Global tectonics of a despun planet

Mercury, the Moon, and many large satellites of the major planets have been tidally despun from an initially faster rotation. These bodies probably possessed equatorial bulges which relaxed as they lost their spin. An analysis of the stresses induced in an elastic shell by the relaxation of an equatorial bulge indicates that differential stresses may reach a few kilobars and that the tectonic pattern developed depends mainly upon the shell thickness. In every model studied the azimuthal stress σ_?? is larger (more compressive) than the meridional stress σθθ. For a thin elastic shell (thickness less than one-twentieth of the planet's radius) the zone from the equator to 48° latitude is characterized by strike-slip faulting. Poleward of this, normal faults and graben trending east-west are expected. Thicker elastic shells acquire an equatorial belt of thrust faults with east-west throw and rough north-south trends. These tectonic styles may be modified by a small (0.05-0.1%) radial expansion or contraction. Expansion shifts the polar normal faulting province toward the equator, while contraction shifts the equatorial provinces poleward. These patterns are not substantially altered by plastic yielding of the shell, although the equatorial thrust fault province is suppressed by strike-slip faulting until strike-slip faults occur poleward of 64.8° latitude. We conclude that there are many tectonic patterns consistent with despinning and radial contraction or expansion, but they must all be consistent with σ_?? > σθθ. These results also indicate that the polar regions of a despun planet are of particular interest in deciding whether a given lineament system is due to stresses induced by the relaxation of the planet's equatorial bulge.     

Global fracture patterns of a despun planet: Application to Mercury

We have determined the global fracture patterns resulting from combinations of stresses due to tidal despinning and contraction or expansion. We find that Mercury's lineament pattern is consistent with a history of despinning and contraction. According to our model, the observed tectonic pattern implies that the despinning process reached completion before the planet ceased contracting. Our model predicts a stress due to contraction which is up to 1.8 times the maximum despinning stress on Mercury. The maximum contractional stress could be as large as 4 times the maximum despinning stress if the oldest fractures on the planet are N-S thrust faults in the equatorial region.     

The velocity dispersion in Saturn's rings

The surface of Mercury exhibits a global tectonic system consisting of an ancient set of NE and NW trending lineaments and a younger set of planimetrically arcuate escarpments interpreted as thrust or high-angle reverse faults. The trends, distribution, and age relations of these tectonic features can be explained by a combination of tidal despinning and global contraction of the planet. In our model, early tidal despinning resulted in conjugate shear fractures trending roughly N60°E and N60°W which were subsequently modified by a variety of surface processes to produce the presently visible set of lineaments. Continued despinning plus global contraction produced thrust faults with roughly north-south trends. Final contraction may have postdated despinning and produced randomly oriented thrust faults. All of these events predated the formation of Caloris basin, because basin-associated deposits blanket both lineaments and arcuate thrust faults.     

Tectonics on Iapetus: Despinning, respinning, or something completely different?

Saturn’s moon Iapetus is unique in that it has apparently despun while retaining a substantial equatorial bulge. Stresses arising from such a non-hydrostatic shape should in principle cause surface deformation (tectonics). As part of a search for such a tectonic signature, lineaments (linear surface features) on Iapetus were mapped on both its bright and dark hemispheres. Lineament orientations were then compared to model stress patterns predicted for spin-down from a rotation period of 16.5 h (or less) to its present synchronous period, and for a range of lithospheric thicknesses. Many lineaments are straight segments of crater rimwalls, which may be faults or joints reactivated during complex crater collapse. Most striking are several large troughs on the bright, trailing hemisphere. These troughs appear to be extensional and are distinctive on that hemisphere, because the interior floors and walls of the troughs contain dark material. Globally, no specific evidence of strike slip or thrust offsets are seen, but this could be due to the age and degraded nature of any such features. We find that observed lineament orientations do not correlate with predicted patterns due to despinning on either hemisphere (the equatorial ridge was specifically excluded from this analysis, and is considered separately). Modest evidence for preferred orientations ±40° from north could be construed as consistent with respinning, which is not necessarily far-fetched. Assuming the rigidity of unfractured ice, predicted maximum lithospheric differential stresses from despinning range from ∼1 MPa to ∼160 MPa for the elastic spheroid and thin lithosphere limits, respectively (although it is only for thicker elastic lithospheres that we expect a nonhydrostatic state to be maintained over geologic time against lithospheric failure). The tectonic signature of despinning may have been obscured over time because the surface of Iapetus is very ancient, Iapetus’ thick lithosphere may have inhibited the full tectonic expression of despinning, or both. Several prominent lineaments strike E–W, and are thus parallel to the equatorial ridge (though not physically close to it), but a tectonic or volcanic origin for the ridge is highly problematic.     

A contraction model for the flattening and equatorial ridge of Iapetus

Others have explained the excess flattening of Iapetus by a model in which the moon formed at a high spin rate, achieved isostatic equilibrium by very rapid interior heating caused by short-lived radioactive isotopes (SLRI), and subsequently cooled, locking in the excess flattening with respect to an equilibrium shape at its present spin rate. Here we propose an alternate model that does not require an unusually high initial spin rate or the SLRI. The initial formation of Iapetus results in a slightly oblate spheroid with porosity >10%. Radioactive heating by long-lived isotopes warms the interior to about 200 K, at which point it becomes ductile and the interior compacts by 10%, while the 120 km-thick exterior shell remains strong. The shell must deform to match the reduced volume of the ductile interior, and we propose that this deformation occurs along the equator, perhaps focused by a thinner equatorial shell. The final shape of the collapsed sphere matches the observed shape of Iapetus today, described as an oblate ellipse, except along the equator where strain concentration forms a broad ridge. To maintain this non-equilibrium shape, the thickness of the shell must exceed 120 km. Testing the equatorial focusing hypothesis will require a model that includes non-linear processes to account for the finite yield strength of the thick lithosphere. Nevertheless, we show that the stress in the lithosphere generated by the contraction of the interior is about 3 times greater than the stress needed to deform the lithosphere, so some type of lithospheric deformation is expected.     

Tectonic patterns on a tidally distorted planet

Tidal deformation of the lithosphere of a synchronously rotating planet or satellite produces stresses that may result in a distinctive tectonic pattern. The lithosphereis treated as a thin elastic shell which maintains the equilibrium shape of a tidally distorted body. Stresses develop as the equilibrium shape changes during orbital evolution. E. M. Anderson's theory of faulting is used to translate this stress pattern into a tectonic pattern of faults on the planet's surface (The Dynamics of Faulting, Oliver & Boyd, Edinburgh, 1951). On a body such as the Moon, which has receded from the Earth, an originally large tidal bulge has collapsed. The predicted tectonic pattern includes N-S striking thrust faults over an area extending roughly 30° in latitude and longitude around the sub-Earth point and its antipode. The polar regions above roughly 70° latitude exhibit normal faults striking from the near side of the Moon toward the far side. Strike slip faults, with offsets consistent with east-west compression, occur near the limbs. Stress differences are largest at the equator on the limbs, and may have reached several hundreds bars over the last few billion years of the Moon's history. The existence of such a tectonic pattern on the Moon can only be resolved by photogeologic mapping. At present, there is little evidence of this pattern; however, the crucial evidence probably lies in the poorly mapped lunar polar regions. These tectonic patterns, which could provide geologic evidence for large tidal distortions, may also be present on the Galilean satellites of Jupiter.     

Global contraction of planetary bodies due to despinning: Application to Mercury and Iapetus

We extend previous work on the global tectonic patterns generated by despinning with a self-consistent treatment of the isotropic despinning contraction that has been ignored. We provide simple analytic approximations that quantify the effect of the isotropic despinning contraction on the global shape and tectonic pattern. The isotropic despinning contraction of Mercury is ∼93 m (T/1 day)⁻², where T is the initial rotation period. If we take into account both the isotropic contraction and the degree-2 deformations associated with despinning, the preponderance of compressional tectonic features on Mercury’s surface requires an additional isotropic contraction ?1 km (T/1 day)⁻², presumably due to cooling of the interior and growth of the solid inner core. The isotropic despinning contraction of Iapetus is ∼9 m (T/16 h)⁻², and it is not sensitive to the presence of a core or the thickness of the elastic lithosphere. The tectonic pattern expected for despinning, including the isotropic contraction, does not explain Iapetus’ ridge. Furthermore, the ridge remains unexplained with the addition of any isotropic compressional stresses, including those generating by cooling.     

The thermal evolution of Mars as constrained by paleo-heat flows

Lithospheric strength can be used to estimate the heat flow at the time when a given region was deformed, allowing us to constrain the thermal evolution of a planetary body. In this sense, the high (>300 km) effective elastic thickness of the lithosphere deduced from the very limited deflection caused by the north polar cap of Mars indicates a low surface heat flow for this region at the present time, a finding difficult to reconcile with thermal history models. This has started a debate on the current heat flow of Mars and the implications for the thermal evolution of the planet. Here we perform refined estimates of paleo-heat flow for 22 martian regions of different periods and geological context, derived from the effective elastic thickness of the lithosphere or from faulting depth beneath large thrust faults, by considering regional radioactive element abundances and realistic thermal conductivities for the crust and mantle lithosphere. For the calculations based on the effective elastic thickness of the lithosphere we also consider the respective contributions of crust and mantle lithosphere to the total lithospheric strength. The obtained surface heat flows are in general lower than the equivalent radioactive heat production of Mars at the corresponding times, suggesting a limited contribution from secular cooling to the heat flow during the majority of the history of Mars. This is contrary to the predictions from the majority of thermal history models, but is consistent with evidence suggesting a currently fluid core, limited secular contraction for Mars, and recent extensive volcanism. Moreover, the interior of Mars could even have been heating up during part of the thermal history of the planet.     

Despinning plus global contraction and the orientation of lobate scarps on Mercury: Predictions for MESSENGER

Observations by the Mariner 10 spacecraft suggest that the lobate scarps on Mercury, which have been interpreted to record at most 1-2 km of radial contraction of the planet after the end of the Late Heavy Bombardment, possess a global, preferred N-S orientation but lack a strong latitudinal dependence on their surface expression. Here, we reexamine the idea that a decrease in the planetary rotation rate (despinning) coupled with global contraction of at least 3-5.5 km prior to the end of Late Heavy Bombardment resulted in global N-S oriented thrust faults. The surface expression of these faults is assumed to have been erased by the end of the Late Heavy Bombardment, and the faults were subsequently reactivated by later global contraction, producing generally N-S oriented thrust faults from an isotropic stress field. We use the estimate of >3-5.5 km contraction prior to ∼4 Ga as an additional constraint to thermomechanical simulations of the evolution of Mercury, finding that a wide range of models are consistent with this observation. The fact that a wide range of states are consistent with the contraction of Mercury prior to the end of Late Heavy Bombardment but only a restricted set of states are consistent with the at most 1-2 km of subsequent contraction bolsters the idea that there may be hidden strain on Mercury, features unseen by Mariner 10 but likely visible to the MESSENGER spacecraft.     

The cause for the north-south orientation of the crustal dichotomy and the equatorial location of Tharsis on Mars

The crustal dichotomy and the Tharsis rise are the most prominent topographic features on Mars. The dichotomy is largely an expression of different crustal thicknesses in the northern and southern hemispheres, while Tharsis is centered near the equator at the dichotomy boundary. However, the cause for the orientation of the dichotomy and the equatorial location of Tharsis remains poorly understood. Here we show that the crustal thickness variations associated with the dichotomy may have driven true polar wander, establishing the north-south orientation of the dichotomy very early in martian history. Such a reorientation that placed the dichotomy boundary near the equator would also have constrained the Tharsis region on the dichotomy boundary to have originated near the equator. We present a scenario for the early generation and subsequent reorientation of the hemispheric dichotomy, although the reorientation is independent of the formation mechanism. Our results also have implications for the sharply different remanent magnetizations between the two hemispheres.     

Ridges and tidal stress on Io

Sets of ridges of uncertain origin are seen in twenty-nine high-resolution Galileo images, which sample seven locales on Io. These ridges are on the order of a few kilometers in length with a spacing of about a kilometer. Within each locale, the ridges have a consistent orientation, but the orientations vary from place to place. We investigate whether these ridges could be a result of tidal flexing of Io by comparing their orientations with the peak tidal stress orientations at the same locations. We find that ridges grouped near the equator are aligned either north-south or east-west, as are the predicted principal stress orientations there. It is not clear why particular groups run north-south and others east-west. The one set of ridges observed far from the equator (52° S) has an oblique azimuth, as do the tidal stresses at those latitudes. Therefore, all observed ridges have similar orientations to the tidal stress in their region. This correlation is consistent with the hypothesis that tidal flexing of Io plays an important role in ridge formation.     

Tectonic patterns on reoriented and despun planetary bodies

Several processes may produce global tectonic patterns on the surface of a planetary body. The stresses associated with distortions of biaxial figures due to despinning or reorientation were first calculated by Vening Meinesz [Vening Meinesz, F.A., 1947. Trans. Am. Geophys. Union 28 (1), 1-23]. We adopt a mathematically equivalent, but physically more meaningful treatment for distortions associated with rotation. The new approach allows us to find analytic solutions for the general case of stresses associated with distortions of biaxial or triaxial planetary figures. Distortions of biaxial figures may be driven by variations in rotation rate, rotation axis orientation, or the combination of both. Distortions of triaxial figures may be driven by the same mechanisms and/or variations in tidal axis orientation for tidally deformed satellites. While the magnitude of the resulting stresses depends on the adopted elastic and physical parameters, the expected tectonic pattern is independent of these parameters for these mechanisms. Reorientation of the rotation/tidal axis alone is expected to produce normal/thrust faulting provinces enclosing the initial rotation/tidal poles, and thrust/normal faulting provinces enclosing the final rotation/tidal poles. Reorientation of both the rotation and tidal axis results in a wide variety of tectonic patterns for different reorientation geometries. On Europa, the tidal axis reorientation which generally accompanies rotation axis reorientations may provide an alternative explanation for tectonic features that have been interpreted as evidence for non-synchronous rotation. The observed tectonic pattern on Enceladus is more easily explained by a large reorientation (∼90°) of the rotation axis, than by rotation rate variations.     

Tectonic patterns on a reoriented planet: Mars

Both geologic and free-air-gravity data suggest that the positive mass anomaly associated with the Tharsis volcanoes may have reoriented Mars' lithosphere by as much as 25°. Since Mars is oblate (with flattening $\text{? ?0.005}$), rotation of the lithosphere over the equatorial bulge by 25° produces membrane stresses of several kilobars, large enough to initiate faulting. These stresses were first evaluated by F.A. Vening-Meinesz (1947, Trans. Amer. Geophys. Union28, 1–61) who treated the lithosphere as a thin elastic shell. The fracture patterns which result from these stresses are determined by the relation between stress and faulting proposed by E.M. Anderson (1951, The Dynamics of Faulting, Oliver & Boyd, Edinburgh). Plots of the magnitude and direction of stresses in a reoriented planet show that near Tharsis the dominant fault type should be north-south- trending normal faults. This normal fault province is centered about 30°N latitude and extends about 45° east and west in longitude. Similar faults should occur at the antipodes, north of Hellas Planitia. The polar regions should be occupied by roughly north-south-trending thrust faults which extend close to the equator south of Tharsis and north of Hellas. The regions between Tharsis and Hellas are subject to compression on a NE-trending axis and extension along a NW axis east of Tharsis (west of Tharsis the directions are NW compression and NE extension), thus predicting a zone of NNW and ENE strike slip faults east of Tharsis (NNE and WNW west of Tharsis). Although these patterns, except for the north-south normal faults north of Tharsis, have not yet been recognized, the discovery of such a tectonic system of the same age as Tharsis would provide strong support for the reorientation idea. Stresses due to reorientation appear to have little to do with Valles Marineris, since the stress normal to the axis of the Valles is predicted to be compressive, whereas geologic evidence suggests extension.     

Early thermal profiles and lithospheric strength of Ganymede from extensional tectonic features

Estimates of the brittle lithosphere thickness derived from the width and spacing of extensional tectonic features, coupled with lithospheric strength envelopes (brittle and ductile yield stress versus depth) appropriate for ice, allow the quantitative determination of early thermal profiles and lithospheric strength and stability on Ganymede. Furrows and grooves indicate brittle lithospheric thicknesses of 5–10 and 2–5 km, respectively, assuming that their spacing is controlled by an extensional instability or that their width is controlled by the intersection depth of their bounding faults. Plots of the brittle and ductile yield stress versus depth for the icy lithosphere of Ganymede show a linear increase in brittle strength with depth to a maximum at the brittle-ductile transition, followed by an exponential decrease in ductile yield stress with depth. Because the depth to the brittle-ductile transition depends primarily on the thermal gradient, the thickness of the brittle lithosphere can be used to calculate early thermal profiles of 1.5–6 and 4.5–20°/km during the formation of the furrows and grooves, respectively. Lithospheric strength, the integral of the yield stress versus depth curve, varied from 30–125 GPa m when the furrows formed to 5–30 GPa m when the grooves formed, which correspond to maximum yield stresses of 6–11 and 2.5–6 MPa, respectively. These results indicate that the thermal gradient and lithospheric strength varied laterally by as much as a factor of 5 and that Ganymede cooled in a highly inhomogeneous manner with significant lateral thermal anomalies. Finally, this analysis provides a straightforward explanation for the stability of large remnants of cratered terrain such as Galileo Regio that had a low thermal gradient and strong lithosphere in contrast to small remnants of cratered terrain that were fractured and broken up by grooved terrain as a result of higher thermal gradients and weaker lithospheres.     

Geo-mechanical and rheological modelling of upper crustal faults and their near-surface expression in the Netherlands

The pattern of fault reactivation, basin deformation and concentration of seismicity along the main trans-Netherlands fault zone, located NW–SE across the centre of the Netherlands, indicates that this zone is a major zone of weakness. Gravity modelling reveals after back-stripping of the sedimentary succession a distinctive continuous positive anomaly that can be explained by lithospheric sources. This zone of weakness is therefore likely to have a major influence on the tectonic processes currently active in the Netherlands region. We give a review of the tectonic history of the Netherlands and then present the results of a quantitative study of the reactivation of basin boundary faults and the influence on the surrounding basin. Well-data, balanced and back-stripped cross-sections are used to constrain the lithosphere rheology. The lithosphere rheology modelling results show a weak coupling between upper crustal deformation and the subcrustal lithosphere. A finite element modelling approach focussing on the upper crust is carried out in which the basin boundary faults are assigned various dips. The modelling results indicate that, for continuous reactivation of basin boundary faults, the presence of both a pre-existing weakness and a reduced friction angle is required. The latter implies that large displacements accommodated by primary faults cannot be directly attributed to the relative weakness of these faults compared to the secondary faults, which is in close accordance with inferences from trenching. A reduced friction angle has a significant effect on lithospheric strength and appears to be the major controlling factor in the reactivation of basin boundary faults.     

The tectonic and volcanic history of Dione

The tectonic and volcanic modifications of Dione are described and interpreted. It is proposed that after the formation of a brittle outer shell, but before the end of heavy meteoritic bombardment, global expansion due to radionuclide heating (and perhaps a loss of oblateness due to tidal despinning and orbital recession) produced a global system of lineaments. An NH₃ · H₂O melt was produced and “erupted” on the surface to form plains units. Cooling of the interior (or a phase change) led to horizontal compression in the surface. Compression of a thick deposit of plains material, possibly overlying a décollement surface, is proposed to explain cratered-plains ridges developed as thrust or high-angle reverse faults. Following formation of ridges and smooth plains, the surface experienced light cratering.     

Limb effect of solar absorption lines

Low-noise limb-effect observations of the non-magnetic line Fei 557.6 nm are presented. Separate measurements along the solar equator and the meridian have been carried out and have been corrected for scattered light. The limb-effect line shifts at the pole and at the equatorial limb are found to be equal. The detailed shape of the limb effect along the meridian is found to differ significantly from that along the equator. This difference can be explained by the presence of a meridional circulation pattern, with horizontal flows < 50 m^–1 from both the equator and poles toward ± 45° latitude. Alternatively the meridian/equator difference may be caused by a combination of latitude dependence of the granular parameters. An increase with latitude of the granular velocity scale height, contrast, or mean sizes could explain the observations.     

Tectonic tests of proposed polar wander paths for Mars and the Moon

We have tested the polar wander paths recently proposed for Mars by Schultz and Lutz-Garihan and for the Moon by Runcorn through a comparison of the lithospheric stress field predicted for rapid global reorientations against observed tectonic features. We have employed the theory of Vening Meinesz and of Melosh to calculate the reorientation stresses, and we argue that the formation of normal faults or graben in broad regions surrounding the former rotation poles should be the minimum tectonic signature of a reorientation that generates lithospheric stresses in excess of the extensional strength of near-surface material. Such regions of normal faults are not present in the vicinity of the most recent proposed paleopoles for Mars, despite the large magnitude of the predicted shear stress (1–2 kbar). The minimum tectonic criterion would not be relaxed by invoking gradual polar wander or by considering the superposition of stresses associated with the global lithospheric response to the Tharsis rise. We conclude that polar wander of the magnitude and timing proposed by Schultz and Kutz-Garihan did not occur. It follows either that Tharsis has always been located near the Martian equator or that Tharsis began to dominate the nonhydrostatic figure prior to the end of heavy bombardment so that any tectonic signature of reorientation has since been obliterated by cratering. The predicted directions of stresses that would result from the most recent episode of proposed polar wander on the Moon, including stresses produced by reorientation of both the rotational and tidal figures, show little or no correspondence to observed tectonic features in the vicinity of the postulated nearside paleopole. The magnitude of the predicted reorientation stress is at most a few tens of bars, however, so that the tectonic test of polar wander on the Moon is inconclusive.     

Evidence for a differentiated crust in Solis Planum, Mars, from lithospheric strength and heat flow

Two independent sets of heat flow estimates provide constraints on the Hesperian-era surface and mantle heat flows, and the thickness of the heat-producing elements (HPE)-enriched upper crust, in the Solis Planum region of Mars. The calculations, which use the concentration of uppermost crust heat sources deduced from orbital gamma ray spectroscopy and soils geochemistry, are based on the effective elastic thickness of the lithosphere and the minimum depth of faults underlying winkle ridges. We find that, for the majority of analyzed settings, the HPE-enriched crust is thinner than the whole crust thickness in this region (∼65 km). Thus, our results strongly support a differentiated martian crust.     

Strength of the lithosphere of the Galilean satellites

Several approaches have been used to estimate the ice shell thickness on Callisto, Ganymede, and Europa. Here we develop a method for placing a strict lower bound on the thickness of the strong part of the shell (lithosphere) using measurements of topography. The minimal assumptions are that the strength of faults in the brittle lithosphere is controlled by lithostatic pressure according to Byerlee's law and the shell has relatively uniform density and thickness. Under these conditions, the topography of the ice provides a direct measure of the bending moment in the lithosphere. This topographic bending moment must be less than the saturation bending moment of the yield strength envelope derived from Byerlee's law. The model predicts that the topographic amplitude spectrum decreases as the square of the topographic wavelength. This explains why Europa is rugged at shorter wavelengths (∼10 km) but extremely smooth, and perhaps conforming to an equipotential surface, at longer wavelengths (>100 km). Previously compiled data on impact crater depth and diameter [Schenk, P.M., 2002. Nature 417, 419-421] on Europa show good agreement with the spectral decrease predicted by the model and require a lithosphere thicker than 2.5 km. A more realistic model, including a ductile lower lithosphere, requires a thickness greater than 3.5 km. Future measurements of topography in the 10-100 km wavelength band will provide tight constraints on lithospheric strength.