. SURFACE DEFORMATION ON GANYMEDE 207 shows a sharp peak 80-90 ° east of north. ~00 We believe that this preferential orientation 4~ o 41, /i, ,.~" °" is predominantly due to the position of the fl n .~ • sun in the Voyager images, where lighting at oblique incidence resulted in nonuniform il- lumination of the crater rims, and intro- duced a systematic bias in the identification of the rim crests. This is supported by the FIG. 6. Geometry of an opening mode I crack in a viscous layer where the displacement remote from the observation that the orientations of crater crack surface is in a direction normal to the crack. If major axes are consistent with the lighting the strain components at the point (r, 0) are known, geometry in the images. then the amount of extension a//3 beneath a wedge of Craters in the range 100-180 ° east of angular width /3 which is separated by a distance a north, which is that expected if lateral mo- from the crack face can be determined. tion of dark terrain blocks has occurred, have an average axial ratio of 0.853 - tance from the tip, then the predicted axial 0.024, which is similar to craters in Uruk ratio of a crater near the tip is Sulcus as a whole. Hence, craters aligned b 1 V~a {[1 7r°'n] [1 cos 201 in the direction predicted by the current po- a Ir &tz J sition of the furrow system do not show 1 [7"rO'nl2/t/2 evidence of large scale shear deformation, + ~ ~S-~--~~, (3) and any lateral motion that may have occurred between Marius and Galileo Re- where & is the rate of angular separation, tz giones must have preceded the formation of is the viscosity of the layer, and crn is the Uruk Sulcus. Thus, the formation of bright normal stress along the crack face. The terrain in this area cannot be directly re- results of Eq. (3) can be compared to the lated to an episode of shear deformation. observed circularity of craters on the surface. The mean axial ratio of 29 craters Deformation around Bright Terrain around 6 wedge-shaped bands is 0.826 -- Wedges 0.018. However, the orientations of these Crater shape can also be used to place an craters again show a sharp peak around 80 °. upper limit on the amount of extension be- Thus, craters do not align in the orienta- neath wedge-shaped bands of bright terrain tions expected around an opening exten- (cf. Voyager Frame 0102J2-001). If wedges sion crack, and therefore much of the dis- formed in a manner similar to a mode I ex- cernible noncircularity of craters around tension crack, then deformation should be band tips is not a consequence of extension concentrated in dark terrain surrounding across the band. Values obtained in this the tips of the wedges. Impact craters analysis, however, define an upper limit on which predate the wedges can be used as a extension. Measurements indicate that the measure of this deformation. As shown in extension across wedges with B > 16°, Fig. 6, the extension a//3 beneath a wedge which occur in several areas of Ganymede, of angular width fl with net angular separa- is less than 100%. Higher resolution images tion a can be found if the components of covering a range of phase angles would be strain at a point (r, 0) are known. The pre- required to recognize smaller amounts of dicted minor/major axes in a deformed cra- deformation or similar amounts associated ter can be determined from the stream func- with narrower wedges. tion solution of an opening crack in a viscous layer. If along the crack face the Penetrative Deformation shear stress vanishes and the tangential dis- To determine whether the deviation of placement is a linear function of the dis- furrows from small circles resulted from de- 208 ZUBER AND PARMENTIER

observed craters in this region fall in that 16 -- Southeast N=,',','58 range; however, most of these craters again 12 have a major axis orientation near 80 °. If a crater deformed in a manner consistent .~ ,---, with the deviation of the furrows from the best-fit small circles, then the orientation of 24 1 ~ Central 2016 '~ ![ N=I06 its major axis should be aligned approximately N-S. Those craters whose major =2"8 :I,/,. I ,/,=20* ,/,=30. axes fall within 30 ° of N-S have a mean axial ratio of 0.894 -+ 0.016, which is not in 1 I-7 the range expected due to the predicted I0 90 .80 70 .60 .50 :40 b/o shear deformation. Therefore if deformation occurred within Galileo Regio, it must FIG. 7. Histogram of crater axial ratios in southeast- have postdated furrows but predated most ern and central Galileo Regio. The mean in each area is represented by the long-short dashed line. The dashed of the observed craters in the area. line is the lunar mean. Shearing angles ~, of 10°, 20 °, Deformation within Galileo Regio would and 30 ° show the axial ratios expected if homogeneous violate the initial assumption that dark shear deformation had occurred within Galileo Regio blocks acted as rigid plates. However, if since the time craters have been present on the sur- deformation has occurred within this area it face. is appropriate to question whether penetrative deformation without large lateral dis- formation of dark terrain after the forma- placement is able to account for the appar- tion of the furrows, crater axial ratios were ent noncircularity of the furrows in Galileo measured for 164 craters in two areas and Marius Regiones. To test this hypothe- within Galileo Regio: the southeast where sis, the small circles around the Galileo Re- furrows deviate most from the best-fit small gio center were extended to pass through circles, and the central region (Voyager 2 the Marius area, as shown in Fig. 8. The fit frames 0546J2-001 and 0449J2-001) where of the Marius furrows to the small circles the furrows show a better fit. Figure 7 about the Galileo center can be compared shows mean axial ratios of 0.828 -+ 0.014 to the small circle fit of furrows in south- and 0.805 -+ 0.012 in these respective re- eastern Galileo Regio. The angle ~ in North gions. and South Marius averages 21 and 28 ° , re- The amount of locally homogeneous de- spectively, which is similar to the deviation formation which may have occurred in a of a number of furrows in southeastern Ga- region can be expressed as an angle of sim- lileo. ple shear, th. The angular deviation of fur- The implications of this are twofold. row segments from the best-fitting small First, the short furrow lengths in Marius circles provides a measure of this angle. Regio seem to preclude the unambiguous From this, the shear strain, 3', can be ob- determination of a best-fit center of curva- tained from the simple relation 3' = tan ture for the area, by either visual or numeri- (Jaeger, 1969). For a given shear strain, it is cal small circle fit. Second, since furrows in possible to calculate the axial ratios which Marius show approximately the same would be expected if the craters in these amount of deviation from small circles regions were present during a period of de- around the Galileo Regio center as many formation. Measurements of the angular furrows in southeastern Galileo, large scale deviation of the furrows in southeastern lateral motion may not be required to ac- Galileo Regio from the corresponding small count for the present configuration of the circle fits in Fig. 3 yields values oftk from 15 system. The nonconcentricity of furrows to 25 ° . This corresponds to axial ratios in between Marius and Galileo Regiones can the range 0.64-0.77. Twenty percent of the alternatively be explained by a component SURFACE DEFORMATION ON GANYMEDE 209

220 ° 200 = 180 = 160 ° 140 = 120 = case those within Galileo Regio are highly 60 ~ ~ ~ r ~ ~ ~ J ~ ~ = ~ 60 ° degraded. N Marius Galileo Regio ~ Regio .~= CONCLUSIONS 40* ~ 40* The apparent offsets of the centers of curvature of the furrow system in Marius and Galileo Regiones suggests that global scale lateral motion of dark terrain blocks may have taken place in Ganymede's past. O' 0 ° If large scale displacement did occur, it must have preceded the emplacement of -20° S Marius "20" bright terrain which separates the two ar- Regio eas. It is not possible to determine the mag-

• GR nitude of the displacement of the blocks be- -40 ° "40" cause numerical solutions for the center of the furrow system in Marius Regio are poorly constrained. Due to the short furrow -60' I I I I I I I I i I I .60 o 220 ° 200 ° 180 = 160 ° 140 • 120 ° lengths in this region the center of curvature based on the resolution of the Voyager FIG. 8. Small circles about the best-fitting center of data is not uniquely defined. Galileo Regio furrows extended to pass through Ma- rius Regio. Since the misfit of the furrows to small Alternatively, lateral motion may not be circles in Marius is similar to that observed for some required by the geometry of the furrow sys- furrows in southeastern Galileo Regio, lateral motion tem. Many furrows in Marius Regio deviate of dark terrain blocks may not be required to account from best-fit small circles by amounts simi- for the present nonconcentricity of the furrow sys- lar to some furrows within Galileo Regio, tem. which suggests that the present geometry could be a consequence of either penetra- of early penetrative deformation without tive deformation or an initially nonconcen- major shear displacement or by an initially tric system. noncircular furrow system. While it is not The assumption that the furrow system possible to rule out global scale lateral mo- was initially circular is difficult to justify, in tion between the regions, the geometry of part because of the morphological differ- the system does not require it. ences between the furrows in Galileo and Impact craters within transverse bright Marius Regiones. There is no definite proof terrain in the Uruk Sulcus region are more that the system was produced by impact, circular than those within longitudinal although this hypothesis remains the most bright terrain. Golombek and Allison (198 l) attractive. The calculated center of curva- suggested that longitudinal terrain in this ture for Galileo Regio lies beneath the area predates the transverse. If this is true, Osiris ejecta blanket and as a result, no then the greater degree of ellipticity associ- trace of the proposed site of impact re- ated with craters in the older terrain may be mains. a consequence of strain associated with Impact craters in Uruk Sulcus are more subsequent bright terrain formation. Cra- circular than those within Galileo Regio. ters in Galileo Regio are more elliptical than This is most likely a function of the degree those in either region of Uruk Sulcus. This of preservation of the crater rims. Both cra- is probably the case because craters in ters in dark and bright terrain are less circu- bright terrain are in general less degraded lar than lunar craters. This may be a conse- (i.e., have sharper rims) than those in dark quence of either the contrasting physical terrain. Most craters in Uruk Sulcus are properties of the lunar and Ganymedian fairly well-preserved, while in almost every surfaces in controlling both the initial form 210 ZUBER AND PARMENTIER and subsequent modification of craters, or LUCCHITTA, B. K. (1980). Grooved terrain on Gany- the resolution of the Voyager images. mede. Icarus 44, 481-501. Measurements of the ellipticity of craters McKINNON, W. B., AND H. J. MELOSH (1980). Evolu- in both bright and dark terrain are strongly tion of planetary lithospheres: Evidence from multiringed structures on Ganymede and Callisto. Icarus affected by the position of the sun on the 44, 454-471. images. Therefore in many cases the actual MELOSH, H. J. (1982). A simple mechanical model of amount of surface deformation must be less Valhalla Basin, Callisto. J. Geophys. Res. 87, 1880- than that measured for the craters in this 1890. analysis. Multiple phase angle coverage of MINSTER, J. B., T. H. JORDAN, P. MOLNAR, AND E. HAINES (1974). Numerical modelling of instantane- the surface would remove the effect of the ous plate tectonics. Geophys. J. R. Astron. Soc. 36, sun and allow the detection of smaller de- 541-576. grees of deformation. The amount of defor- PARMENTIER, E. M., S. W. SQUYRES, J. W. HEAD, mation associated with several wedges of AND M. L. ALLISON (1982). The tectonics of Gany- bright terrain on the surface of Ganymede mede. Nature 295, 290-293. PARMENTIER, E. M., AND M. Z. ZUBER (1982). Gany- is <100%, which is consistent with bright mede tectonics: Progressive lithospheric fragmenta- terrain formation by finite lithospheric ex- tion due to planetary expansion. Lunar Planet. Sci. tension. Conf. XIII, 617-618. The circularity of impact craters within PASSEY, Q. R., AND E. M. SHOEMAKER(1982). Craters Galileo Regio suggests that only limited and basins on Ganymede and Callisto: Morphologi- cal indicators of crustal evolution. In The Satellites penetrative deformation has occurred over t~fJupiter (D. Morrison, Ed.), pp. 379-434. Univ. of the period of time in which present impact Arizona Press, Tucson. craters are preserved. For the greatest part REMSBERG, A. R. (1981). A structural analysis of Val- of its evolution, Ganymede's lithosphere halla Basin, Callisto. Lunar Planet. Sci. Conf. XIL has behaved rigidly and has been domi- 874-876. nated by extensional tectonics with defor- RONCA, L. B., AND J. W. SALISBURY (1966). Lunar history as suggested by the circularity index of lunar mation concentrated in regions of bright craters, h'aras 5, 130-138. terrain. This extensional deformation was SHOEMAKER, E. M., B. K. LUCCHITTA, J. B. PLESC1A, confined to a period of time during or S. W. SQUYRES, AND D. E. WILHELMS (1982). The shortly after bright terrain emplacement. Geology of Ganymede. In The Satellites of Jupiter (D. Morrison, Ed.), pp. 435-520. Univ. of Arizona Press, Tucson. ACKNOWLEDGMENTS SMITH, B. A., L. A. SODERBLOM, T. V. JOHNSON, A. Comments by three anonymous reviewers improved P. INGERSOLL, S. A. COLLINS, E. M. SHOEMAKER, the paper. We thank Clyde Nishimura for helpful dis- G. E. HUNT, H. MASURSKY, M. H. CARR, M. E. cussions regarding error analysis on a sphere, and Jim DAVIES, A. F. COOK 1I, J. BOYCE, G. E. DANIEL- Garvin and Paul Helfenstein for programming sugges- SON, T. OWEN, C. SAGAN, R. F. BEEBE, J. tions and software. This research was supported by VEVERKA, R. G. STROM, J. F. McCAULEY, D. NASA Grant NSG-7605. MORRISON, G. A. BRIGGS, AND V. E. SUOMI (1979a). The Jupiter system through the eyes of Voyager I. Science (Washington, D.C.) 204, 951- REFERENCES 972. DRAPER, N. R., AND H. SMITH (1977), Applied Re- SMITH, B. A., L. A. SODERBLOM, R. 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