Global shear patterns driven by tidal stress
Gregory Hoppa*, B. Randall Tufts*, Richard Greenberg*, Paul Geissler*
For submission to Icarus
August 31, 1998
*Lunar and Planetary Laboratory
University of Arizona
Tucson, AZ 85721-0092
Send all correspondence to:
Lunar and Planetary Laboratory
University of Arizona
1629 E. University Blvd.
Tucson, AZ 85721-0092
Send all correspondence to:
Lunar and Planetary Laboratory
University of Arizona
1629 E. University Blvd.
Tucson, AZ 85721-0092
Strike-slip faults on Europa:
Global shear patterns driven by tidal stress
Diurnal tides due to orbital eccentricity may drive strike-slip motion on Europa through a process of "walking" in which faults open and close out of phase with alternate right and left-lateral shear.
Mapping of five different regions on Europa has revealed 121 strike-slip faults including Astypalaea Linea a 800 km long fault with 42 km of right-lateral offset. At high southern latitudes near Astypalaea all of the strike slip faults identified were right-lateral. Europa appears to preferentially form right-lateral faults in the southern hemisphere and left-lateral faults in the northern hemisphere, consistent with tidal walking.
At the five locations, non-synchronous rotation explains the azimuthal orientations and distribution of sense of shear, which fit formation ~60f to 90f west of their current positions. Alternatively, stress due to differential rotation might also explain the observed shear patterns.
Nearly all identified strike-slip faults were associated
with double ridges or bands, but none were detected along ridgeless cracks
(even older ones). Thus, cracks without ridges may not have penetrated
to a decoupling layer, consistent with the models for ridge formation that
require cracks to penetrate to a liquid water ocean.
Key words: Europa, Satellites of Jupiter, tides, shear
Diurnal tides due to orbital eccentricity may be a primary driver of tectonic activity on Europa. If Europa were in a circular orbit, there would be no diurnal variation because the tidal elongation would have a constant amplitude always oriented in the direction of Jupiter. However, Europa has a non-zero eccentricity (e=0.01) due to the Laplace resonance with Io and Ganymede, so every orbital period (3.6 days) the tides increase and decrease as Europa approaches pericenter and apocenter, respectively. Moreover, the tidal-raising potential follows the direction of Jupiter. Therefore, midway between pericenter and apocenter the center of the tidal bulge is oriented ~1f west of the prime meridian, (expressed in radians, this angle is twice Europa's orbital eccentricity). Half an orbit later, it is centered 1f east of the prime meridian. The diurnal change in orientation and amplitude of the tide, as well as other longer-term tidal variations, results in significant stress on the surface which may contribute to the formation of cracks and associated linear ridges (Helfenstein and Parmentier 1983 & 1985, McEwen 1986, Leith and McKinnon 1996, Greenberg et al. 1998), followed by displacement along such cracks.
II. Astypalaea Linea
Strike-slip motion on Europa may be due to the diurnal tides. As an example, consider the prominent feature Astypalaea Linea, a strike-slip fault similar to the Earth's San Andreas, both in its length (~800km) and in the sense of its shear (Tufts 1996). The shear is "right-lateral", meaning that to an observer looking across the fault, the opposite side would be moving to the right. Astypalaea and its offset are visible in images taken by the Voyager spacecraft in 1979 (Fig. 1a). Fig. 1b shows five lineaments that were crossed by Astypalaea and have been offset by the right-lateral shear by 42 km. Moreover, near the northern end there is a rhomboidal gap which appears to have been opened by 42 km of shear along the fault (Tufts 1996).
Diurnal tidal variation can drive that shear. Fig. 2 shows the diurnal stress field for this region. At apocenter (Fig. 2a), the diurnal tides are aligned such that tension is perpendicular to Astypalaea, tending to open the fault. Next, a quarter orbit following apocenter (Fig. 2b), the stresses are aligned at approximately 45f with respect to the fault, driving right-lateral shear. At pericenter, the stress is exactly the opposite of what it was at apocenter. Thus the fault is squeezed closed, because the compressive component of stress is now perpendicular to Astypalaea. Over the next quarter of the orbit, the left-lateral shear stress develops. However, because the fault has just been closed, friction prevents reversal of any right-lateral shear that may have occurred half an orbit earlier. Thus this sequence of stresses "walks" the fault in a manner closely analogous to actual walking, creating shear displacement (Tufts et al. 1997, Greenberg et al. 1998).
III. Observations of strike-slip faults
Additional evidence supporting "walking" can be found by looking at the distribution of strike-slip faults at various sites where there is adequate imaging. Fig. 3 shows a mercator map of Europa with white boxes representing four regions of high-resolution coverage where we have mapped the distribution of strike-slip faults in addition to the Astypalaea region. Strike-slip faults much smaller than Astypalaea Linea can be easily identified by realigning or "reconstructing" linear features that are truncated by a lineament. Identification of a strike-slip feature requires at least two unambiguous piercing points which can be reconstructed to show the relative motion across the fault. Table 1 summarizes the statistics of 121 strike-slip features in the five different regions of Europa discussed below.
A. Astypalaea Linea Region
The high southern latitudes of Europa have not yet been imaged by Galileo at high resolution. However, moderate resolution Voyager and Galileo images indeed reveal five additional features in the vicinity of Astypalaea Linea that show evidence of right-lateral motion (Tufts 1998). While the amount of lateral motion (10-20 km) is less than at Astypalaea Linea, the diurnal stress field for these features would be very similar to the stress field shown in Fig. 2.
B. Wedges Region
The wedges region in the southern hemisphere shows an abundance of strike-slip faults. Within a single Galileo image (s038639400) centered on -15f S, 195f W we have identified 22 strike-slip features, 21 of which are right-lateral (Fig. 4). The average amplitude of lateral motion is 2 km, with the largest feature showing 5.5 km of right-lateral displacement.
Higher resolution images within the wedges region have revealed additional strike-slip faults. During Galileo's 12th orbit, images at 50 m/pixel and 25 m/pixel were taken of this region. Within the four image mosaic at 50 m/pixel, 19 strike-slip features can be seen. Six of these features had already been identified within the lower resolution image. Of the 13 new faults, 12 were right-lateral. Additional high resolution images at 25 m/pixel revealed 8 additional strike-slip faults. Again most (7 of 8) of these features were right-lateral.
In total, among the three sets of images of the wedges region, 43 strike-slip features have been identified; 40 out of 43 are right-lateral (as shown in Table 1). Two other characteristics of the population of strike-slip faults in this region are striking: first, among the 43 features the azimuthal orientation of strike-slip faults appears to be randomly distributed within this region (Fig. 5). Second, the higher resolution images reveal that most (~55%) of the strike-slip faults are along double ridges. Most of the other faults occur along bands or multiple ridge systems. Three cases of strike-slip motion are observed along cracks (linear features without evidence of associated ridge topography) even though many cracks are clearly visible at high resolution. Thus, cross-cutting relationships within this region suggest that right-lateral motion has been the dominant direction of strike-slip motion throughout the recent geologic past. All these characteristics are discussed in Sec. V below.
C. Conamara Chaos Region
High-resolution images slightly north of the equator near the center of the trailing hemisphere were obtained during Galileo's 6th orbit. Within this region (10f N, 270f W), dominated by Conamara Chaos and the triple bands Agave and Asterius, we have identified 38 strike-slip features, on images acquired at 180 m/pixel and 22 m/pixel (Fig. 6). Half of the strike-slip features in this region are left-lateral faults, and half are right-lateral. There appear to be favored azimuthal orientations for the strike-slip faults within this region (Fig. 7) which are consistent with the dominant orientations of all linear features within this region (Spaun et al. 1998).
D. Northern hemisphere bright plains
High resolution images acquired during Galileo's 15th orbit show the bright plains near 23f N, 225f W (Fig. 3). Within two images at 230 m/pixel we have identified 15 strike-slip features, 12 of which are left-lateral (Fig. 8). In one case an older band was identified to have been broken in four places by left-lateral faults. Average offsets along these features are 6 km with the largest having 30 km of strike-slip motion. The azimuthal distribution of the faults in this region is shown in Fig. 9. This distribution may be random but it is difficult to determine due to the small number of faults identified here.
E. Tyre Region
During Galileo's 14th orbit, high-resolution imaging was obtained near Tyre, a multi-ring impact structure, located at 34f N, 146f W (Moore et al. 1998). Although this imaging sequence focused on mapping an impact structure, numerous tectonic features are also present within this region. As with the northern bright plains region, strike-slip faults in the Tyre region are predominantly left-lateral. Twenty strike-slip faults were identified near Tyre, fifteen faults of which were left-lateral (Fig. 10). The azimuthal distribution of the faults within this region may show some preference for left-lateral faults oriented in the east-west direction (Fig. 11) However, the small number statistics can not identify a random distribution or preferential directions of shear.
F. Summary of Observations
This survey of five different regions on Europa has revealed 121 strike-slip faults. At high southern latitudes near Astypalaea all of the strike-slip faults identified were right-lateral. Closer to the equator, but still in the southern hemisphere, nearly 95% of the strike-slip faults in the wedges region were right-lateral. Very close to the equator in the northern hemisphere, near Conamara chaos, the distribution of strike-slip faults is nearly equal between left-lateral and right-lateral faults. At 23f north of the equator (bright plains) 80% of the strike-slip faults are left-lateral. Further north at 35f, 75% of the strike-slip faults are also left-lateral. Based on these observations, Europa appears to preferentially support the formation of right-lateral faults in the southern hemisphere and left-lateral faults in the northern hemisphere.
IV. A closer look at the theory of "walking"
The process of "walking" by diurnal tides not only fits the case of Astypalaea, but it may also explain the abundance of right-lateral faults in the southern hemisphere and left-lateral faults in the northern hemisphere of Europa. At some of these locations the diurnal stress does not yield a walking process as obvious as at Astypalaea Linea, so a more quantitative determination of the effects of diurnal stress on shear motion is needed. To characterize the walking process, we resolve the stress field along each fault to be considered into two components: the shear stress along the fault and the normal stress perpendicular to it. These components can each be plotted as a function of time to represent the stress experienced over a diurnal cycle.
First, we apply this method to the case of Astypalaea Linea to confirm the result in Sec. II, which was based on Fig. 2. Fig. 12 shows the resolved stress field for Astypalaea as a function of time. Tension across the fault is defined as negative, compression positive (dashed line), while shear stress (solid line) in the right and left-lateral directions are defined as positive and negative, respectively. The tendency for right-lateral motion along Astypalaea can be inferred from Fig. 12 (which gives a more complete description of the time dependence shown in Fig. 2), assuming that Astypalaea does represent a crack through the ice. During the tensile phase (when tension is perpendicular to the fault) between 1/4 orbit before apocenter and 1/4 orbit after apocenter, the crack is open so the shear motion may readily take place. The rise in the shear stress curve (in Fig. 12) indicates that right-lateral displacement occurs during this phase (which is analogous to moving one's foot forward while walking). Then, during the compressive phase (starting 1/4 orbit after apocenter), left-lateral shear stress builds up along the fault, but shear displacement along the fault is resisted because the fault is squeezed shut by the compression. Then, if the ice were perfectly elastic, when the fault reopens (1/4 orbit after apocenter), the lithosphere should spring back to its configuration at the beginning of the previous tension phase (one orbit earlier). More likely, there is some hysteresis that inhibits the ice from fully springing back. For example, the spring-back would be limited by any inelasticity in the ice, or by any displacement of the adjacent plates that may have taken place as the shear stress was applied (analogous to the motion of one's body forward during the part of a step when the foot is on the ground). Whatever such mechanism it is, as long as some of the accumulated stress during the compressive phase can relax before the fault reopens, then small right-lateral steps can take place along Astypalaea every 3.5 days.
The analogy of this process for strike-slip motion to human walking is very close. When a person lifts up her foot, she may take a step forward. Similarly faults on Europa may take a step when the tidal stress opens up a crack. Forward motion of the foot temporarily stops when it is placed back on the ground. Likewise on Europa the lateral motion along a crack ends when the fault closes due to compression. When the foot is lifted again it does not spring back to its original position because the main body (adjacent plate) has moved forward; instead the foot is free to take another step. Similarly, faults too may take another step when the crack reopens, assuming that the ice does not spring back to its original position.
Based on examination of the resolved tidal stresses (e.g. Fig. 12), the preferred direction of "walking" (left-lateral or right-lateral) can be predicted for any location or orientation on the surface. The criterion for predicting the direction of motion of a fault is the direction of the change in the shear stress curve during the tension phase. Right-lateral motion would be predicted for Astypalaea because the shear stress curve moved upward during the tension phase in Fig. 12. If the curve had a net downward motion during the tension phase, the fault would walk in the left-lateral sense.
Due to regional variations in the tidal stress, the resolved stress field can be more complicated at different latitudes, longitudes and orientations than at Astypalaea. Consider, for example, the tidal stress associated with the wedges region (15f S, 195f W). Fig. 13 shows the resolved stress for a fault oriented in the east-west direction there. The fault represented in Fig. 13 would be predicted to move in the right-lateral direction because the shear stress curve is higher when the fault closes than when it opens. In that way, it is similar to Astypalaea. However, the shear stress behavior here is much more complicated than at Astypalaea Linea. During the time that the fault is open (normal stress < 0) the displacement moves back and forth. In the human walking analogy, this behavior can be represented by a person who lifts her foot and shuffles it forward and back before deciding where to put it down. The critical issue though is whether she puts her foot down in front of or behind where she lifted it. Likewise the critical issue in Fig. 13 is that the shear stress ends higher (more positive) at the end of the tension phase than at the beginning.
Fig. 14 shows another example, the stresses for a feature in the wedges region oriented in the north-south direction. Left-lateral motion is predicted in this case because the shear stress becomes more left-lateral (net downward shift in the curve in Fig. 14) while the fault is open (i.e. during the tension phase, while the dashed line is negative).
Based on this criterion, Fig. 15 shows the predicted distribution of left-lateral and right-lateral faults on Europa as a function of position and azimuth. At latitudes greater than 30f, this tidal stress model predicts that there should be an abundance of left-lateral faults in the northern hemisphere and an abundance of right-lateral faults in the southern hemisphere regardless of their orientation. At lower latitudes, this model predicts equal numbers of left-lateral and right-lateral faults near the sub-Jupiter and anti-Jupiter points. Near the apex of the leading and trailing hemispheres (i.e. longitudes 90f and 270f W) an abundance of left-lateral faults is predicted in the northern hemisphere at all latitudes (right-lateral for the southern hemisphere). Over all, this model predicts that there should be more left-lateral faults in the northern hemisphere and more right-lateral faults in the southern hemisphere.
V. Comparison of theory with observations
The measured distribution of strike-slip faults in the five regions discussed in Sec. III shows that there indeed is an abundance of right-lateral faults in the southern hemisphere and left-lateral faults in the northern hemisphere, consistent with the above theoretical model.
In the wedges region (10f S: 20f S, 190f W: 200f W ), theory (Fig. 15) predicts that the distribution of left-lateral and right-lateral faults should be equal. However, 95% of the faults observed in this region are right-lateral (Table 1). This discrepancy can not be explained by the azimuthal orientations of the faults, because they are not clustered in a direction that would favor right-lateral shear (e.g. east-west according to Fig. 15). Instead, the discrepancy is best explained by non-synchronous rotation (Greenberg and Weidenschilling 1984). Assuming non-synchronous rotation, the older features in the wedges region were probably formed to the west of their current position (i.e. further west relative to the anti-Jupiter point). There, our model predicts higher fractions of right-lateral faults; the portion is 100% right-lateral 75f west of the current position in any orientation (Fig. 15). The formation of most of the right-lateral faults at that location would be consistent with the random azimuthal distribution of faults observed (Fig. 5). The three left-lateral cases (clustered near 150f azimuth (Fig. 5)), may have formed after an additional 30f - 60f of rotation, where this terrain was at longitudes where such shear offset in that sense is produced for faults with that orientation, according to Fig. 15. Thus, while areas like the wedges region near the sub-Jupiter and anti-Jupiter points currently favor the formation of equal numbers of right and left-lateral faults, most of the faults in this region probably formed tens of degrees west of their current position.
In the Conamara region (5f N: 18f N, 266f W: 280f W ), theory (Fig. 15) predicts that all of the current strike-slip faults in this region should be left-lateral. However, our measurements show that only 50% of the faults observed in this region are left-lateral (Table 1). Can this discrepancy here also (as at the wedges) be explained by non-synchronous rotation? In fact, our theory does predict an equal distribution of strike-slip faults 60f - 90f west of Conamara, which would agree with the numbers observed. However, the azimuthal orientations of the observed faults must also be considered within this scenario. The orientations of observed left-lateral faults (Fig. 7) are clustered at values predicted by theory (Fig. 15) for 90f to the west of Conamara's current position. However, the observed orientations of the right lateral faults (Fig. 7) are not clustered in the north-south direction as predicted by Fig. 15 at that location. In part this discrepancy for the right-lateral statistics may be due to the fact that fewer linear features are oriented in the north-south direction in this region (Spaun et al. 1998), limiting the possibility for right-lateral faults in the north-south direction. The observed right-lateral shear displacements may have formed 60f (rather than 90f) ago. The lack of left-lateral faults oriented in the north-south direction may also be due in part to the paucity of linear features oriented that in direction. In summary, as with the wedges region, shear displacement observed near Conamara is consistent with formation 60f - 90f west of their current position.
In the northern hemisphere bright plains (20f N: 25f N, 218f W: 234f W ), theory (Fig. 15) predicts that half of the present day strike-slip features should be left-lateral and half right-lateral. However, 85% of the strike-slip features are found to be left-lateral (Table 1). Again, the statistics would be better explained by shear displacement ~60f back in rotation. At longitudes 45f - 75f to the west of the bright plains Fig. 15 predicts that >3/4 of the strike slip faults should be left-lateral, which is consistent with the measured distribution. The azimuthal orientations of all of the left-lateral faults in this region are also consistent with the formation of all of these features between 45f - 75f in the past. However, the azimuths of the three right-lateral faults are not consistent with their formation 45f - 75f to the west of their current longitude. Instead azimuths of the right-lateral faults require that they formed between 75f - 90f ago (where the fraction of left-lateral faults should be between 1/2 and 3/4). Actually one of the three right-lateral faults is associated with an east-west trending global scale triple band over ~1000 km in length. Theory (Fig. 15) does not predict the formation of any right-lateral features in the east-west direction at any longitude (between 20f and 25f N). However, to the west and east of this region, this triple band curves toward the equator. The right-lateral motion along this feature may be due to shear stress at lower latitudes.
In the Tyre region (26f N: 44f N, 135f W: 154f W), theory (Fig. 15) predicts that >2/3 of the strike-slip features in this region should be left-lateral for shear offset motion at the current location or any place up to 90f backward in rotation (i.e. to the west). This prediction fits the observation that 75% of the strike-slip features are left-lateral (Table 1). The azimuthal orientations of the left-lateral faults (Fig. 11) are equally consistent with formation anywhere over the last 90f of rotation. However, the orientations of 3 right-lateral faults (0f - 30f) (Fig. 11) are difficult to explain at any longitude by the theory (Fig. 15), but those statistics are small. Thus, the Tyre region also fits the non-synchronous story.
In the Astypalaea region (60f S: 80f S, 191f W: 285f W), theory (Fig. 15) predicts that all of the shear features should be right-lateral regardless of azimuthal orientation and that is indeed the case (Fig. 15). At this latitude, right-lateral shear displacement is theoretically expected at all longitudes at all orientations, so this result is consistent with formation at a different location due to non-synchronous rotation, but does not require it.
The observations of preferentially left-lateral faults in Europa's northern hemisphere and right-lateral faults in the southern hemisphere agree with the theoretical model for "walking" based on the diurnal tidal stress. Within every region discussed here, cross-cutting relationships show that these features have formed throughout Europa's geologic history. Strike-slip motion was common in the past and perhaps is ongoing today. Therefore, if non-synchronous rotation is taking place on Europa, then many of the strike-slip features observed by Galileo and Voyager did not form at their current longitude with respect to the direction of Jupiter. The current diurnal tidal stress can not fully explain the observed strike-slip motion. Instead, the average effects of at least the past 60f of non-synchronous rotation can be invoked, as discussed in Sec. V, to explain the abundance of right-lateral faults in the wedges region, and the left-lateral faults in the northern plains and Tyre region.
Most of these strike-slip features appear along ridge systems. Little evidence of lateral motion is observed along the many apparent cracks, that do not have associated ridges. The presence of strike-slip faults along double ridge pairs suggests that the medial trough represents a plate boundary i.e. a crack that must penetrate through the ice to a decoupling layer. Our results suggest that cracks without ridges apparently have not generally penetrated that deep, consistent with the model by Greenberg et al. (1998) that the ridges form only along cracks that penetrate to a liquid water ocean. In that process, diurnal tidal working of a crack squeezes slush to the surface and builds ridges, in addition to the role such tides play in walking the shear.
A final implication of the process of walking is that, on Europa at least, shear motion along cracks actually drives the motion of adjacent plates, rather than the fault being simply an expression of what happens as plates slide by one another driven by other forces. The latter has generally been assumed to be the case for terrestrial strike-slip faults. However, our discovery that tides can drive shear, which in turn pushes plates, suggests that it may be worth considering whether such effects may be relevant on the Earth. If it is, it would provide another mechanism for driving terrestrial tectonics, perhaps on a large scale. In that case, Tufts' (1996) discovery of a San Andreas sized strike-slip fault on Europa (Astypalaea Linea) may have important implications for the home planet of the original San Andreas fault.
We thank the technical staff of the Galileo project for making this study possible. D. Durda and the members of the Galileo imaging team, led by Mike Belton, and their associates for their comments and suggestions. C. Phillips and M. Milazzo for the mosaics used to identify the features discussed here. Theoretical aspects of this work were supported by NASA's Planetary Geology and Geophysics program.
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