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Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension
Accepted Manuscript
Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension Michael T. Bland, William B. McKinnon PII: DOI: Reference:
S0019-1035(17)30223-3 10.1016/j.icarus.2017.10.017 YICAR 12652
To appear in:
Icarus
Received date: Revised date: Accepted date:
17 March 2017 11 October 2017 12 October 2017
Please cite this article as: Michael T. Bland, William B. McKinnon, Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension, Icarus (2017), doi: 10.1016/j.icarus.2017.10.017
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Highlights • We simulate grooved terrain formation with large-amplitude pre-existing topography • When initial topographic relief is ¿50 m, groove-like structures fail to form.
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• Forming grooves directly from dark terrain by tectonic resurfacing is difficult. • Viscous relaxation of pre-existing topography enables tectonic resurfacing.
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• Resurfacing occurred by viscous relaxation, tectonics, and cryovolcanism combined.
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Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension
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Michael T. Bland1 and William B. McKinnon2
U. S. Geological Survey, Astrogeology Science Center, Flagstaff AZ 86001
Department of Earth and Planetary Sciences and McDonnell Center for the Space
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Sciences, Washington University in St. Louis, Saint Louis, MO 63130
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65 Total pages, including 20 Figures Resubmitted to Icarus October 13, 2017
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Corresponding Author: Michael T. Bland U. S. Geological Survey, Astrogeology Science Center
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2255 N. Gemini
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Proposed Running Head: Viscous relaxation and tectonic resurfacing on Ganymede.
Flagstaff, AZ 86001 [email protected] phone: (928) 556-7080
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fax: (928) 556-7014
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Abstract Ganymede’s bright terrain formed during a near-global resurfacing event (or events) that
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produced both heavily tectonized and realatively smooth terrains. The mechanism(s) by
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which resurfacing occurred on Ganymede (e.g., cryovolcanic or tectonic), and the relationship
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between the older, dark and the younger, bright terrain are fundamental to understanding
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the geological evolution of the satellite. Using a two-dimensional numerical model of litho-
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spheric extension that has previously been used to successfully simulate surface deformation
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consistent with grooved terrain morphologies, we investigate whether large-amplitude preex-
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isting topography can be resurfaced (erased) by extension (i.e., tectonic resurfacing). Using
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synthetically produced initial topography, we show that when the total relief of the initial
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topography is larger than 25-50 m, periodic groove-like structures fail to form. Instead, ex-
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tension is localized in a few individual, isolated troughs. These results pose a challenge to the
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tectonic resurfacing hypothesis. We further investigate the effects of preexisting topography
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by performing suites of simulations initialized with topography derived from digital terrain
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models of Ganymede’s surface. These include dark terrain, fresh (relatively deep) impact
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craters, smooth bright terrain, and a viscously relaxed impact crater. The simulations using
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dark terrain and fresh impact craters are consistent with our simulations using synthetic
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topography: periodic groove-like deformation fails to form. In contrast, when simulations
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were initialized with bright smooth terrain topography, groove-like deformation results from
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a wide variety of heat flow and surface temperature conditions. Similarly, when a viscously
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relaxed impact crater was used, groove-like structures were able to form during extension.
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These results suggest that tectonic resurfacing may require that the amplitude of the initial
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topography be reduced before extension begins. We emphasize that viscous relaxation may be the key to enabling tectonic resurfacing, as the heat fluxes associated with groove terrain
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formation are also capable of reducing crater topography through viscous relaxation. For
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long-wavelength topography (large craters) viscous relaxation is unavoidable. We propose
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that the resurfacing of Ganymede occurred through a combination of viscous relaxation,
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tectonic resurfacing, cryovolcanism and, at least in a few cases, band formation. Variations 3
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in heat flow and strain magnitudes across Ganymede likely produced the complex variety of
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terrain types currently observed.
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Keywords: Ganymede; Tectonics.
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Ganymede’s terrains and evidence for resurfacing At large scales, Ganymede’s surface is composed of two types of terrain: relatively dark
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terrain with higher crater densities, and relatively bright terrain with lower crater densities
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(Fig. 1). The dark terrain likely represents an ancient, though not necessarily primordial
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(e.g., crater densities are higher on neighboring Callisto (Zahnle et al., 2003; Schenk et al.,
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2004)) crust. The bright terrain, in contrast, is a resurfaced unit formed during Ganymede’s
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mid-life (∼2 Ga ago (Zahnle et al., 2003), although uncertainties are at least 1 Ga (Schenk
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et al., 2004)). Understanding how the bright (and often “grooved”) terrain was emplaced and
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the relationship between Ganymede’s dark and bright terrains are central to understanding
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the overall geologic history of the satellite.
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Ganymede’s dark terrain comprises roughly one-third of its surface (e.g., Patterson et al.,
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2010) and is heavily cratered, with numerous knobs and massifs (Shoemaker et al., 1982;
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Prockter et al., 1998) (Fig. 1A). The low albedo material is probably a relatively thin,
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silicate-rich veneer that overlies an icier substrate (Prockter et al., 1998). This substrate is
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apparently exposed in the rims of furrows (troughs) and craters, where the dark surface lag
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has sloughed-off down-slope and accumulated in topographic lows. The icy substrate is also
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exposed in crater palimpsests and the relatively bright ejecta associated with many dark
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terrain craters (e.g., Osiris) (Pappalardo et al., 2004).
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Within the dark terrain and far from the boundaries with the bright terrain (e.g., within
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the the central portion of Galileo Regio), tectonic deformation is limited (Prockter et al.,
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1998), consisting primarily of ancient, arcuate furrows up to ∼1 km deep, that may have
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formed during ancient, basin-scale impacts (McKinnon and Melosh, 1980; Schenk and McK-
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innon, 1987; Murchie et al., 1990; Prockter et al., 1998). Development and modification of the dark terrain’s furrows, massifs and knobs (possibly remnants of crater rims) likely
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occurred during an older epoch, and in a different deformation style, than that of the bright
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grooved terrain (Prockter et al., 1998, 2000). Nearer the dark-bright terrain boundary, more
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substantial tectonic deformation has occurred. In some cases the dark terrain is heavily
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fractured, and takes on a morphology similar to that of the bright terrain (Patterson et al., 5
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2010; and Fig. 1B). Because of their similar morphology and spatial association with bright
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terrain, the tectonized dark terrain may be a precursor or transitional unit to the bright
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terrain (Prockter et al., 2000; Patterson et al., 2010). The remaining two-thirds of Ganymede’s surface consists of a brighter patchwork of broad
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polygons that are often (though not always) separated from the dark terrain by deep bound-
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ing troughs (Pappalardo et al., 1998). Surface morphologies within each polygon are highly
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variable, but range from highly tectonized “grooved terrain” (Fig. 1C) to relatively smooth
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plains (Fig. 1D). The classic grooved terrain morphology consists of sets of periodically
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spaced ridges and troughs with amplitudes of several hundred meters and ridge spacing of
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3-17 km, varying from one set of grooves to the next (see Pappalardo et al., 1998, 2004,
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for comprehensive reviews). High resolution Galileo data have also revealed a second set of
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finer-scale lineations with a characteristic spacing of 1 km (Pappalardo et al., 1998). This
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iconic morphology is found throughout the bright terrain; however, substantial variation ex-
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ists, with isolated troughs and more subdued tectonic deformation found across the surface
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(Patterson et al., 2010).
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The bright terrain likely formed during extension of Ganymede’s ice lithosphere (Pap-
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palardo et al., 1998), possibly during an epoch of global satellite expansion caused by differ-
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entiation (e.g., Squyres, 1980; Mueller and McKinnon, 1988), or melting during resonance
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passage (Showman et al., 1997; Bland et al., 2009). The iconic ridges and troughs of the
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grooved terrain are thought to have formed via an extensional instability that deformed
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the lithosphere into periodically spaced pinches and swells (Pappalardo et al., 1998; Collins
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et al., 1998; Dombard and McKinnon, 2001; Bland and Showman, 2007), a process essentially
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identical to boudinage formation but at lithospheric scale (Fletcher and Hallet, 1983). Re-
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cent numerical models that include strain localization effects (e.g., via material weakening and/or non-associated plasticity) support this interpretation, permitting the formation of
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large-amplitude, periodic deformation at relatively small strains (Bland et al., 2010; Bland
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and McKinnon, 2015).
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The lower crater density within the bright terrain suggests that these terrains formed
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at the expense of the darker, heavily cratered terrain during an epoch of near-planetary-
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scale resurfacing; however, the process or processes by which such resurfacing has occurred
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remain poorly understood. Resurfacing by cryovolcanism (i.e., the eruption of a fluid onto the
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surface), tectonism (i.e., the disruption and erasure of preexisting terrains through tectonic
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deformation alone), and Europa-like band formation (i.e., the emplacement of new material
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during extension of the surface) have all been proposed.
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Cryovolcanism has been invoked as a resurfacing mechanism on Ganymede since the
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Voyager-era. In these models, an initial period of extension forms broad graben, which
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are subsequently flooded with cryovolcanic material (water, warm ice, or slush) that buries
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preexisting topography. The grooved terrain then forms during a continuing or later period
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of extensional tectonism (Golombek and Allison, 1981; Allison and Clifford, 1987), possibly
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with subsequent viscous relaxation or mass wasting of the resulting topography (Squyres,
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1982; Parmentier et al., 1982). Evidence for cryovolcanic resurfacing comes from numerous,
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unusually smooth regions on the surface (Fig. 2) as well as a number of unusual, caldera-like
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features (Schenk et al., 2001). Although high-resolution imaging is limited, at least some of
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the smooth regions appear to embay nearby topography (Fig. 2) (Allison and Clifford, 1987;
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Schenk et al., 2001), and occur in topographic lows (Schenk et al., 2001).
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Cryovolcanic resurfacing of Ganymede faces several theoretical and observational chal-
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lenges. Any cryovolcanic resurfacing mechanism proposed for icy satellites must address the
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difficulty of erupting relatively higher density fluid (e.g., salty water) through the lower den-
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sity ice shell. Such eruptions may be driven by gases entrained in the fluid (Crawford and
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Stevenson, 1988) or by topographically induced pressure gradients that drive near-surface
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fluid onto the surface (Showman et al., 2004), but the exact mechanism remains elusive.
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Additionally, there is a paucity of direct evidence for associated cryovolcanic source vents in higher-resolution Galileo images, although numerous enigmatic caldera-like features have
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been identified in the Mummu Sulci region (previously identified as the Sippar Sulcus region)
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and elsewhere (Schenk et al., 2001). Further, at least some regions that appeared smooth in
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low-resolution Voyager and Galileo images (e.g., Harpagia Sulcus) appear lightly tectonized
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when seen in higher-resolution imaging (Pappalardo et al., 2004). Evidence for tectonic imbrication (Pappalardo et al., 1998; Collins et al., 1998), the iden-
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tification of nascent rifts within the dark terrain (Prockter et al., 2000), and the challenges
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faced by cryovolcanic resurfacing described above have led to the hypothesis that Ganymede
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may have been resurfaced through tectonism alone (Head et al., 1997) (Fig. 3). In this view,
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grooved terrain forms directly from dark terrain by fault imbrication and block rotation,
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which completely erases dark terrain topography without large-scale cryovolcanic resurfac-
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ing (Head et al., 1997; Pappalardo and Collins, 2005). Key to this process is the removal of
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the dark surface lag by slumping of dark material into topographic lows (Patel et al., 1999).
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The existence of geologic units that are morphologically and stratigraphically transitional
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between “traditional” bright and dark terrain (e.g., the dark lineated units described above)
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may indicate a progression from dark terrain to bright terrain. These transitional units
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always occur adjacent to bright terrain and generally share its structural fabric (Patterson
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et al., 2010). The tectonic resurfacing paradigm has also recently been reinforced by Cassini
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observations of numerous fault cut craters on Enceladus (e.g., Crow-Willard and Pappalardo,
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2015). Yet the tectonic resurfacing hypothesis is not without its challenges. Analog models
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of Ganymede-like extension reproduce many of the distinctive characteristics of the grooved
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terrain, including extensive faulting and block rotation (Sims et al., 2014). Models that in-
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cluded preexisting craters, however, failed to result in resurfacing: in a blind test, 95% of the
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initially imposed craters were still identifiable after 33% extension of the surface (Wyrick,
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2012). Models with larger strains (e.g., Pappalardo and Collins (2005) observed Ganymede
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craters deformed by >50% extension) have not yet been performed. Although supported
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by mapping and structural analysis, the detailed mechanics of tectonic resurfacing requires
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further investigation. Head et al. (2002) suggested Europa-like band formation as an alternative (or additional)
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mechanism of resurfacing on Ganymede. Band formation is common on Europa (see Prockter
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and Patterson, 2009, and references therein), and is generally thought to involve complete
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separation of the lithosphere and the emplacement of new material as warmer ice wells
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upward from below (Prockter et al., 2002). The principal type locality for possible band
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formation on Ganymede is Arbela Sulcus, a narrow swath of relatively smooth terrain that
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can be “closed” to reconstruct the preexisting surface (Fig. 4). Such tectonic reconstructions
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are rare on Ganymede (though see Pizzi et al., 2017, for potential additional examples), but
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the importance of band formation as a resurfacing mechanism is difficult to assess given the
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general lack of high-resolution imaging available for Ganymede. On Europa, band formation
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may be associated with substantial amounts of surface strain (Bland and McKinnon, 2012).
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In reality it is possible that all three mechanisms (cryovolcanism, tectonism, and band
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formation) have operated on Ganymede at either some specific point in time, some particu-
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lar locality, or in concert. In this paper we assess the plausibility and conditions necessary
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for resurfacing Ganymede through tectonic deformation alone. That is, we seek to specif-
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ically test the tectonic resurfacing hypothesis through numerical modeling. In doing so,
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however, we also indirectly address the potential role of cryovolcanic resurfacing. We also
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identify a process that appears critical to enabling tectonic resurfacing: viscous relaxation
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of preexisting topography.
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Methods and previous modeling To numerically simulate lithospheric extension on Ganymede, we follow an identical ap-
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proach to that of Bland and McKinnon (2015), with the exception of the initial topography
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imposed. We use the viscoelastic-plastic finite element code Tekton (v2.3) (Melosh and Raef-
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sky, 1980) in a two-dimensional Cartesian plane strain geometry. Many features of rifting
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on terrestrial planets and icy worlds exhibit along-strike symmetry and are therefore con-
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ducive to a two-dimensional modeling approach. Indeed, the majority of investigations of rifting on Earth have utilized a two-dimensional geometry, which facilitates the investigation
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of large parameter spaces at high resolution (e.g., Bassi, 1991; Govers and Wortel, 1995;
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Beaumont et al., 1996; Buck et al., 1999; Gerbault et al., 1999; Lavier et al., 2000; Huis-
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mans and Beaumont, 2002, 2003; Wijns et al., 2005; Nagel and Buck, 2007; Delescluse et al.,
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2008; Whitney et al., 2013; Gueydan and Pr´ecigout, 2014, and many others). Furthermore,
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three-dimensional simulations of the rifting of terrestrial continental crust indicate that the
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resulting deformation is fundamentally two-dimensional in nature (Sharples et al., 2015),
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and most three-dimensional studies focus on along-strike rift propagation (e.g., Dunbar and
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Sawyer, 1996; Van Wijk and Blackman, 2005; Allken et al., 2011, 2012). Despite this, the
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interaction between extension, strain localization, and large-scale preexisting topography has
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received little investigation, and strain localization during extension may be modified when
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a fully three dimensional geometry is used. The hazards of modeling a three-dimensional
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process with two-dimensional simulations are discussed more fully in section 4.6. The mod-
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els presented here are therefore a necessary first-step to numerically investigating tectonic
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resurfacing, but do not tell the complete story. Three-dimensional simulations of groove
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formation are currently in progress (Bland and Wyrick, 2017).
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Our two-dimensional simulation domain is initially 80 km long and 24 km deep, ensuring
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edge and bottom boundary effects are negligible, and allowing numerous instability wave-
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lengths to develop at the surface. The bottom boundary is fixed in the vertical and free slip
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in the horizontal, and the sides are free slip in the vertical. Extension is imposed by keeping
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the left edge of the domain fixed in the horizontal and imposing a constant velocity boundary
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condition on the right edge of the domain. We impose up to 10% extension at a strain rate
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of 10−13 s−1 (i.e., 1% extension every ∼3000 yrs). Decreasing the strain rate, which may
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be more geologically plausible (Dombard and McKinnon, 2001; Stempel et al., 2005), has
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only a small effect on our results, and generally leads to increased instability amplification
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rates (Bland and McKinnon, 2015; Dombard and McKinnon, 2001). The top surface is free,
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and we impose initial topography as described below. Each simulation is initialized with a
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lithostatic stress state using a surface gravity of 1.4 m s−2 . The density of the ice is assumed to be 950 kg m−3 , consistent with cold, somewhat dirty ice.
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The simulations include all relevant viscous flow mechanisms for ice I, including dislo-
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cation creep (three regimes), grain boundary sliding (GBS), basal slip (BS), and diffusion
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creep. Each flow mechanism can act simultaneously, although GBS and BS rate-limit each
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other such that the slower mechanism dominates (Goldsby and Kohlstedt, 2001). At the
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stress, strain rate, and temperatures used in our simulations, deformation is predominantly
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controlled by GBS flow and dislocation creep regime ‘B’ (see Durham and Stern, 2001). More
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detail is provided in Bland and McKinnon (2015) and Bland and Showman (2007). We use
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elastic parameters consistent with cold intact ice: a Young’s modulus (E) of 9.33 GPa and
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a Poisson’s ratio of 0.325 (Gammon et al., 1983). A pervasively fractured lithosphere might
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have a lower E (e.g. Pritchard and Stevenson, 2000; Klimczak et al., 2015), which would
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generally suppresses amplification rates (Bland and Showman, 2007); however, said fractures
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would also produce a compensating effect by lowering the conductivity and thus increasing
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the thermal gradient and instability growth rate.
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Brittle behavior is modeled using non-associative plasticity, which results in strong lo-
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calization of brittle deformation (Rudnicki and Rice, 1975; Vermeer and de Borst, 1984;
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Poliakov and Herrmann, 1994). Non-associated plasticity is appropriate for granular geo-
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logic materials (including ice (Lade, 2002; Pritchard, 1988)) that undergo limited dilation
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during shear failure (Vermeer and de Borst, 1984). Plastic failure occurs when the second in-
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variant of the deviatoric stress reaches the defined yield criterion. We use a Drucker-Praeger
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yield criterion (Owen and Hinton, 1980; Vermeer and de Borst, 1984; Iwashita and Oda,
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1999) with a nominal cohesion of 1 MPa (Beeman et al., 1988) and an internal friction angle
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of 30◦ . The Drucker-Praeger criterion is similar to a Mohr-Coulomb criterion but is more
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numerically stable. We also investigate how using a lower cohesion (100 kPa) affects our
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results. This lower cohesion is more consistent with the failure threshold inferred for cycloid
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formation on Europa (Rhoden and Hurford, 2013). Our implementation of non-associative
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plasticity is described in detail in Bland and McKinnon (2015).
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Although Tekton does not include thermodynamics, we impose a thermal structure
through the temperature-dependent viscosity. For each simulation we choose a heat flux
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(F ) and surface temperature (Ts ), and assume a temperature-dependent thermal conduc-
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tivity appropriate for intact ice (k = 651 W m−1 /T ) (Petrenko and Whitworth, 1999) to
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calculate the temperature of each element as a function of depth (z) assuming a conductive
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steady state: T (z) = Ts exp F z/651 W m−1 .
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We use the temperature of each element to calculate its rheologic parameters (i.e., the effec-
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tive viscosity for each of the flow mechanism described above). For the simulations shown
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here we use only constant (in time) thermal/viscosity structures (cf. Bland et al., 2017). The
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temperature and viscosity field is not updated during the simulation itself, so isotherms are
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advected with the material contours. Some consequences of this simplification are discussed
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in section 4.3.1. We nominally use a surface temperature of 100 K, but investigate the effect
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of surface temperatures between 70 K and 120 K, as appropriate for colder polar regions and
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warmer equatorial dark terrain, respectively. We investigate heat fluxes ranging from 70 to
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150 mW m−2 , consistent with previous inferences for grooved terrain formation (Dombard
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and McKinnon, 2001; Bland and Showman, 2007). Note that in reality, the thermal con-
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ductivity may be substantially lower than that of intact ice due to both micro and macro
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porosity throughout Ganymede’s lithosphere; however, decreasing the conductivity has the
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same effect as increasing the heat flux. Modifying either (or both) effectively changes the
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thickness of the lithosphere, and the length scale over which the ice transitions from brittle
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to ductile behavior (i.e., the rheologic contrast between the ice lithosphere and subjacent ice
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asthenosphere).
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The significant difference between the simulations described here and those described in
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Bland and McKinnon (2015) is the initial topography imposed at the surface of the simulation
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domain. In our previous successful simulations, we used semi-random topography created by
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randomly phase shifting and co-adding sinusoidal perturbations with wavelengths from 1 to
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80 km. This topography was generally normalized to have a maximum total relief (i.e., the difference between the highest and lowest point) of just 15 m. In these simulations, the goal
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was to provide enough initial topography to allow an instability to initiate and naturally
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establish a dominant wavelength, which is a function of the thickness of the deforming layer
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(e.g., Fletcher and Hallet, 1983; Herrick and Stevenson, 1990; Dombard and McKinnon,
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2001; Bland and Showman, 2007, and many others). An example of a successful simulation 12
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using low-amplitude topography is shown in Fig 5. Extension of the initial topography in
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panel A results in the periodic groove-like deformation shown in panel B. The simulation
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used Ts =70 K and F =100 mW m−2 . The resulting surface deformation is similar to the
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topography of Ganymede’s archetypal grooved terrain as shown in panel D. Clearly, these
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simulations can successfully reproduce the wavelength, amplitude, and general morphology of
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Ganymede’s grooved terrain when low-amplitude initial topography is used. The simulations
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are described more fully in Bland and McKinnon (2015)
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As clearly illustrated in Fig. 5, however, the amplitude of the initial topography used in
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our previous simulations (panel A) is inconsistent with the amplitude of dark terrain topog-
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raphy that may have predated groove formation on Ganymede (panel C), which if resurfacing
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of dark terrain occurred by tectonism, consisted of knobs, massifs, and hummocky terrain
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with amplitudes of several hundred meters. Further, many groove lanes appear to disrupt
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older groove sets, the ridges and troughs of which were also likely several hundred meters
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in amplitude. In either case, groove formation had to modify large-amplitude preexisting
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topography if tectonic resurfacing was the dominant resurfacing mechanism. In this work
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we examine how such large amplitude deformation modifies the previous results of Bland
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and McKinnon (2015). To do this we utilize two types (or cases) of initial topography. The
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first case uses “synthetic” topography created using the methods described above, but at
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a variety of initial amplitudes (Section 3). This permits us to systematically examine how
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the amplitude of the initial topography affects groove formation. In the second case we use
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topography extracted from digital terrain models (DTMs) of Ganymede’s surface (Section
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4). This permits us to investigate how grooves may have formed in the presence of different
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initial terrain types. In both cases, surface topography is imposed simply by varying the
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position of surface and near-surface nodes, with the topographic perturbation decaying with depth such that “flat” material contours are reached at depth (i.e., vertical nodal position
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is unperturbed). After describing the results of these two investigations, we discuss the
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implications of our modeling for resurfacing on Ganymede (Section 5).
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Simulating tectonic resurfacing with synthetic initial topography In order to examine how initial topographic amplitude affects our simulations of groove
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terrain formation, we performed a suite of simulations in which we kept the form of the
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initial topography constant but varied its initial amplitude from 1 m to 200 m of total
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relief (left column of Fig. 6). Each simulation was otherwise identical: a strain rate of
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10−13 s−1 and 10% total extension, Ts =100 K, F =100 mW m−2 , and a cohesion of 1 MPa.
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Figure 6 shows the effect of increasing initial topographic amplitudes. For reference, the
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simulations described in Bland and McKinnon (2015) used an initial amplitude of 12 m.
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At relatively small initial amplitudes (1 to 25 m) extension results in strongly periodic
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deformation. Little, if any, signature of the pre-existing terrain remains. These results are
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consistent with Bland and McKinnon (2015). As the initial amplitude becomes larger (50-
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100 m), however, the deformation that results from extension becomes less periodic with
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strain preferentially localizing in several individual troughs, which deepen at the expense of
294
more distributed deformation. At the largest initial amplitudes investigated (150-200 m),
295
extension results in the formation of several isolated troughs ∼500 m deep, with little or no
296
periodicity in the final topography.
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The decrease in the periodicity of the simulated final topography as the amplitude of the
298
initial topography is increased was quantified using Fourier analysis of the final simulated
299
deformation (Fig. 7). As expected, the initial topography has an extremely broad power
300
spectrum that includes contributions from many wavelengths (inset of Fig. 7). When small-
301
amplitude initial topography is used, the power spectrum of the final topography is strongly
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peaked with a wavelength of 6 km. The full width half maximum (FWHM) of the peak is 1.5 km. Note that because the resolution of the spectrum decreases with increasing wavelength,
304
the exact FWHM is poorly resolved. As the amplitude of the initial topography is increased,
305
the peak in the final topography power spectrum broadens. That is, a broader range of
306
wavelengths contribute to the topography, and the topography is less periodic. In the 200 m 14
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amplitude simulation, the resulting power spectrum has a peak with a FWHM of ∼10 km.
308
These values compare poorly to Fourier analysis of Ganymede’s actual grooved terrain,
309
which indicate that groove spacing is strongly periodic, with a power spectrum FWHM of
310
just 2-3 km (Grimm and Squyres, 1985; Patel et al., 1999). The observed power spectra are
311
therefore consistent with our simulations that use low-amplitude initial topography, but not
312
those that use larger initial amplitudes.
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The influence of the initial topography is further illustrated in Fig. 8, which compares
314
the development of surface deformation for two simulations that used 25 m and 200 m
315
amplitude initial topography, respectively, but were otherwise identical. When initial topo-
316
graphic amplitudes are small, the dominant wavelength of the necking and/or localization
317
instability resulting from lithospheric extension controls the surface deformation. Horizon-
318
tal strain becomes partitioned periodically throughout the lithosphere and the surface is
319
consequently deformed into periodic structures with an amplitude of ∼150 m (a factor of
320
6 increase after 10% extension). In contrast, when the initial topography is larger in am-
321
plitude, strain preferentially becomes partitioned into preexisting structures as extension
322
occurs. In the simulation shown in Fig. 8B these structures are generally topographic lows.
323
As extension occurs, strain is accommodated nearly entirely within these structures (Fig.
324
8d), which deepen at the expense of surrounding regions. The final surface is composed
325
of isolated troughs a few kilometers wide and (in some cases) more than 500 m deep, each
326
separated by relatively undeformed regions (i.e., having similar small-scale topography as
327
initially present) 10-20 km wide. This morphology generally does not resemble Ganymede’s
328
archetypal grooved terrain.
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Figures 6, 7, and 8 indicate that simulations that utilize small-amplitude topography (up
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to 25-50 m) will result in periodic groove-like deformation, whereas simulations that utilize initial topography with a total relief >50 m may result in non-periodic deformation (deep
332
isolated troughs). To assess whether this result depends on our model assumptions, we per-
333
formed a suite of simulations that varied the heat flux (70-150 mW m−2 ), surface temperature
334
(70-120 K), and strain rate (10−13 s−1 - 10−14 s−1 ). Variations in the mechanical properties of 15
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the ice were also explored and are discussed further below. These simulations indicate that
336
the basic result described above is largely independent of the physical parameters assumed.
337
Figure 9 compares the results of pairs of identical simulations that used a variety of physical
338
conditions, but with initial topographic amplitudes (maximum relief) of 25 m and 150 m.
339
In general, cold surface temperatures result in larger deformation amplitudes compared to
340
warm surface temperatures, and high heat fluxes result in shorter wavelength (and lower
341
amplitude) deformation than lower heat fluxes. These results are consistent with those of
342
Bland and McKinnon (2015), where they are described in greater detail. More notably, in
343
every case the simulations initialized with low-amplitude topography resulted in periodic or
344
semi-periodic groove-like deformation whereas simulations initialized with large amplitude
345
topography resulted in a few (or in some cases single) deep, isolated troughs. We conclude
346
that the qualitative results described above are general, and do not depend on the physical
347
parameters assumed during groove formation.
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The transition between relatively periodic deformation and the formation of isolated
349
troughs consistently occurs when initial topographic relief is 25-50 m in amplitude. That is, in
350
each case considered, simulations initialized with topography with relief greater than (and in
351
many cases equal to) 50 m result in isolated troughs rather than periodic structures. However,
352
some conditions lead to greater strain localization than others. Cold surface temperatures
353
(e.g., 70 K), and low heat fluxes (70 mW m−2 ) both result in strong localization such that
354
strain is often partitioned into a single isolated trough (e.g., Fig. 9D and H). As shown in
355
Fig. 9C, E, G, and I, simulations that produce large-amplitude periodic structures when
356
initialized with low-amplitude topography yield stronger localization when large-amplitude
357
initial topography is used. In contrast, warm surface temperatures (120 K, Fig. 9F) result
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in relatively more periodic (although still somewhat localized) deformation even when large amplitude initial topography is used. This pattern reflects the tendency of the assumed parameters to result in large-amplitude deformation in general.
361
Fundamentally, localization of strain within troughs is the result of higher stresses, and
362
hence greater brittle failure, within the troughs. If one considers the lithosphere as a plate
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with variable thickness (due to topography) that is subjected to an axial force (Fa ) that
364
is constant with depth, the axial stress on a vertical surface through the plate is simply
365
Fa /h(x), where h(x) is the thickness at horizontal point x. Since the base of the lithosphere
366
is initially flat (or flatter), large-scale topography (like a trough) reduces h locally, and so the
367
stress is increased locally. The increase stress results in somewhat higher strain rates in these
368
regions, but more importantly increases the likelihood of brittle failure in those elements.
369
The higher strain rate associated with brittle failure, and the localization effects of non-
370
associated plasticity, results in additional local thinning, which further increases the local
371
stresses, such that a positive feedback results. This pattern has been verified by examining
372
the stress field early in the simulations. For low-amplitude topography this effect is small,
373
and other processes (e.g., periodic necking) dominate. When initial topography is large
374
however, such continuous necking (thinning in a single region) can occur. As described
375
above, conditions that favor brittle deformation (e.g., a cold lithosphere) more easily localize
376
strain in this manner.
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Our simulations using synthetic topography challenge the tectonic model of resurfacing
378
Ganymede. They suggest that low-amplitude initial topography with .25–50 m total relief
379
can easily be “erased” and replaced by periodic ridges and troughs, whereas larger amplitude
380
topography is harder to resurface, resulting in localized isolated troughs. Even excluding
381
impact craters, typical dark terrain on Ganymede (from which the grooved terrain is thought
382
to form) includes topographic amplitudes of several hundred meters (see below). The sim-
383
ulations described above suggest that simply extending such terrain does not easily result
384
in groove-like deformation. Other resurfacing mechanisms, perhaps working in concert with
385
tectonic resurfacing, are apparently required. Below we use topography derived from a vari-
387
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ety of actual terrains on Ganymede to further investigate the interaction between extension and initial topography.
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388
4
Simulating tectonic resurfacing with DTM-derived initial topography
389
To further evaluate how lithospheric extension has modified pre-existing structures on
391
Ganymede, we performed simulations of lithospheric extension that were initialized with to-
392
pography derived directly from Ganymede’s surface. The investigation focused on four types
393
of terrain or landforms: dark terrain, smooth terrain, fresh impact craters, and viscously re-
394
laxed impact craters. Each terrain type is discussed in detail below.
395
4.1
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Forming grooves from dark terrain
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As described above, the tectonic resurfacing hypothesis postulates that Ganymede’s
397
bright grooved terrain formed directly from dark terrain (Head et al., 1997; Prockter et al.,
398
2000; Pappalardo and Collins, 2005). Although generally uniform in appearance at low
399
spatial resolution, the dark terrain is quite rough when viewed at high resolution, and the
400
individual knobs, hummocks, and massifs constitute relatively large-amplitude topography.
401
As demonstrated in section 3, the formation of periodically spaced tectonic structures, in
402
which strain is broadly distributed, from such large-amplitude topography is challenging.
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To more directly assess how grooved terrain might have formed directly from dark terrain
404
we performed a suite of simulations that explicitly used dark terrain topography as their
405
initial condition. We extracted topographic profiles from a region of dark terrain in northern
406
Marius Regio. The region is bounded by Nippur Sulcus to the east and northeast, Byblus
407
Sulcus to the west and Philus Sulcus to the north. The DTM and topographic profiles derived
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from it are shown in Fig. 10. The DTM used was derived from Galileo-based photoclinometry (e.g., Schenk, 1989; Bierhaus and Schenk, 2010), and has a horizontal resolution of ∼1 km
410
and a vertical uncertainty of ∼5%. The profiles were intentionally selected to avoid large-
411
scale craters or crater forms. Modification of impact craters is discussed in detail in section
412
4.3. Based on these 14 profiles, topographic relief associated with the largest individual
413
topographic features (hummock or knobs) is typically 200 m, with one feature exceeding 18
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400 m. Many knobs are significantly smaller (∼100 m). Over longer wavelengths (tens to
415
hundreds of kilometers), total relief in this region of dark terrain can exceed 400 m (e.g.,
416
profiles 11, 13, and 14 in Fig. 10). Two topographic profiles were selected for use in our finite
417
element simulations (1 and 3 in Fig. 10). These profiles were selected because they appear
418
typical of the dark terrain (total relief in profile 1 and 3 is 325 m, and 300 m respectively)
419
and have limited long wavelength (∼50-100 km) slopes.
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For both profiles, an 80 km-long portion was extracted, interpolated to the resolution
421
of the finite element model, and imposed on the surface of the model domain. Extension
422
was imposed as described above under a variety of conditions. Figure 11 shows the defor-
423
mation of the surface and lithosphere resulting from 10% extension with a Ts =100 K and
424
F =100 mW m−2 . The result is similar to that shown in Fig. 8B. For profile 1 (Fig. 11A),
425
extension has been primarily accommodated within two narrow (<5 km wide) troughs that
426
reach depths of 500 m and >1 km, respectively. These deep troughs originate in topographic
427
lows in the initial preexisting topography. Lower-amplitude (150-200 m) ridges and troughs
428
have formed between the deep troughs. Spectral analysis of the surface deformation suggests
429
limited periodicity: the power spectrum of the final topography is peaked at 12 km, but the
430
FWHM is greater than 10 km. Overall, the surface deformation, particularly the 1 km-deep
431
trough, is inconsistent with the morphology of Ganymede’s grooved terrain (although see
432
discussion in section 4.3).
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The initial topography in profile 3 is more subdued and the resulting deformation is also
434
lower in in amplitude. Like the simulation using profile 1, the strain is primarily accommo-
435
dated in a several (3-6) troughs that have deepened at the expense of adjacent ridges and
436
troughs. The deepest trough in this case is 500-600 m deep. Unlike the deformation of profile
438
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1, these troughs, while shallower, are separated by 10-15 km-wide regions of essentially flat terrain. The simulated surface deformation is unlike Ganymede’s archetypal grooved terrain (Fig. 5D).
440
Figure 12 illustrates (for profile 1) how the final deformation depends on the thermal
441
structure used in the simulation. Cold lithospheres (lower Ts and F ) generally result in 19
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stronger localization of deformation within a single trough, whereas warmer lithospheres
443
(higher Ts and F ) tend to result in more distributed deformation. As noted in section 3, this is
444
due to the predominance of brittle deformation, which readily leads to localization, in the cold
445
lithosphere. In the simulation with Ts =120 K and F =100 mW m−2 , the isolated troughs
446
have an amplitude of ∼600 m, which is still larger than, but considerably closer to, typical
447
groove amplitudes. The increased periodicity of the deformation for warmer lithospheres
448
results from the general decrease in the amplitude growth rate under warm conditions, which
449
has consistently been observed in numerical models of tectonic deformation on icy worlds
450
(Bland et al., 2010; Bland and McKinnon, 2012, 2013, 2015). In these simulations, the weaker
451
viscosity contrast between the relatively warm near-surface ice and the even warmer ice at
452
depth retards growth of the necking and localization instabilities, including the run-away
453
localization of strain within a few troughs. The result is lower amplitude but more periodic
454
deformation.
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As with the simulations that used large-amplitude synthetic topography, the simulations
456
that were initialized with dark terrain topography generally fail to produce groove-like defor-
457
mation under thermal conditions typical of groove formation on Ganymede1 . Instead, strain
458
becomes localized within preexisting topographic lows, resulting in troughs ∼1 km deep that
459
are separated by lower amplitude ridges and troughs. These simulations suggest that forming
460
grooved terrain simply by “tectonically resurfacing” the dark terrain is unlikely. Further-
461
more, the simulations described above intentionally avoided large-scale crater forms, which,
462
as discussed below, provide an even greater challenge to the tectonic resurfacing mechanism.
463
We note, however, that our model has inherent limitations due to their two-dimensional
464
nature. Isolated knobs and depressions within the dark terrain act like ridges and troughs
466
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in a two-dimensional profile, and localization may be less efficient when three-dimensional effects are accounted for (see discussion in section 4.6). 1
Dombard and McKinnon (2001) argue that strains up to 50% - 100% may be necessary to form “grooves”
in dark terrain
20
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467
4.2
Forming grooves from bright smooth terrain
The simulations described above suggest that forming grooved terrain by tectonically
469
resurfacing dark terrain terrain is challenging. An alternative end-member hypothesis is that
470
groove terrain formation occurred in several stages that included cryovolcanic resurfacing.
471
In this scenario, cryovolcanism locally provides a topographically smooth lane upon which
472
the ridges and troughs of the grooved terrain subsequently formed. To directly assess how
473
grooved terrain might have formed from such smooth terrain, we used the topography of
474
bright, relatively smooth sulci on Ganymede as the initial topography for our simulations of
475
lithospheric extension. Six topographic profiles were extracted from Nippur Sulcus and Elam
476
Sulci using the same DTM described in section 4.1 (Fig. 13), and interpolated for use in our
477
simulations. In these profiles, local relief was ∼50 m, and up to 250 m of relief is present at
478
long wavelengths (∼100 km). For our simulations we selected the first 80 km of profile 1, but
479
removed the regional slope using a second order polynomial. Our objective was to use the
480
smoothest surface available, which would be consistent with cryovolcanic resurfacing. This
481
also permits us to clearly delineate these simulations from those that utilized dark terrain
482
(described above). The initial topography used in our simulations is shown in Fig. 14A.
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Simulations of extension that utilize the “smooth” initial topography described above
484
result in strongly periodic groove-like structures. Figure 14 shows the final surface defor-
485
mation for three simulations that utilized a range of thermal structures (Ts =70-120 K, and
486
F =70-150 mW m−2 ). Each simulation resulted in periodic deformation. For Ts =100 K and
487
F =100 mW m−2 , the deformation has a wavelength of 6 km and an amplitude of 150-200 m
488
(Fig. 14B). Perhaps not surprisingly, the deformation is consistent with that resulting from
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low amplitude synthetic initial topography under identical surface temperature and heat flux (Fig. 6). Decreasing the surface temperature and heat flux increases the wavelength and
491
amplitude of the final deformation, but the surface remains periodic (λ ≈18 km for Ts =70 K,
492
and F =70 mW m−2 , Fig. 14C). Conversely, increasing surface temperature and heat flux
493
decreases the wavelength and amplitude of the deformation (λ ≈3 km for Ts =120 K, and
494
F =150 mW m−2 , Fig. 14D). The relationship between heat flux, surface temperature, and 21
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495
deformation morphology is consistent with previous modeling results (Bland et al., 2010;
496
Bland and McKinnon, 2015). The relative “ease” with which groove-like deformation can be produced from initially
498
smooth terrain compared with the difficulty of tectonically resurfacing dark terrain suggests
499
that cryovolcanic resurfacing may have played an important if not critical role in the forma-
500
tion of the grooved terrain. These simulations generally support the post-Voyager hypothesis
501
that bright grooved terrain formed through a multi-stage process including both volcanism
502
and tectonism a` la Golombek and Allison (1981) and Allison and Clifford (1987). The cry-
503
ovolcanic resurfacing hypothesis certainly has problems (as outlined above), but forming
504
broadly distributed extensional deformation from the relatively smooth canvas it provides
505
is more obviously feasible than directly modifying the large-scale topography of the dark
506
terrain.
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Tectonic resurfacing of impact craters
In the dark-terrain simulations described above (section 4.1) we intentionally utilized
509
topographic profiles that did not include large impact craters. Impact craters provide one
510
of the greatest challenges to the tectonic resurfacing mechanism. Whereas elongated craters
511
have been documented within Ganymede’s dark terrain (Pappalardo and Collins, 2005),
512
few (if any) “ghost craters”, in which subtle evidence of crater rims remain but the crater
513
itself does not, have been observed within broad expanses of grooved terrain. This suggests
514
that the resurfacing that produced the bright terrain was extremely efficient. In contrast,
515
physical analog models of tectonic resurfacing fail to erase craters, even while producing
517
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periodic graben-like structures (Wyrick, 2012). To investigate how the extending lithosphere interacts with impact craters, we performed
518
a suite of simulations that utilized impact crater topography derived from our DTM of Marius
519
Regio. The topographic profiles are shown in Fig. 15, along with those of a nearby viscously
520
relaxed crater (see below). The crater is 21 km in diameter, ∼900 m deep, and relatively
521
fresh. We use an 80 km portion of profile c1 (centered on the crater) and interpolate to the 22
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522
resolution of our finite element mesh. The disruption and erasure of craters in numerical simulations is challenging because their
524
substantial depth creates a locally thin region of the lithosphere that, as discussed in section
525
3, localizes horizontal stresses, brittle failure, and extensional stain. Figure 16 shows the
526
surface and lithospheric deformation for a simulation initialized with the crater topography
527
described above and a relatively cold and thick lithosphere (Ts =70 K, and F =70 mW m−2 ).
528
In this case, extension is more-or-less entirely accommodated within the crater itself, and the
529
crater actually deepens and narrows by a factor of two during extension, reaching a depth
530
of ∼2 km (with respect to the ground plane), and width of ≈10 km. The pervasive plastic
531
deformation within the crater may be sufficient to completely disrupt the crater-form through
532
imbricate faulting; however, the end result is a single deep trough rather than distributed,
533
periodic deformation. Here again, three-dimensional effects may be important (section 4.6).
534
In our two-dimensional simulations the crater effectively acts as a deep trough. In reality, a
535
crater is an isolated depression and strain localization may be modified. However, we note
536
that fractures and faults within Ganymede’s dark terrain (e.g., Nicholson Regio, Fig. 4), and
537
on Enceladus, often develop through the center of craters, suggesting that they do localize
538
brittle deformation in three-dimensions.
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When the lithosphere is warmer (Ts =100 K, and F =100 mW m−2 ) different behavior
540
results (Fig. 17). In this case the imposed impact crater undergoes rapid viscous relaxation
541
during the initial period of extension, such that by 1% extension most of the impact crater
542
topography is removed (Fig. 17A). We emphasize that flattening of the crater is not due to
543
tectonic resurfacing, but rather primarily to viscous relaxation (cf. Bland et al., 2017; Singer
544
et al., 2017). Despite the reduction in topography, the combination of viscous relaxation and
546
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extension leads to the formation of a weak zone at the location of the former crater (indicated by the colored portions of the lithosphere). As extension of the lithosphere continues, the
547
majority of the strain is accommodated within this zone (Fig. 17B and C). The result is
548
the formation of a relatively isolated, narrow, v-shaped trough nearly 800 m deep, similar to
549
the depth of the original crater (Fig. 17D). Critically, the regions adjacent to the crater are
23
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essentially undeformed: the initial, non-crater topography present at time zero still remains
551
after ∼5% extension. As in the colder simulation, extensive faulting is likely to disrupt the
552
crater (including its rim). This pervasive faulting is similar to tectonically disrupted, but still
553
visible craters in dark terrain (Pappalardo and Collins, 2005) (Fig. 3D). Whereas the crater
554
has effectively been removed (i.e., the rim and interior are likely disrupted), the resulting
555
topography is not consistent with grooved terrain morphologies.
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Further increasing the lithospheric temperature yields similar behavior to the warm simu-
557
lation. Figure 18 illustrates this effect for simulations with F =150 mW m−2 and Ts ≥100 K.
558
For the two cases shown, the initially imposed crater is essentially flattened by relaxation
559
after just 1-2% extension. Again the majority of the strain is accommodated within the
560
weak zone associated with the initial crater, and extension results in an isolated, flat-floored
561
graben or v-shaped trough. The topography is generally inconsistent with grooved terrain
562
morphologies.
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In the warm lithosphere case, the failure to form groove-like deformation is predominantly
564
the result of the weak zone that remains after viscous relaxation has occurred, rather than
565
the amplitude of the topography. Whereas viscous relaxation can result in plastic failure of
566
the near-surface (Dombard and McKinnon, 2006), the deep failure zone in our model results
567
from the concomitant extensional strain. However, it is plausible that rather than relaxation
568
and extension occurring simultaneously, viscous relaxation preceded extension. Such a two-
569
step scenario might prevent the development of a weak zone beneath the crater as long
570
as thermal steady state can be achieved. Further, micro- and macro-porosity that results
571
from brittle failure during viscous relaxation may thermally sinter or anneal (a process not
572
included here) under the warm conditions of the lithosphere, thus further healing any weak
574
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zone that forms. Shoemaker et al. (1982) argued that at temperatures greater than ∼130 K, vapor transport and deposition through the regolith (or “damaged” zones) can re-cement
575
the ice lithosphere. Besserer et al. (2013) showed that viscous compaction is also capable of
576
removing porosity that might result from fracturing.
577
To further assess this scenario, we performed a suite of simulations using topography
24
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derived from a viscously relaxed crater within Marius Regio (Fig. 15). Like the fresh crater
579
described above, the relaxed crater is 21 km in diameter, with a central rebounded floor
580
that is at the level of the surrounding terrain. Surrounding the relaxed center is a circular
581
moat approximately 200 m deep. The crater retains obvious rims (short wavelength topog-
582
raphy is preserved during viscous relaxation) that stand 160-300 m above the surrounding
583
terrain. Figure 19 shows the post-extension deformation of the surface and lithosphere for
584
the relaxed topography. For intermediate and warm surface temperatures, the surface is
585
deformed into quasi-periodic ridges and troughs. This is especially true for the warmest
586
temperatures (Ts =120 K) in which plastic strain is distributed in numerous trough-like
587
features. The amplification of the surface deformation is quite limited: the total relief of the
588
final deformation is smaller after extension than before extension in the Ts =120 K simula-
589
tion. Further extension of the domain (the simulations shown here have been extended by
590
5%) results in similar surface deformation, although strain begins to localize more strongly
591
within individual troughs in the Ts =100 K simulation. These simulations illustrate that,
592
unsurprisingly, when topography is reduced by viscous relaxation before extension occurs,
593
subsequent groove terrain formation is more easily achieved. Tectonic resurfacing of impact
594
craters is likely enabled by concomitant viscous relaxation as the lithosphere begin to warm.
595
4.3.1
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Thermal effects and deep crater topography
Because Tekton does not include thermodynamics, the simulations described in section
597
4.3 must be interpreted carefully. The simulations shown here use a laterally constant sur-
598
face temperature. Thus, beneath the crater the distance between the constant-temperature
599
surface and a “flat” isotherm at depth is reduced compared to adjacent regions. The litho-
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spheric thermal gradient is therefore greater beneath the crater than in the surrounding region. This effect is negligible for small amplitude topography, but beneath a ∼1 km-deep
602
crater isotherms in our simulations are compressed by 20-50% (depending on the imposed
603
heat flux). Qualitatively, the increase is realistic (Seiferlin, 2009), but because we do not
604
actually solve the thermodynamics, it is only an approximation. 25
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Thermal effects are exacerbated as the simulation proceeds and extensional necking oc-
606
curs. Because isotherms (technically iso-viscous contours) are advected with the deforming
607
material, warm, low-viscosity material rises into the necked regions beneath the crater (e.g.,
608
Fig. 16). As long as the lithosphere remains several kilometers thick, the thermal diffusion
609
timescale is much longer than the simulation timescale and the advection of warm material
610
is realistic (i.e., the material would remain warm over the timescale simulated). For a litho-
611
spheric thickness of 1 km, however, the timescales for thermal diffusion and extension are
612
similar. In those cases (the simulation in Fig. 17 approaches this2 ) the material rising into
613
the necked region should cool, increase in viscosity, and act to stabilize the necked region.
614
Neglecting these thermal effects enhances the rate at which strain is localized during exten-
615
sion. This effect should be most significant when heat fluxes are large and the lithosphere
616
becomes very thin beneath the crater.
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To further investigate these effects, we performed a suite of simulations that initialized
618
the temperature structure such that the heat flow was truly uniform (i.e., isotherms fol-
619
lowed the surface topography). In these simulations strain localization is, in fact, retarded,
620
and while the majority of the strain is accommodated within the crater, small amounts of
621
extensional strain is also partitioned quasi-periodically throughout the lithosphere. This pe-
622
riodic strain partitioning is insufficient to modify the surface, however, and the final surface
623
deformation, which is marked by a deep, isolated trough rather than periodic deformation,
624
is consistent with our nominal simulations. The primary difference between the results of
625
these simulations and our nominal simulations is the magnitude of the strain that is accom-
626
modated. For example, for conditions analogous to those shown in Fig. 17, a similar state
627
is reached in these simulations after 8-9% extension rather than 5% extension. Despite the
629
630
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617
similarity in surface deformation, it is notable that the boundary between the ice lithosphere and asthenosphere is much flatter than in our nominal cases. These simulations indicate that our basic results are qualitatively insensitive to thermodynamic effects, at least for the 2
Viscous relaxation in Fig. 17 is faster than thermal adjustment to steady state: 1% extension occurs in
3000 yrs, whereas the thermal diffusion time for the 2-km thick lithosphere is about twice as long.
26
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lithospheric thicknesses we have modeled.
632
4.4
Effect of ice shell properties
The simulations discussed above have explored a range of physical parameters, focused
634
primarily on the heat flux and surface temperature. In addition, the properties of the ice
635
shell are likely critical to understanding the formation of Ganymede’s grooved terrain. The
636
simulations described here assume a cohesion of 1 MPa, consistent with laboratory data
637
(Beeman et al., 1988). However, it’s possible that at geologic scales the effective strength of
638
an ice lithosphere is much lower. The formation of cycloids on Europa, for example, seem
639
to require a relatively weak ice shell (Rhoden and Hurford, 2013), and models of mobile lid
640
convection in an ice shell generally must assume a low yield stress (Barr, 2008; Han et al.,
641
2012). Former numerical models of groove formation had to assume a high cohesion (high
642
strength contrast with deeper warm ice) in order to produce significant amplitude growth
643
(Bland et al., 2007, 2010); however the introduction of more realistic non-associated plasticity
644
in recent models has removed this requirement (Bland and McKinnon, 2015).
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To assess how the assumed strength of the lithosphere affects groove formation in the
646
presence of large-amplitude initial topography, we repeated all of the simulations described
647
above using a cohesion of 100 kPa (one order of magnitude lower than our nominal model).
648
Figure 20 compares these low cohesion simulations to those that used our nominal value of
649
1 MPa for the case where dark terrain is used as the initial topography. In general, the
650
simulations that used a lower cohesion result in lower growth of the necking (or localizing)
651
instability. This also results in a reduction in the localization of strain within individual
653
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troughs. Simulations with cold and intermediate lithospheric temperatures (Ts =70 K and 100 K) still result in deep troughs that dominate the deformation. In contrast, the simula-
654
tion with a warm lithosphere (Ts =120 K) results in semi-periodic structures of relatively
655
consistent amplitude. This deformation is consistent with Ganymede’s grooves.
656
Critically, the groove-like deformation in this simulation (Fig. 20C) does not result from
657
substantial changes in the amplitude of the initial topography. With a warm surface temper27
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658
ature and weak brittle ice shell, instability growth is limited (the strength contrast between
659
the lithosphere and deeper ice is reduced). Growth rates are large enough for a “dominant”
660
wavelength to develop, but insufficient to produce large-amplitude structures. These simula-
661
tions suggest that a weaker ice shell might assist tectonic resurfacing of Ganymede, although
662
the cohesion assumed is relatively unimportant for the cold polar regions. Reducing the cohesion also does not have an appreciable effect on the tectonic resurfacing
664
of relatively fresh, deep craters, and the qualitative results described in section 4.3 hold
665
whether a cohesion of 1 MPa or 100 kPa is used. In these cases, the depth of the trough
666
that results from extension is reduced when a lower cohesion is used, but the difference is
667
not substantial enough to allow direct resurfacing. Even when high heat fluxes are used,
668
reducing the cohesion of the lithosphere does not enable periodic structures to form from
669
preexisting cratered terrain.
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In summary, assuming a low cohesion for Ganymede’s ice lithosphere does not further en-
671
able widespread tectonic resurfacing on Ganymede. However, a lower cohesion may prevent
672
strain from strongly localizing within a narrow trough. It therefore may play an impor-
673
tant role in resurfacing terrain that has already been “smoothed” by viscous relaxation or
674
cryovolcanism.
675
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The role of small-scale faulting
The tectonic resurfacing mechanism depends critically on the development of numerous
677
imbricated faults and subsequent rotation of fault blocks (Head et al., 1997). The block
678
rotation exposes brighter subsurface ice, and contributes to the complete erasure of preex-
680
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isting structures like crater rims. Our numerical simulations result in strong localization of plastic strain into narrow, linear, fault-like structures (see Bland and McKinnon, 2015,
681
for details). The width and spacing of these faults is limited, however, by the resolution
682
of our simulations, which in the examples shown here is 167 m. Any discrete, smaller-scale
683
faulting cannot be captured by our simulations. Despite this, fault-like slip along planes of
684
elements does occur, only limited by the resolution of the mesh (see discussion in Bland and 28
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McKinnon (2015). A full “test” of the tectonic resurfacing mechanism should include a more realistic im-
687
plementation of true fault-like behavior, perhaps by combining increased resolution with a
688
strain- or strain-rate-dependent reduction in brittle strength (e.g., Buck et al., 2005; Bland
689
et al., 2010). These concerns are somewhat mitigated, however, by physical analog mod-
690
els of the extension of ice lithospheres. As described above, these models provide much
691
insight into fault processes on Ganymede, and reproduce many of the fault geometries (in-
692
cluding rotation) observed (Sims et al., 2014). Despite the development of these geometries,
693
faulting and block rotation apparently does not erase preexisting impact crater topography
694
(Wyrick, 2012). These models are therefore in broad agreement with our numerical simula-
695
tions. The analog models, however, do not include viscous deformation, and it may be that
696
a combination of viscous flow that reduces long-wavelength topography (crater bowls), and
697
small-scale faulting and fracturing that removes short-wavelength topography (e.g., crater
698
rims), is necessary to completely resurface preexisting terrain. We therefore conclude that
699
our simulations may underestimate the degree to which short wavelength topography can
700
be disrupted by fracturing and faulting, but they provide a relatively realistic depiction of
701
lithospheric behavior at longer wavelengths.
702
4.6
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Localization in three-dimensions
In our two-dimensional simulations, strain localizes relatively easily within topographic
704
lows or thin regions of the lithosphere. These are regions of high stress and thus increased
705
plastic (brittle) strain, which readily localizes via non-associated plasticity. As described
707
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above, this localization often results in isolated troughs rather than widespread deformation, and thus inhibits tectonic resurfacing. Strain localization in three-dimensions is likely more
708
complex. For example, the two-dimensional cross section of an impact crater is essentially
709
a trough, which easily localizes strain. In reality, a crater is an isolated depression, and
710
although it may be a locally thin region of the lithosphere, the regions adjacent to the crater
711
are not. Thus, whereas the crater may be a locus of brittle failure (see, e.g., Fig. 4), fail29
ACCEPTED MANUSCRIPT
ure must propagate laterally to form a continuous trough. Normal faults generally form by
713
linkage of smaller-scale fractures and faults (e.g., Peacock and Sanderson, 1991; Anders and
714
Schlische, 1994; Dawers and Anders, 1995; Mansfield and Cartwright, 2001; Wyrick et al.,
715
2011; Cartwright et al., 2016). If fault linkage is inhibited, periodic necking (a viscous insta-
716
bility) may dominate and prevent strain from localizing within a single crater. It is therefore
717
plausible that such strain localization is less efficient in three dimensions, more readily per-
718
mitting the development of periodic structures even when the preexisting topography is large.
719
How strain localizes in three-dimensions to produce grooves that are continuous along strike
720
for hundred of kilometers has not yet been addressed, and a complete understanding of the
721
resurfacing of Ganymede will not be achieved until the three-dimensional nature of groove
722
terrain formation is understood. Fully three-dimensional simulations (Bland and Wyrick,
723
2017) and more robust analog modeling (Wyrick et al., 2017) are warranted.
724
5
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A new scenario for resurfacing Ganymede Collectively, the simulations described in section 4 suggest several modifications may be
726
necessary to the prevailing picture of resurfacing on Ganymede. Our simulations with large-
727
amplitude initial topography, whether synthetically produced or derived from Ganymede’s
728
dark terrain, fail to produce distributed, periodic surface deformation. This is particularly
729
true when the preexisting surface includes impact craters hundreds of meters or kilometers
730
deep. Creating archetypical grooved terrain directly from Ganymede’s dark terrain therefore
731
appears challenging. Forming periodic ridges and troughs is much easier if the preexisting to-
732
pography is low-amplitude, either due to cryovolcanic resurfacing or viscous relaxation. This
734
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does not imply, however, that tectonic imbrication, block rotation, and pervasive fracturing does not play a critical role in disrupting older bright terrains. There is good observational
735
evidence that such processes occur (Head et al., 1997; Prockter et al., 2000; Pappalardo and
736
Collins, 2005, and see Fig. 3). Rather, we suggest that tectonic resurfacing is a critical
737
resurfacing process on Ganymede, but is likely enabled by viscous relaxation either before or
30
ACCEPTED MANUSCRIPT
738
during extension. As noted above, the heat fluxes commonly associated with the formation
739
of grooved terrain will necessarily result in viscous relaxation of long-wavelength topography
740
(e.g., craters). Based on these results, we propose that Ganymede’s resurfacing has occurred in several
742
stages. Models of grooved terrain formation (Dombard and McKinnon, 2001; Bland and
743
Showman, 2007), viscous relaxation of impact craters (Bland et al., 2017), and Ganymede’s
744
interior evolution (Showman et al., 1997; Bland et al., 2009) all indicate that the global expan-
745
sion associated with resurfacing was accompanied by substantial warming of the lithosphere.
746
This warming may have been associated with incipient mobile lid convection (Hammond and
747
Barr, 2014), resulting in a non-uniform distribution of heat flux and surface strain. That is,
748
regions of high heat flux and high strain are correlated and localized (Hammond and Barr,
749
2014). Where heat fluxes were highest, long wavelength surface topography – principally
750
impact craters – likely underwent rapid viscous relaxation, reducing the amplitude of the
751
pre-existing topography. The subsequent onset of extensional strain within these regions
752
of high-heat flow resulted in the formation of the periodic, distributed deformation associ-
753
ated with the grooved terrain. Where heat flow was especially highly localized, complete
754
separation of the thin lithosphere might have occurred, resulting in band formation (e.g.,
755
Head et al., 2002). Differences in preexisting dark-terrain topography (e.g., predominant
756
topographic wavelengths – affecting viscous relaxation rates) may have also contributed to
757
differences in the style of dark-terrain breakup.
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Away from the regions of localized extension and high heat fluxes, the dark terrain
759
would remain intact. These regions might correspond to convective down-wellings in the
760
mobile-lid model of Hammond and Barr (2014). Between these more quiescent regions and
762
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the highly deforming regions (e.g., around the edges of a convective plume) transitional geologic units would be expected to develop with a variety of morphologies. Regions that
763
experienced relatively high strains, but comparatively low heat fluxes might develop heavily
764
tectonized but marginally intact impact craters, such as those shown in Fig. 3B and D,
765
and the simulation shown in Fig. 16. Unlike the now-gone craters that might have existed
31
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before bright terrain formation, these impact craters were preserved (though disrupted)
767
because heat fluxes were insufficient (or too short lived) to permit viscous relaxation before
768
or during extension. Extensional strain localized within these craters, rather than producing
769
the distributed strain patterns (and surface brighting) associated with the grooved terrain.
770
Where only moderate surface strain occurred, tectonism might have proceeded without fully
771
disrupting the dark surface lag deposits to produce surface brightening, resulting in the
772
formation of dark lineated terrains. In contrast, where surface strains were low but heat
773
fluxes were elevated, widespread viscous relaxation would be expected without tectonism.
774
Such widespread viscous relaxation is observed in regions such as northern Marius Regio
775
(Singer et al., 2017), which is situated adjacent to expansive regions of grooved and smooth
776
bright terrain.
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The scenario described above depends only upon regional differences in heat flow and
778
surface strain. Mobile lid convection, as suggested by Hammond and Barr (2014), is one
779
mechanism to achieve such differences, but is not explicitly required. Mobile lid convection
780
implies large surface strains: extensional in the bright terrain and contractional in the dark
781
terrain. The former are not required by our simulations of groove formation, and little, if
782
any, evidence is observed for the latter. We do not dismiss the possibility of mobile lid
783
convection, but the mechanism, and its implications for Ganymede’s resurfacing, require
784
further investigation (e.g., with convection models that include plastic rheology).
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The above discussion does not preclude a significant role for cryovolcanism during resur-
786
facing. The high heat flow and extension would have been conducive to the production of
787
melt, which could have been locally driven to the surface by exsolved gases (Crawford and
788
Stevenson, 1988) or topographic gradients (Showman et al., 2004). This is particularly true
790
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789
CE
785
if Ganymede’s ice shell was thin during the epoch of resurfacing (Bland et al., 2009). Cryovolcanism could have occurred at any point during the resurfacing process. If (or where)
791
it proceeded extension, it would have provided a bright, “clean canvas” for the formation of
792
periodic ridges and troughs (as demonstrated by the simulations shown in Fig. 14). This
793
might have been the case for regions such as Bubastis Sulcus, where the swaths of grooved
32
ACCEPTED MANUSCRIPT
terrain are broad, the ridges and troughs are both high-amplitude and strongly periodic,
795
evidence of embayment by smooth material is observed (Allison and Clifford, 1987), and the
796
cold temperatures make resurfacing by tectonism alone difficult even if viscous relaxation
797
occurred. In these regions, the tectonism that followed cryovolcanic resurfacing may have
798
erased most evidence of vents. In contrast, if (or where) cryovolcanism occurred either after
799
extension was complete, or where surface strain was limited, smooth bright terrain would
800
result. There, resurfacing would have occurred predominately by cryovolcanism alone, ei-
801
ther by covering the recently formed grooved swath in the former case, or low-lying dark
802
terrain in the latter. In these regions, we expect vent structures to be preserved, such as the
803
caldera-like features in the Mumma Sulci and elsewhere (Schenk et al., 2001).
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This discussion also does not preclude a significant role for band formation as an agent
805
of resurfacing. Although not a focus of this paper, bands on Ganymede resemble pull-apart
806
bands on Europa (Prockter et al., 2002; Prockter and Patterson, 2009), and formation of
807
relatively smooth terrain during rifting and separation of preexisting dark and grooved ter-
808
rain blocks (e.g., Fig. 4) would clearly provide the subdued topography that would allow
809
full development of ridges and troughs (i.e., grooves) via extensional instability (Sec. 4.2).
810
Bands form with subdued tectonic or cryovolcanic fabrics along strike to begin with, but
811
high-amplitude grooves (Tiamat Sulcus, Fig. 1C, may be an example) as well as complex
812
grooved domain patterns (e.g., Uruk Sulcus, (Golombek and Allison, 1981)) require addi-
813
tional extension.
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804
In summary, resurfacing on Ganymede was likely the result of a complex interplay be-
815
tween tectonism, viscous relaxation, band formation, and cryovolcanism. In broad terms,
816
each terrain type observed on Ganymede may simply reflect which process locally dominated
818
AC
817
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814
the evolution, with the dominant process determined by local heat flux and surface strain. Ganymede’s dark terrain clearly experienced the lowest heat fluxes and limited strain. Tec-
819
tonism and evidence for high heat fluxes there date to an early epoch of Ganymede’s history
820
(e.g., Prockter et al., 1998). On the other end of the spectrum, the bright grooved ter-
821
rain likely experienced heat fluxes high enough to viscously relax preexisting impact craters,
33
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enabling concomitant or subsequent extension to result in broadly distributed lithospheric
823
deformation and tectonic resurfacing. Between these extremes, the relative amount of strain
824
and heating resulted in dark lineated terrain, localized tectonic disruption of craters, and
825
viscous relaxation without tectonism. Throughout the process, cryovolcanism both enabled
826
groove terrain formation, and resurfaced both dark terrain and newly formed grooved swaths.
827
The end result is the complex patchwork of bright and dark, tectonized and smooth, old and
828
young terrains observed on Ganymede today. Despite the new insight provided by these sim-
829
ulations, the relative importance of tectonic resurfacing, cryovolcanism, and band formation
830
in resurfacing Ganymede will remain an open question until new data, including imaging,
831
altimetry, and radar sounding are acquired (e.g., by ESA’s JUICE mission).
832
Acknowledgments
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This work was supported by NASA’s Outer Planets research program (NNH14AY69I to
834
MTB) and NASA’s Planetary Geology and Geophysics program (NNX11AP16G to WBM).
835
DTMs were generously provided by Paul Schenk. Comments from Chris Okubo, Francis
836
Nimmo, Geoff Collins, and an anonymous reviewer strengthened and clarified this work.
837
Any use of trade, firm, or product names is for descriptive purposes only and does not imply
838
endorsement by the U.S. Government.
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Figure 1: Several of the basic terrain types identified on Ganymede. A. Dark terrain in Nicholson Regio. B. Dark lineated terrain near Harpagia Sulcus. C. A swath of bright
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grooved terrain (Tiamat Sulcus) disrupting the dark terrain of Marius Regio. D. Bright smooth terrains of Nippur Sulcus and Elam Sulci. A and B after Patterson et al. (2010),
which describes these and other terrain types in detail.
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Figure 2: Examples of possible cryovolcanic resurfacing on Ganymede. A. Voyager 2 mosaic
of a portion of Bubastis Sulci (near the south pole) showing smooth bright terrain interspersed with archetypal grooved terrain. Portions of the smooth material appears to embay adjacent ridges and troughs (white arrows). B. Portion of Sippar Sulcus showing a lane of
smooth material that embays adjacent reticulate terrain (white arrows). After Schenk et al. (2001), who also showed that the smooth material generally stands lower than adjacent terrain.
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Figure 3: Examples of possible tectonic resurfacing on Ganymede. A. The intersection of bright grooved terrain in Nippur Sulcus and Philus Sulcus, dark terrain in Marius Regio,
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and smooth terrain in Elam Sulci. The edges of both the dark and smooth terrain appear to be disrupted by imbricated faulting. An enlarged view of such imbrication is shown in B. C. A disrupted crater in Nicholson Regio (lower left). Whereas the crater is still obvious, its center (including its rim) are completely disrupted by a set of parallel, closely spaced fractures. If the bright scarps are interpreted as normal faults they imply the fracture set is down-dropped by several hundred meters relative to the crater floor. D. A pervasively faulted and fractured crater in Nicholson Regio (17 km in diameter, 9◦ N, 18.5◦ E). Only the bright crater rim is visible (white arrows). The image location is indicated in Fig. 4. C 48 and D are modified from Pappalardo and Collins (2005).
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Figure 4: Galileo image mosaic of Arbela Sulcus. Head et al. (2002) suggest Arbela (the north-south trending lane of smooth material) formed as a Europa-like band, involving complete separation of the lithosphere and emplacement of warm, clean ice from below. The white box indicates the location of Fig. 3D.
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Figure 5: Comparison of the initial and final surface deformation from our “successful” model
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(A and B, respectively, with Ts =70 K, F =100 mW m−2 , ε˙ =10−13 s−1 , 10% extension), and typical dark terrain and grooved terrain topography (C and D, respectively). The
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enlarged view) is inconsistent with (not a good match to) the dark terrain (C).
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Figure 6: The surface deformation (right column) that results from extension of a model ice lithosphere initialized with topography of varying initial amplitude (left column). Each simulation used Ts =100 K, F =100 mW m−2 , a strain rate of 10−13 s−1 , and a cohesion of 1 MPa. The form of the initial topography used is identical in each case, only the total amplitude of the relief is changed. From top to bottom: 1 m, 10 m, 25 m, 50 m, 100 m, 150 m, 200 m. Note the difference in scale between left and right columns.
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Figure 7: Power spectrum of the final deformation after 10% extension produced by simu-
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lations with initial topographic relief of 1 m (dark blue), 25 m (light blue), 100 m, (green), and 200 m (red) as labeled (simulations are those shown in Fig. 6). The black curve shows
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the spectrum of the initial topography, which is also shown in the inset for clarity. Note that spectral resolution decreases with increasing wavelength (power at long wavelengths becomes “smeared” out).
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Figure 8: Illustration of the differences in the development of surface deformation for two identical simulations (Ts =100 K, F =100 mW m−2 ) with different initial topographic relief
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(25 m in A and C; 200 m in B and D). A and B show the surface deformation as a function of strain. The top curve is the initial topography and each subsequent curve is
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shown at increments of 1% extension. The red curve indicates 10% extension. C and D show the distribution of strain (lower plot) and deformation of the surface (upper plot) at 10% extension (identical to red curves in A and B).
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Figure 9: Comparison of the surface deformation produced by simulations with initial topographic relief of 25 m (left column, initial topography shown in A) and 150 m (right
column, initial topography shown in B). The pairs of simulations used identical parameters (except where noted here, other parameters were identical to those used in Fig. 6): C and
D, Ts =70 K; E and F, Ts =120 K; G and H, Ts =70 K and F =150 mW m−2 ; I and J a strain rate of 10−14 s−1 . All simulations are shown after 10% extension except F, which is shown after 9%. 54
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Figure 10: Digital terrain model (see text for details) of the northern portion of Marius
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Regio. The topographic profiles illustrate typical dark terrain, but intentionally avoid deep, fresh craters. Portions of profile 1 and profile 3 were used in the finite element simulations
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Figure 11: The initial topography (top), final topography (middle), and final lithospheric
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Figure 12: The effect of changing the surface temperature and heat flux on the resulting surface deformation for simulations initialized with dark terrain topography (top panel -
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profile 1 of Fig. 10). Each curve shows the deformation after 10% extension, and are offset for clarity. Red: Ts = 70 K, F = 100 mW m−2 ; gold: Ts = 100 K, F = 70 mW m−2 ;
teal: Ts = 100 K, F = 100 mW m−2 (identical to the simulation shown in Fig. 11A); blue: Ts = 100 K, F = 150 mW m−2 ; violet: Ts = 120 K, F = 100 mW m−2 .
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Figure 13: DTM and topographic profiles of Ganymede’s smooth terrain. The DTM is the same as that shown in Fig. 10, but profiles were extracted from Nippur Sulcus and Elam Sulci. Note the difference in vertical scale between the profiles shown here and those in Fig. 10.
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Figure 14: Forming grooves from smooth initial topography. A. The initial topography (a portion of profile 1 in Fig. 13, but with the long wavelength slope removed), B. Ts =100 K,
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Figure 15: DTM (as in Fig. 10) showing the locations where crater topography was extracted for both the fresh and viscously relaxed cases. The simulations shown in Figs. 16, 17, and 18 used a portion of profile c1. The simulations shown in Fig. 19 used a portion of profile r3.
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Figure 16: The initial topography (top), final topography (middle), and final lithospheric deformation (bottom) for a simulations with a relatively cold and thick lithosphere (Ts = 70 K,
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Figure 17: The topography (top) and lithospheric deformation (bottom) for a simulation
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Fig. 15, and is the same as that in Fig. 16. After 1% extension most of the initial crater topography is removed by viscous relaxation, but a residual zone of weakened lithosphere
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Figure 18: The initial topography (top), final topography (middle), and final lithospheric
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deformation (bottom) for simulations with a warm and thin lithosphere. A. Ts = 100 K, and F = 150 mW m−2 after 2% extension. B. As in A but after 8% extension. C. Ts = 120 K,
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and F = 150 mW m−2 after 1% extension. D. As in C but after 5% extension. In all cases, the initial topography was derived from profile c1 in Fig. 15 and is the same as that in Fig. 16 and Fig. 17A. Note the rapid removal of crater topography in A and C.
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Figure 19: The initial topography (top), final topography (middle), and final lithospheric deformation (bottom) for simulations initialized with topography derived from a viscously
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Figure 20: Comparison of the final surface deformation after 10% extension for pairs of simulations of dark terrain extension that used a cohesion of 1 MPa (black curves) and 100 kPa (grey curves), but were otherwise identical. A. Ts = 70 K, and F = 150 mW m−2 ;
B. Ts = 100 K, and F = 100 mW m−2 ; C. Ts = 120 K, and F = 100 mW m−2 . Compare with Fig. 11.
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Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension Michael T. Bland, William B. McKinnon PII: DOI: Reference:
S0019-1035(17)30223-3 10.1016/j.icarus.2017.10.017 YICAR 12652
To appear in:
Icarus
Received date: Revised date: Accepted date:
17 March 2017 11 October 2017 12 October 2017
Please cite this article as: Michael T. Bland, William B. McKinnon, Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension, Icarus (2017), doi: 10.1016/j.icarus.2017.10.017
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Highlights • We simulate grooved terrain formation with large-amplitude pre-existing topography • When initial topographic relief is ¿50 m, groove-like structures fail to form.
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• Forming grooves directly from dark terrain by tectonic resurfacing is difficult. • Viscous relaxation of pre-existing topography enables tectonic resurfacing.
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• Resurfacing occurred by viscous relaxation, tectonics, and cryovolcanism combined.
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Viscous relaxation as a prerequisite for tectonic resurfacing on Ganymede: Insights from numerical models of lithospheric extension
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Michael T. Bland1 and William B. McKinnon2
U. S. Geological Survey, Astrogeology Science Center, Flagstaff AZ 86001
Department of Earth and Planetary Sciences and McDonnell Center for the Space
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Sciences, Washington University in St. Louis, Saint Louis, MO 63130
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65 Total pages, including 20 Figures Resubmitted to Icarus October 13, 2017
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Corresponding Author: Michael T. Bland U. S. Geological Survey, Astrogeology Science Center
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2255 N. Gemini
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Proposed Running Head: Viscous relaxation and tectonic resurfacing on Ganymede.
Flagstaff, AZ 86001 [email protected] phone: (928) 556-7080
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fax: (928) 556-7014
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Abstract Ganymede’s bright terrain formed during a near-global resurfacing event (or events) that
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produced both heavily tectonized and realatively smooth terrains. The mechanism(s) by
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which resurfacing occurred on Ganymede (e.g., cryovolcanic or tectonic), and the relationship
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between the older, dark and the younger, bright terrain are fundamental to understanding
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the geological evolution of the satellite. Using a two-dimensional numerical model of litho-
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spheric extension that has previously been used to successfully simulate surface deformation
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consistent with grooved terrain morphologies, we investigate whether large-amplitude preex-
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isting topography can be resurfaced (erased) by extension (i.e., tectonic resurfacing). Using
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synthetically produced initial topography, we show that when the total relief of the initial
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topography is larger than 25-50 m, periodic groove-like structures fail to form. Instead, ex-
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tension is localized in a few individual, isolated troughs. These results pose a challenge to the
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tectonic resurfacing hypothesis. We further investigate the effects of preexisting topography
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by performing suites of simulations initialized with topography derived from digital terrain
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models of Ganymede’s surface. These include dark terrain, fresh (relatively deep) impact
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craters, smooth bright terrain, and a viscously relaxed impact crater. The simulations using
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dark terrain and fresh impact craters are consistent with our simulations using synthetic
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topography: periodic groove-like deformation fails to form. In contrast, when simulations
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were initialized with bright smooth terrain topography, groove-like deformation results from
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a wide variety of heat flow and surface temperature conditions. Similarly, when a viscously
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relaxed impact crater was used, groove-like structures were able to form during extension.
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These results suggest that tectonic resurfacing may require that the amplitude of the initial
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topography be reduced before extension begins. We emphasize that viscous relaxation may be the key to enabling tectonic resurfacing, as the heat fluxes associated with groove terrain
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formation are also capable of reducing crater topography through viscous relaxation. For
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long-wavelength topography (large craters) viscous relaxation is unavoidable. We propose
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that the resurfacing of Ganymede occurred through a combination of viscous relaxation,
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tectonic resurfacing, cryovolcanism and, at least in a few cases, band formation. Variations 3
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in heat flow and strain magnitudes across Ganymede likely produced the complex variety of
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terrain types currently observed.
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Keywords: Ganymede; Tectonics.
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Ganymede’s terrains and evidence for resurfacing At large scales, Ganymede’s surface is composed of two types of terrain: relatively dark
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terrain with higher crater densities, and relatively bright terrain with lower crater densities
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(Fig. 1). The dark terrain likely represents an ancient, though not necessarily primordial
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(e.g., crater densities are higher on neighboring Callisto (Zahnle et al., 2003; Schenk et al.,
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2004)) crust. The bright terrain, in contrast, is a resurfaced unit formed during Ganymede’s
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mid-life (∼2 Ga ago (Zahnle et al., 2003), although uncertainties are at least 1 Ga (Schenk
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et al., 2004)). Understanding how the bright (and often “grooved”) terrain was emplaced and
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the relationship between Ganymede’s dark and bright terrains are central to understanding
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the overall geologic history of the satellite.
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Ganymede’s dark terrain comprises roughly one-third of its surface (e.g., Patterson et al.,
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2010) and is heavily cratered, with numerous knobs and massifs (Shoemaker et al., 1982;
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Prockter et al., 1998) (Fig. 1A). The low albedo material is probably a relatively thin,
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silicate-rich veneer that overlies an icier substrate (Prockter et al., 1998). This substrate is
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apparently exposed in the rims of furrows (troughs) and craters, where the dark surface lag
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has sloughed-off down-slope and accumulated in topographic lows. The icy substrate is also
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exposed in crater palimpsests and the relatively bright ejecta associated with many dark
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terrain craters (e.g., Osiris) (Pappalardo et al., 2004).
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Within the dark terrain and far from the boundaries with the bright terrain (e.g., within
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the the central portion of Galileo Regio), tectonic deformation is limited (Prockter et al.,
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1998), consisting primarily of ancient, arcuate furrows up to ∼1 km deep, that may have
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formed during ancient, basin-scale impacts (McKinnon and Melosh, 1980; Schenk and McK-
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innon, 1987; Murchie et al., 1990; Prockter et al., 1998). Development and modification of the dark terrain’s furrows, massifs and knobs (possibly remnants of crater rims) likely
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occurred during an older epoch, and in a different deformation style, than that of the bright
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grooved terrain (Prockter et al., 1998, 2000). Nearer the dark-bright terrain boundary, more
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substantial tectonic deformation has occurred. In some cases the dark terrain is heavily
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fractured, and takes on a morphology similar to that of the bright terrain (Patterson et al., 5
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2010; and Fig. 1B). Because of their similar morphology and spatial association with bright
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terrain, the tectonized dark terrain may be a precursor or transitional unit to the bright
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terrain (Prockter et al., 2000; Patterson et al., 2010). The remaining two-thirds of Ganymede’s surface consists of a brighter patchwork of broad
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polygons that are often (though not always) separated from the dark terrain by deep bound-
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ing troughs (Pappalardo et al., 1998). Surface morphologies within each polygon are highly
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variable, but range from highly tectonized “grooved terrain” (Fig. 1C) to relatively smooth
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plains (Fig. 1D). The classic grooved terrain morphology consists of sets of periodically
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spaced ridges and troughs with amplitudes of several hundred meters and ridge spacing of
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3-17 km, varying from one set of grooves to the next (see Pappalardo et al., 1998, 2004,
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for comprehensive reviews). High resolution Galileo data have also revealed a second set of
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finer-scale lineations with a characteristic spacing of 1 km (Pappalardo et al., 1998). This
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iconic morphology is found throughout the bright terrain; however, substantial variation ex-
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ists, with isolated troughs and more subdued tectonic deformation found across the surface
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(Patterson et al., 2010).
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The bright terrain likely formed during extension of Ganymede’s ice lithosphere (Pap-
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palardo et al., 1998), possibly during an epoch of global satellite expansion caused by differ-
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entiation (e.g., Squyres, 1980; Mueller and McKinnon, 1988), or melting during resonance
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passage (Showman et al., 1997; Bland et al., 2009). The iconic ridges and troughs of the
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grooved terrain are thought to have formed via an extensional instability that deformed
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the lithosphere into periodically spaced pinches and swells (Pappalardo et al., 1998; Collins
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et al., 1998; Dombard and McKinnon, 2001; Bland and Showman, 2007), a process essentially
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identical to boudinage formation but at lithospheric scale (Fletcher and Hallet, 1983). Re-
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cent numerical models that include strain localization effects (e.g., via material weakening and/or non-associated plasticity) support this interpretation, permitting the formation of
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large-amplitude, periodic deformation at relatively small strains (Bland et al., 2010; Bland
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and McKinnon, 2015).
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The lower crater density within the bright terrain suggests that these terrains formed
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at the expense of the darker, heavily cratered terrain during an epoch of near-planetary-
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scale resurfacing; however, the process or processes by which such resurfacing has occurred
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remain poorly understood. Resurfacing by cryovolcanism (i.e., the eruption of a fluid onto the
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surface), tectonism (i.e., the disruption and erasure of preexisting terrains through tectonic
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deformation alone), and Europa-like band formation (i.e., the emplacement of new material
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during extension of the surface) have all been proposed.
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Cryovolcanism has been invoked as a resurfacing mechanism on Ganymede since the
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Voyager-era. In these models, an initial period of extension forms broad graben, which
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are subsequently flooded with cryovolcanic material (water, warm ice, or slush) that buries
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preexisting topography. The grooved terrain then forms during a continuing or later period
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of extensional tectonism (Golombek and Allison, 1981; Allison and Clifford, 1987), possibly
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with subsequent viscous relaxation or mass wasting of the resulting topography (Squyres,
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1982; Parmentier et al., 1982). Evidence for cryovolcanic resurfacing comes from numerous,
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unusually smooth regions on the surface (Fig. 2) as well as a number of unusual, caldera-like
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features (Schenk et al., 2001). Although high-resolution imaging is limited, at least some of
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the smooth regions appear to embay nearby topography (Fig. 2) (Allison and Clifford, 1987;
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Schenk et al., 2001), and occur in topographic lows (Schenk et al., 2001).
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Cryovolcanic resurfacing of Ganymede faces several theoretical and observational chal-
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lenges. Any cryovolcanic resurfacing mechanism proposed for icy satellites must address the
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difficulty of erupting relatively higher density fluid (e.g., salty water) through the lower den-
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sity ice shell. Such eruptions may be driven by gases entrained in the fluid (Crawford and
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Stevenson, 1988) or by topographically induced pressure gradients that drive near-surface
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fluid onto the surface (Showman et al., 2004), but the exact mechanism remains elusive.
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Additionally, there is a paucity of direct evidence for associated cryovolcanic source vents in higher-resolution Galileo images, although numerous enigmatic caldera-like features have
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been identified in the Mummu Sulci region (previously identified as the Sippar Sulcus region)
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and elsewhere (Schenk et al., 2001). Further, at least some regions that appeared smooth in
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low-resolution Voyager and Galileo images (e.g., Harpagia Sulcus) appear lightly tectonized
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when seen in higher-resolution imaging (Pappalardo et al., 2004). Evidence for tectonic imbrication (Pappalardo et al., 1998; Collins et al., 1998), the iden-
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tification of nascent rifts within the dark terrain (Prockter et al., 2000), and the challenges
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faced by cryovolcanic resurfacing described above have led to the hypothesis that Ganymede
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may have been resurfaced through tectonism alone (Head et al., 1997) (Fig. 3). In this view,
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grooved terrain forms directly from dark terrain by fault imbrication and block rotation,
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which completely erases dark terrain topography without large-scale cryovolcanic resurfac-
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ing (Head et al., 1997; Pappalardo and Collins, 2005). Key to this process is the removal of
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the dark surface lag by slumping of dark material into topographic lows (Patel et al., 1999).
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The existence of geologic units that are morphologically and stratigraphically transitional
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between “traditional” bright and dark terrain (e.g., the dark lineated units described above)
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may indicate a progression from dark terrain to bright terrain. These transitional units
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always occur adjacent to bright terrain and generally share its structural fabric (Patterson
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et al., 2010). The tectonic resurfacing paradigm has also recently been reinforced by Cassini
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observations of numerous fault cut craters on Enceladus (e.g., Crow-Willard and Pappalardo,
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2015). Yet the tectonic resurfacing hypothesis is not without its challenges. Analog models
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of Ganymede-like extension reproduce many of the distinctive characteristics of the grooved
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terrain, including extensive faulting and block rotation (Sims et al., 2014). Models that in-
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cluded preexisting craters, however, failed to result in resurfacing: in a blind test, 95% of the
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initially imposed craters were still identifiable after 33% extension of the surface (Wyrick,
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2012). Models with larger strains (e.g., Pappalardo and Collins (2005) observed Ganymede
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craters deformed by >50% extension) have not yet been performed. Although supported
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by mapping and structural analysis, the detailed mechanics of tectonic resurfacing requires
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further investigation. Head et al. (2002) suggested Europa-like band formation as an alternative (or additional)
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mechanism of resurfacing on Ganymede. Band formation is common on Europa (see Prockter
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and Patterson, 2009, and references therein), and is generally thought to involve complete
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separation of the lithosphere and the emplacement of new material as warmer ice wells
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upward from below (Prockter et al., 2002). The principal type locality for possible band
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formation on Ganymede is Arbela Sulcus, a narrow swath of relatively smooth terrain that
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can be “closed” to reconstruct the preexisting surface (Fig. 4). Such tectonic reconstructions
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are rare on Ganymede (though see Pizzi et al., 2017, for potential additional examples), but
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the importance of band formation as a resurfacing mechanism is difficult to assess given the
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general lack of high-resolution imaging available for Ganymede. On Europa, band formation
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may be associated with substantial amounts of surface strain (Bland and McKinnon, 2012).
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In reality it is possible that all three mechanisms (cryovolcanism, tectonism, and band
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formation) have operated on Ganymede at either some specific point in time, some particu-
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lar locality, or in concert. In this paper we assess the plausibility and conditions necessary
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for resurfacing Ganymede through tectonic deformation alone. That is, we seek to specif-
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ically test the tectonic resurfacing hypothesis through numerical modeling. In doing so,
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however, we also indirectly address the potential role of cryovolcanic resurfacing. We also
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identify a process that appears critical to enabling tectonic resurfacing: viscous relaxation
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of preexisting topography.
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Methods and previous modeling To numerically simulate lithospheric extension on Ganymede, we follow an identical ap-
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proach to that of Bland and McKinnon (2015), with the exception of the initial topography
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imposed. We use the viscoelastic-plastic finite element code Tekton (v2.3) (Melosh and Raef-
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sky, 1980) in a two-dimensional Cartesian plane strain geometry. Many features of rifting
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on terrestrial planets and icy worlds exhibit along-strike symmetry and are therefore con-
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ducive to a two-dimensional modeling approach. Indeed, the majority of investigations of rifting on Earth have utilized a two-dimensional geometry, which facilitates the investigation
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of large parameter spaces at high resolution (e.g., Bassi, 1991; Govers and Wortel, 1995;
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Beaumont et al., 1996; Buck et al., 1999; Gerbault et al., 1999; Lavier et al., 2000; Huis-
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mans and Beaumont, 2002, 2003; Wijns et al., 2005; Nagel and Buck, 2007; Delescluse et al.,
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2008; Whitney et al., 2013; Gueydan and Pr´ecigout, 2014, and many others). Furthermore,
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three-dimensional simulations of the rifting of terrestrial continental crust indicate that the
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resulting deformation is fundamentally two-dimensional in nature (Sharples et al., 2015),
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and most three-dimensional studies focus on along-strike rift propagation (e.g., Dunbar and
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Sawyer, 1996; Van Wijk and Blackman, 2005; Allken et al., 2011, 2012). Despite this, the
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interaction between extension, strain localization, and large-scale preexisting topography has
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received little investigation, and strain localization during extension may be modified when
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a fully three dimensional geometry is used. The hazards of modeling a three-dimensional
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process with two-dimensional simulations are discussed more fully in section 4.6. The mod-
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els presented here are therefore a necessary first-step to numerically investigating tectonic
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resurfacing, but do not tell the complete story. Three-dimensional simulations of groove
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formation are currently in progress (Bland and Wyrick, 2017).
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Our two-dimensional simulation domain is initially 80 km long and 24 km deep, ensuring
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edge and bottom boundary effects are negligible, and allowing numerous instability wave-
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lengths to develop at the surface. The bottom boundary is fixed in the vertical and free slip
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in the horizontal, and the sides are free slip in the vertical. Extension is imposed by keeping
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the left edge of the domain fixed in the horizontal and imposing a constant velocity boundary
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condition on the right edge of the domain. We impose up to 10% extension at a strain rate
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of 10−13 s−1 (i.e., 1% extension every ∼3000 yrs). Decreasing the strain rate, which may
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be more geologically plausible (Dombard and McKinnon, 2001; Stempel et al., 2005), has
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only a small effect on our results, and generally leads to increased instability amplification
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rates (Bland and McKinnon, 2015; Dombard and McKinnon, 2001). The top surface is free,
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and we impose initial topography as described below. Each simulation is initialized with a
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lithostatic stress state using a surface gravity of 1.4 m s−2 . The density of the ice is assumed to be 950 kg m−3 , consistent with cold, somewhat dirty ice.
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The simulations include all relevant viscous flow mechanisms for ice I, including dislo-
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cation creep (three regimes), grain boundary sliding (GBS), basal slip (BS), and diffusion
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creep. Each flow mechanism can act simultaneously, although GBS and BS rate-limit each
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other such that the slower mechanism dominates (Goldsby and Kohlstedt, 2001). At the
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stress, strain rate, and temperatures used in our simulations, deformation is predominantly
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controlled by GBS flow and dislocation creep regime ‘B’ (see Durham and Stern, 2001). More
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detail is provided in Bland and McKinnon (2015) and Bland and Showman (2007). We use
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elastic parameters consistent with cold intact ice: a Young’s modulus (E) of 9.33 GPa and
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a Poisson’s ratio of 0.325 (Gammon et al., 1983). A pervasively fractured lithosphere might
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have a lower E (e.g. Pritchard and Stevenson, 2000; Klimczak et al., 2015), which would
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generally suppresses amplification rates (Bland and Showman, 2007); however, said fractures
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would also produce a compensating effect by lowering the conductivity and thus increasing
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the thermal gradient and instability growth rate.
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Brittle behavior is modeled using non-associative plasticity, which results in strong lo-
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calization of brittle deformation (Rudnicki and Rice, 1975; Vermeer and de Borst, 1984;
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Poliakov and Herrmann, 1994). Non-associated plasticity is appropriate for granular geo-
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logic materials (including ice (Lade, 2002; Pritchard, 1988)) that undergo limited dilation
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during shear failure (Vermeer and de Borst, 1984). Plastic failure occurs when the second in-
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variant of the deviatoric stress reaches the defined yield criterion. We use a Drucker-Praeger
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yield criterion (Owen and Hinton, 1980; Vermeer and de Borst, 1984; Iwashita and Oda,
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1999) with a nominal cohesion of 1 MPa (Beeman et al., 1988) and an internal friction angle
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of 30◦ . The Drucker-Praeger criterion is similar to a Mohr-Coulomb criterion but is more
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numerically stable. We also investigate how using a lower cohesion (100 kPa) affects our
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results. This lower cohesion is more consistent with the failure threshold inferred for cycloid
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formation on Europa (Rhoden and Hurford, 2013). Our implementation of non-associative
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plasticity is described in detail in Bland and McKinnon (2015).
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Although Tekton does not include thermodynamics, we impose a thermal structure
through the temperature-dependent viscosity. For each simulation we choose a heat flux
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(F ) and surface temperature (Ts ), and assume a temperature-dependent thermal conduc-
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tivity appropriate for intact ice (k = 651 W m−1 /T ) (Petrenko and Whitworth, 1999) to
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calculate the temperature of each element as a function of depth (z) assuming a conductive
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steady state: T (z) = Ts exp F z/651 W m−1 .
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We use the temperature of each element to calculate its rheologic parameters (i.e., the effec-
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tive viscosity for each of the flow mechanism described above). For the simulations shown
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here we use only constant (in time) thermal/viscosity structures (cf. Bland et al., 2017). The
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temperature and viscosity field is not updated during the simulation itself, so isotherms are
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advected with the material contours. Some consequences of this simplification are discussed
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in section 4.3.1. We nominally use a surface temperature of 100 K, but investigate the effect
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of surface temperatures between 70 K and 120 K, as appropriate for colder polar regions and
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warmer equatorial dark terrain, respectively. We investigate heat fluxes ranging from 70 to
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150 mW m−2 , consistent with previous inferences for grooved terrain formation (Dombard
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and McKinnon, 2001; Bland and Showman, 2007). Note that in reality, the thermal con-
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ductivity may be substantially lower than that of intact ice due to both micro and macro
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porosity throughout Ganymede’s lithosphere; however, decreasing the conductivity has the
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same effect as increasing the heat flux. Modifying either (or both) effectively changes the
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thickness of the lithosphere, and the length scale over which the ice transitions from brittle
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to ductile behavior (i.e., the rheologic contrast between the ice lithosphere and subjacent ice
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asthenosphere).
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The significant difference between the simulations described here and those described in
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Bland and McKinnon (2015) is the initial topography imposed at the surface of the simulation
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domain. In our previous successful simulations, we used semi-random topography created by
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randomly phase shifting and co-adding sinusoidal perturbations with wavelengths from 1 to
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80 km. This topography was generally normalized to have a maximum total relief (i.e., the difference between the highest and lowest point) of just 15 m. In these simulations, the goal
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was to provide enough initial topography to allow an instability to initiate and naturally
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establish a dominant wavelength, which is a function of the thickness of the deforming layer
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(e.g., Fletcher and Hallet, 1983; Herrick and Stevenson, 1990; Dombard and McKinnon,
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2001; Bland and Showman, 2007, and many others). An example of a successful simulation 12
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using low-amplitude topography is shown in Fig 5. Extension of the initial topography in
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panel A results in the periodic groove-like deformation shown in panel B. The simulation
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used Ts =70 K and F =100 mW m−2 . The resulting surface deformation is similar to the
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topography of Ganymede’s archetypal grooved terrain as shown in panel D. Clearly, these
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simulations can successfully reproduce the wavelength, amplitude, and general morphology of
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Ganymede’s grooved terrain when low-amplitude initial topography is used. The simulations
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are described more fully in Bland and McKinnon (2015)
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As clearly illustrated in Fig. 5, however, the amplitude of the initial topography used in
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our previous simulations (panel A) is inconsistent with the amplitude of dark terrain topog-
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raphy that may have predated groove formation on Ganymede (panel C), which if resurfacing
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of dark terrain occurred by tectonism, consisted of knobs, massifs, and hummocky terrain
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with amplitudes of several hundred meters. Further, many groove lanes appear to disrupt
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older groove sets, the ridges and troughs of which were also likely several hundred meters
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in amplitude. In either case, groove formation had to modify large-amplitude preexisting
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topography if tectonic resurfacing was the dominant resurfacing mechanism. In this work
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we examine how such large amplitude deformation modifies the previous results of Bland
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and McKinnon (2015). To do this we utilize two types (or cases) of initial topography. The
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first case uses “synthetic” topography created using the methods described above, but at
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a variety of initial amplitudes (Section 3). This permits us to systematically examine how
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the amplitude of the initial topography affects groove formation. In the second case we use
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topography extracted from digital terrain models (DTMs) of Ganymede’s surface (Section
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4). This permits us to investigate how grooves may have formed in the presence of different
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initial terrain types. In both cases, surface topography is imposed simply by varying the
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position of surface and near-surface nodes, with the topographic perturbation decaying with depth such that “flat” material contours are reached at depth (i.e., vertical nodal position
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is unperturbed). After describing the results of these two investigations, we discuss the
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implications of our modeling for resurfacing on Ganymede (Section 5).
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Simulating tectonic resurfacing with synthetic initial topography In order to examine how initial topographic amplitude affects our simulations of groove
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terrain formation, we performed a suite of simulations in which we kept the form of the
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initial topography constant but varied its initial amplitude from 1 m to 200 m of total
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relief (left column of Fig. 6). Each simulation was otherwise identical: a strain rate of
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10−13 s−1 and 10% total extension, Ts =100 K, F =100 mW m−2 , and a cohesion of 1 MPa.
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Figure 6 shows the effect of increasing initial topographic amplitudes. For reference, the
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simulations described in Bland and McKinnon (2015) used an initial amplitude of 12 m.
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At relatively small initial amplitudes (1 to 25 m) extension results in strongly periodic
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deformation. Little, if any, signature of the pre-existing terrain remains. These results are
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consistent with Bland and McKinnon (2015). As the initial amplitude becomes larger (50-
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100 m), however, the deformation that results from extension becomes less periodic with
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strain preferentially localizing in several individual troughs, which deepen at the expense of
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more distributed deformation. At the largest initial amplitudes investigated (150-200 m),
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extension results in the formation of several isolated troughs ∼500 m deep, with little or no
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periodicity in the final topography.
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The decrease in the periodicity of the simulated final topography as the amplitude of the
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initial topography is increased was quantified using Fourier analysis of the final simulated
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deformation (Fig. 7). As expected, the initial topography has an extremely broad power
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spectrum that includes contributions from many wavelengths (inset of Fig. 7). When small-
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amplitude initial topography is used, the power spectrum of the final topography is strongly
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peaked with a wavelength of 6 km. The full width half maximum (FWHM) of the peak is 1.5 km. Note that because the resolution of the spectrum decreases with increasing wavelength,
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the exact FWHM is poorly resolved. As the amplitude of the initial topography is increased,
305
the peak in the final topography power spectrum broadens. That is, a broader range of
306
wavelengths contribute to the topography, and the topography is less periodic. In the 200 m 14
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amplitude simulation, the resulting power spectrum has a peak with a FWHM of ∼10 km.
308
These values compare poorly to Fourier analysis of Ganymede’s actual grooved terrain,
309
which indicate that groove spacing is strongly periodic, with a power spectrum FWHM of
310
just 2-3 km (Grimm and Squyres, 1985; Patel et al., 1999). The observed power spectra are
311
therefore consistent with our simulations that use low-amplitude initial topography, but not
312
those that use larger initial amplitudes.
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The influence of the initial topography is further illustrated in Fig. 8, which compares
314
the development of surface deformation for two simulations that used 25 m and 200 m
315
amplitude initial topography, respectively, but were otherwise identical. When initial topo-
316
graphic amplitudes are small, the dominant wavelength of the necking and/or localization
317
instability resulting from lithospheric extension controls the surface deformation. Horizon-
318
tal strain becomes partitioned periodically throughout the lithosphere and the surface is
319
consequently deformed into periodic structures with an amplitude of ∼150 m (a factor of
320
6 increase after 10% extension). In contrast, when the initial topography is larger in am-
321
plitude, strain preferentially becomes partitioned into preexisting structures as extension
322
occurs. In the simulation shown in Fig. 8B these structures are generally topographic lows.
323
As extension occurs, strain is accommodated nearly entirely within these structures (Fig.
324
8d), which deepen at the expense of surrounding regions. The final surface is composed
325
of isolated troughs a few kilometers wide and (in some cases) more than 500 m deep, each
326
separated by relatively undeformed regions (i.e., having similar small-scale topography as
327
initially present) 10-20 km wide. This morphology generally does not resemble Ganymede’s
328
archetypal grooved terrain.
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Figures 6, 7, and 8 indicate that simulations that utilize small-amplitude topography (up
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to 25-50 m) will result in periodic groove-like deformation, whereas simulations that utilize initial topography with a total relief >50 m may result in non-periodic deformation (deep
332
isolated troughs). To assess whether this result depends on our model assumptions, we per-
333
formed a suite of simulations that varied the heat flux (70-150 mW m−2 ), surface temperature
334
(70-120 K), and strain rate (10−13 s−1 - 10−14 s−1 ). Variations in the mechanical properties of 15
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the ice were also explored and are discussed further below. These simulations indicate that
336
the basic result described above is largely independent of the physical parameters assumed.
337
Figure 9 compares the results of pairs of identical simulations that used a variety of physical
338
conditions, but with initial topographic amplitudes (maximum relief) of 25 m and 150 m.
339
In general, cold surface temperatures result in larger deformation amplitudes compared to
340
warm surface temperatures, and high heat fluxes result in shorter wavelength (and lower
341
amplitude) deformation than lower heat fluxes. These results are consistent with those of
342
Bland and McKinnon (2015), where they are described in greater detail. More notably, in
343
every case the simulations initialized with low-amplitude topography resulted in periodic or
344
semi-periodic groove-like deformation whereas simulations initialized with large amplitude
345
topography resulted in a few (or in some cases single) deep, isolated troughs. We conclude
346
that the qualitative results described above are general, and do not depend on the physical
347
parameters assumed during groove formation.
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The transition between relatively periodic deformation and the formation of isolated
349
troughs consistently occurs when initial topographic relief is 25-50 m in amplitude. That is, in
350
each case considered, simulations initialized with topography with relief greater than (and in
351
many cases equal to) 50 m result in isolated troughs rather than periodic structures. However,
352
some conditions lead to greater strain localization than others. Cold surface temperatures
353
(e.g., 70 K), and low heat fluxes (70 mW m−2 ) both result in strong localization such that
354
strain is often partitioned into a single isolated trough (e.g., Fig. 9D and H). As shown in
355
Fig. 9C, E, G, and I, simulations that produce large-amplitude periodic structures when
356
initialized with low-amplitude topography yield stronger localization when large-amplitude
357
initial topography is used. In contrast, warm surface temperatures (120 K, Fig. 9F) result
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in relatively more periodic (although still somewhat localized) deformation even when large amplitude initial topography is used. This pattern reflects the tendency of the assumed parameters to result in large-amplitude deformation in general.
361
Fundamentally, localization of strain within troughs is the result of higher stresses, and
362
hence greater brittle failure, within the troughs. If one considers the lithosphere as a plate
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with variable thickness (due to topography) that is subjected to an axial force (Fa ) that
364
is constant with depth, the axial stress on a vertical surface through the plate is simply
365
Fa /h(x), where h(x) is the thickness at horizontal point x. Since the base of the lithosphere
366
is initially flat (or flatter), large-scale topography (like a trough) reduces h locally, and so the
367
stress is increased locally. The increase stress results in somewhat higher strain rates in these
368
regions, but more importantly increases the likelihood of brittle failure in those elements.
369
The higher strain rate associated with brittle failure, and the localization effects of non-
370
associated plasticity, results in additional local thinning, which further increases the local
371
stresses, such that a positive feedback results. This pattern has been verified by examining
372
the stress field early in the simulations. For low-amplitude topography this effect is small,
373
and other processes (e.g., periodic necking) dominate. When initial topography is large
374
however, such continuous necking (thinning in a single region) can occur. As described
375
above, conditions that favor brittle deformation (e.g., a cold lithosphere) more easily localize
376
strain in this manner.
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Our simulations using synthetic topography challenge the tectonic model of resurfacing
378
Ganymede. They suggest that low-amplitude initial topography with .25–50 m total relief
379
can easily be “erased” and replaced by periodic ridges and troughs, whereas larger amplitude
380
topography is harder to resurface, resulting in localized isolated troughs. Even excluding
381
impact craters, typical dark terrain on Ganymede (from which the grooved terrain is thought
382
to form) includes topographic amplitudes of several hundred meters (see below). The sim-
383
ulations described above suggest that simply extending such terrain does not easily result
384
in groove-like deformation. Other resurfacing mechanisms, perhaps working in concert with
385
tectonic resurfacing, are apparently required. Below we use topography derived from a vari-
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ety of actual terrains on Ganymede to further investigate the interaction between extension and initial topography.
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4
Simulating tectonic resurfacing with DTM-derived initial topography
389
To further evaluate how lithospheric extension has modified pre-existing structures on
391
Ganymede, we performed simulations of lithospheric extension that were initialized with to-
392
pography derived directly from Ganymede’s surface. The investigation focused on four types
393
of terrain or landforms: dark terrain, smooth terrain, fresh impact craters, and viscously re-
394
laxed impact craters. Each terrain type is discussed in detail below.
395
4.1
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Forming grooves from dark terrain
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As described above, the tectonic resurfacing hypothesis postulates that Ganymede’s
397
bright grooved terrain formed directly from dark terrain (Head et al., 1997; Prockter et al.,
398
2000; Pappalardo and Collins, 2005). Although generally uniform in appearance at low
399
spatial resolution, the dark terrain is quite rough when viewed at high resolution, and the
400
individual knobs, hummocks, and massifs constitute relatively large-amplitude topography.
401
As demonstrated in section 3, the formation of periodically spaced tectonic structures, in
402
which strain is broadly distributed, from such large-amplitude topography is challenging.
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To more directly assess how grooved terrain might have formed directly from dark terrain
404
we performed a suite of simulations that explicitly used dark terrain topography as their
405
initial condition. We extracted topographic profiles from a region of dark terrain in northern
406
Marius Regio. The region is bounded by Nippur Sulcus to the east and northeast, Byblus
407
Sulcus to the west and Philus Sulcus to the north. The DTM and topographic profiles derived
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from it are shown in Fig. 10. The DTM used was derived from Galileo-based photoclinometry (e.g., Schenk, 1989; Bierhaus and Schenk, 2010), and has a horizontal resolution of ∼1 km
410
and a vertical uncertainty of ∼5%. The profiles were intentionally selected to avoid large-
411
scale craters or crater forms. Modification of impact craters is discussed in detail in section
412
4.3. Based on these 14 profiles, topographic relief associated with the largest individual
413
topographic features (hummock or knobs) is typically 200 m, with one feature exceeding 18
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400 m. Many knobs are significantly smaller (∼100 m). Over longer wavelengths (tens to
415
hundreds of kilometers), total relief in this region of dark terrain can exceed 400 m (e.g.,
416
profiles 11, 13, and 14 in Fig. 10). Two topographic profiles were selected for use in our finite
417
element simulations (1 and 3 in Fig. 10). These profiles were selected because they appear
418
typical of the dark terrain (total relief in profile 1 and 3 is 325 m, and 300 m respectively)
419
and have limited long wavelength (∼50-100 km) slopes.
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For both profiles, an 80 km-long portion was extracted, interpolated to the resolution
421
of the finite element model, and imposed on the surface of the model domain. Extension
422
was imposed as described above under a variety of conditions. Figure 11 shows the defor-
423
mation of the surface and lithosphere resulting from 10% extension with a Ts =100 K and
424
F =100 mW m−2 . The result is similar to that shown in Fig. 8B. For profile 1 (Fig. 11A),
425
extension has been primarily accommodated within two narrow (<5 km wide) troughs that
426
reach depths of 500 m and >1 km, respectively. These deep troughs originate in topographic
427
lows in the initial preexisting topography. Lower-amplitude (150-200 m) ridges and troughs
428
have formed between the deep troughs. Spectral analysis of the surface deformation suggests
429
limited periodicity: the power spectrum of the final topography is peaked at 12 km, but the
430
FWHM is greater than 10 km. Overall, the surface deformation, particularly the 1 km-deep
431
trough, is inconsistent with the morphology of Ganymede’s grooved terrain (although see
432
discussion in section 4.3).
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The initial topography in profile 3 is more subdued and the resulting deformation is also
434
lower in in amplitude. Like the simulation using profile 1, the strain is primarily accommo-
435
dated in a several (3-6) troughs that have deepened at the expense of adjacent ridges and
436
troughs. The deepest trough in this case is 500-600 m deep. Unlike the deformation of profile
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1, these troughs, while shallower, are separated by 10-15 km-wide regions of essentially flat terrain. The simulated surface deformation is unlike Ganymede’s archetypal grooved terrain (Fig. 5D).
440
Figure 12 illustrates (for profile 1) how the final deformation depends on the thermal
441
structure used in the simulation. Cold lithospheres (lower Ts and F ) generally result in 19
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stronger localization of deformation within a single trough, whereas warmer lithospheres
443
(higher Ts and F ) tend to result in more distributed deformation. As noted in section 3, this is
444
due to the predominance of brittle deformation, which readily leads to localization, in the cold
445
lithosphere. In the simulation with Ts =120 K and F =100 mW m−2 , the isolated troughs
446
have an amplitude of ∼600 m, which is still larger than, but considerably closer to, typical
447
groove amplitudes. The increased periodicity of the deformation for warmer lithospheres
448
results from the general decrease in the amplitude growth rate under warm conditions, which
449
has consistently been observed in numerical models of tectonic deformation on icy worlds
450
(Bland et al., 2010; Bland and McKinnon, 2012, 2013, 2015). In these simulations, the weaker
451
viscosity contrast between the relatively warm near-surface ice and the even warmer ice at
452
depth retards growth of the necking and localization instabilities, including the run-away
453
localization of strain within a few troughs. The result is lower amplitude but more periodic
454
deformation.
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As with the simulations that used large-amplitude synthetic topography, the simulations
456
that were initialized with dark terrain topography generally fail to produce groove-like defor-
457
mation under thermal conditions typical of groove formation on Ganymede1 . Instead, strain
458
becomes localized within preexisting topographic lows, resulting in troughs ∼1 km deep that
459
are separated by lower amplitude ridges and troughs. These simulations suggest that forming
460
grooved terrain simply by “tectonically resurfacing” the dark terrain is unlikely. Further-
461
more, the simulations described above intentionally avoided large-scale crater forms, which,
462
as discussed below, provide an even greater challenge to the tectonic resurfacing mechanism.
463
We note, however, that our model has inherent limitations due to their two-dimensional
464
nature. Isolated knobs and depressions within the dark terrain act like ridges and troughs
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in a two-dimensional profile, and localization may be less efficient when three-dimensional effects are accounted for (see discussion in section 4.6). 1
Dombard and McKinnon (2001) argue that strains up to 50% - 100% may be necessary to form “grooves”
in dark terrain
20
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467
4.2
Forming grooves from bright smooth terrain
The simulations described above suggest that forming grooved terrain by tectonically
469
resurfacing dark terrain terrain is challenging. An alternative end-member hypothesis is that
470
groove terrain formation occurred in several stages that included cryovolcanic resurfacing.
471
In this scenario, cryovolcanism locally provides a topographically smooth lane upon which
472
the ridges and troughs of the grooved terrain subsequently formed. To directly assess how
473
grooved terrain might have formed from such smooth terrain, we used the topography of
474
bright, relatively smooth sulci on Ganymede as the initial topography for our simulations of
475
lithospheric extension. Six topographic profiles were extracted from Nippur Sulcus and Elam
476
Sulci using the same DTM described in section 4.1 (Fig. 13), and interpolated for use in our
477
simulations. In these profiles, local relief was ∼50 m, and up to 250 m of relief is present at
478
long wavelengths (∼100 km). For our simulations we selected the first 80 km of profile 1, but
479
removed the regional slope using a second order polynomial. Our objective was to use the
480
smoothest surface available, which would be consistent with cryovolcanic resurfacing. This
481
also permits us to clearly delineate these simulations from those that utilized dark terrain
482
(described above). The initial topography used in our simulations is shown in Fig. 14A.
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Simulations of extension that utilize the “smooth” initial topography described above
484
result in strongly periodic groove-like structures. Figure 14 shows the final surface defor-
485
mation for three simulations that utilized a range of thermal structures (Ts =70-120 K, and
486
F =70-150 mW m−2 ). Each simulation resulted in periodic deformation. For Ts =100 K and
487
F =100 mW m−2 , the deformation has a wavelength of 6 km and an amplitude of 150-200 m
488
(Fig. 14B). Perhaps not surprisingly, the deformation is consistent with that resulting from
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low amplitude synthetic initial topography under identical surface temperature and heat flux (Fig. 6). Decreasing the surface temperature and heat flux increases the wavelength and
491
amplitude of the final deformation, but the surface remains periodic (λ ≈18 km for Ts =70 K,
492
and F =70 mW m−2 , Fig. 14C). Conversely, increasing surface temperature and heat flux
493
decreases the wavelength and amplitude of the deformation (λ ≈3 km for Ts =120 K, and
494
F =150 mW m−2 , Fig. 14D). The relationship between heat flux, surface temperature, and 21
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495
deformation morphology is consistent with previous modeling results (Bland et al., 2010;
496
Bland and McKinnon, 2015). The relative “ease” with which groove-like deformation can be produced from initially
498
smooth terrain compared with the difficulty of tectonically resurfacing dark terrain suggests
499
that cryovolcanic resurfacing may have played an important if not critical role in the forma-
500
tion of the grooved terrain. These simulations generally support the post-Voyager hypothesis
501
that bright grooved terrain formed through a multi-stage process including both volcanism
502
and tectonism a` la Golombek and Allison (1981) and Allison and Clifford (1987). The cry-
503
ovolcanic resurfacing hypothesis certainly has problems (as outlined above), but forming
504
broadly distributed extensional deformation from the relatively smooth canvas it provides
505
is more obviously feasible than directly modifying the large-scale topography of the dark
506
terrain.
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Tectonic resurfacing of impact craters
In the dark-terrain simulations described above (section 4.1) we intentionally utilized
509
topographic profiles that did not include large impact craters. Impact craters provide one
510
of the greatest challenges to the tectonic resurfacing mechanism. Whereas elongated craters
511
have been documented within Ganymede’s dark terrain (Pappalardo and Collins, 2005),
512
few (if any) “ghost craters”, in which subtle evidence of crater rims remain but the crater
513
itself does not, have been observed within broad expanses of grooved terrain. This suggests
514
that the resurfacing that produced the bright terrain was extremely efficient. In contrast,
515
physical analog models of tectonic resurfacing fail to erase craters, even while producing
517
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periodic graben-like structures (Wyrick, 2012). To investigate how the extending lithosphere interacts with impact craters, we performed
518
a suite of simulations that utilized impact crater topography derived from our DTM of Marius
519
Regio. The topographic profiles are shown in Fig. 15, along with those of a nearby viscously
520
relaxed crater (see below). The crater is 21 km in diameter, ∼900 m deep, and relatively
521
fresh. We use an 80 km portion of profile c1 (centered on the crater) and interpolate to the 22
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resolution of our finite element mesh. The disruption and erasure of craters in numerical simulations is challenging because their
524
substantial depth creates a locally thin region of the lithosphere that, as discussed in section
525
3, localizes horizontal stresses, brittle failure, and extensional stain. Figure 16 shows the
526
surface and lithospheric deformation for a simulation initialized with the crater topography
527
described above and a relatively cold and thick lithosphere (Ts =70 K, and F =70 mW m−2 ).
528
In this case, extension is more-or-less entirely accommodated within the crater itself, and the
529
crater actually deepens and narrows by a factor of two during extension, reaching a depth
530
of ∼2 km (with respect to the ground plane), and width of ≈10 km. The pervasive plastic
531
deformation within the crater may be sufficient to completely disrupt the crater-form through
532
imbricate faulting; however, the end result is a single deep trough rather than distributed,
533
periodic deformation. Here again, three-dimensional effects may be important (section 4.6).
534
In our two-dimensional simulations the crater effectively acts as a deep trough. In reality, a
535
crater is an isolated depression and strain localization may be modified. However, we note
536
that fractures and faults within Ganymede’s dark terrain (e.g., Nicholson Regio, Fig. 4), and
537
on Enceladus, often develop through the center of craters, suggesting that they do localize
538
brittle deformation in three-dimensions.
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When the lithosphere is warmer (Ts =100 K, and F =100 mW m−2 ) different behavior
540
results (Fig. 17). In this case the imposed impact crater undergoes rapid viscous relaxation
541
during the initial period of extension, such that by 1% extension most of the impact crater
542
topography is removed (Fig. 17A). We emphasize that flattening of the crater is not due to
543
tectonic resurfacing, but rather primarily to viscous relaxation (cf. Bland et al., 2017; Singer
544
et al., 2017). Despite the reduction in topography, the combination of viscous relaxation and
546
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extension leads to the formation of a weak zone at the location of the former crater (indicated by the colored portions of the lithosphere). As extension of the lithosphere continues, the
547
majority of the strain is accommodated within this zone (Fig. 17B and C). The result is
548
the formation of a relatively isolated, narrow, v-shaped trough nearly 800 m deep, similar to
549
the depth of the original crater (Fig. 17D). Critically, the regions adjacent to the crater are
23
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essentially undeformed: the initial, non-crater topography present at time zero still remains
551
after ∼5% extension. As in the colder simulation, extensive faulting is likely to disrupt the
552
crater (including its rim). This pervasive faulting is similar to tectonically disrupted, but still
553
visible craters in dark terrain (Pappalardo and Collins, 2005) (Fig. 3D). Whereas the crater
554
has effectively been removed (i.e., the rim and interior are likely disrupted), the resulting
555
topography is not consistent with grooved terrain morphologies.
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Further increasing the lithospheric temperature yields similar behavior to the warm simu-
557
lation. Figure 18 illustrates this effect for simulations with F =150 mW m−2 and Ts ≥100 K.
558
For the two cases shown, the initially imposed crater is essentially flattened by relaxation
559
after just 1-2% extension. Again the majority of the strain is accommodated within the
560
weak zone associated with the initial crater, and extension results in an isolated, flat-floored
561
graben or v-shaped trough. The topography is generally inconsistent with grooved terrain
562
morphologies.
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In the warm lithosphere case, the failure to form groove-like deformation is predominantly
564
the result of the weak zone that remains after viscous relaxation has occurred, rather than
565
the amplitude of the topography. Whereas viscous relaxation can result in plastic failure of
566
the near-surface (Dombard and McKinnon, 2006), the deep failure zone in our model results
567
from the concomitant extensional strain. However, it is plausible that rather than relaxation
568
and extension occurring simultaneously, viscous relaxation preceded extension. Such a two-
569
step scenario might prevent the development of a weak zone beneath the crater as long
570
as thermal steady state can be achieved. Further, micro- and macro-porosity that results
571
from brittle failure during viscous relaxation may thermally sinter or anneal (a process not
572
included here) under the warm conditions of the lithosphere, thus further healing any weak
574
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zone that forms. Shoemaker et al. (1982) argued that at temperatures greater than ∼130 K, vapor transport and deposition through the regolith (or “damaged” zones) can re-cement
575
the ice lithosphere. Besserer et al. (2013) showed that viscous compaction is also capable of
576
removing porosity that might result from fracturing.
577
To further assess this scenario, we performed a suite of simulations using topography
24
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derived from a viscously relaxed crater within Marius Regio (Fig. 15). Like the fresh crater
579
described above, the relaxed crater is 21 km in diameter, with a central rebounded floor
580
that is at the level of the surrounding terrain. Surrounding the relaxed center is a circular
581
moat approximately 200 m deep. The crater retains obvious rims (short wavelength topog-
582
raphy is preserved during viscous relaxation) that stand 160-300 m above the surrounding
583
terrain. Figure 19 shows the post-extension deformation of the surface and lithosphere for
584
the relaxed topography. For intermediate and warm surface temperatures, the surface is
585
deformed into quasi-periodic ridges and troughs. This is especially true for the warmest
586
temperatures (Ts =120 K) in which plastic strain is distributed in numerous trough-like
587
features. The amplification of the surface deformation is quite limited: the total relief of the
588
final deformation is smaller after extension than before extension in the Ts =120 K simula-
589
tion. Further extension of the domain (the simulations shown here have been extended by
590
5%) results in similar surface deformation, although strain begins to localize more strongly
591
within individual troughs in the Ts =100 K simulation. These simulations illustrate that,
592
unsurprisingly, when topography is reduced by viscous relaxation before extension occurs,
593
subsequent groove terrain formation is more easily achieved. Tectonic resurfacing of impact
594
craters is likely enabled by concomitant viscous relaxation as the lithosphere begin to warm.
595
4.3.1
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Thermal effects and deep crater topography
Because Tekton does not include thermodynamics, the simulations described in section
597
4.3 must be interpreted carefully. The simulations shown here use a laterally constant sur-
598
face temperature. Thus, beneath the crater the distance between the constant-temperature
599
surface and a “flat” isotherm at depth is reduced compared to adjacent regions. The litho-
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spheric thermal gradient is therefore greater beneath the crater than in the surrounding region. This effect is negligible for small amplitude topography, but beneath a ∼1 km-deep
602
crater isotherms in our simulations are compressed by 20-50% (depending on the imposed
603
heat flux). Qualitatively, the increase is realistic (Seiferlin, 2009), but because we do not
604
actually solve the thermodynamics, it is only an approximation. 25
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Thermal effects are exacerbated as the simulation proceeds and extensional necking oc-
606
curs. Because isotherms (technically iso-viscous contours) are advected with the deforming
607
material, warm, low-viscosity material rises into the necked regions beneath the crater (e.g.,
608
Fig. 16). As long as the lithosphere remains several kilometers thick, the thermal diffusion
609
timescale is much longer than the simulation timescale and the advection of warm material
610
is realistic (i.e., the material would remain warm over the timescale simulated). For a litho-
611
spheric thickness of 1 km, however, the timescales for thermal diffusion and extension are
612
similar. In those cases (the simulation in Fig. 17 approaches this2 ) the material rising into
613
the necked region should cool, increase in viscosity, and act to stabilize the necked region.
614
Neglecting these thermal effects enhances the rate at which strain is localized during exten-
615
sion. This effect should be most significant when heat fluxes are large and the lithosphere
616
becomes very thin beneath the crater.
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To further investigate these effects, we performed a suite of simulations that initialized
618
the temperature structure such that the heat flow was truly uniform (i.e., isotherms fol-
619
lowed the surface topography). In these simulations strain localization is, in fact, retarded,
620
and while the majority of the strain is accommodated within the crater, small amounts of
621
extensional strain is also partitioned quasi-periodically throughout the lithosphere. This pe-
622
riodic strain partitioning is insufficient to modify the surface, however, and the final surface
623
deformation, which is marked by a deep, isolated trough rather than periodic deformation,
624
is consistent with our nominal simulations. The primary difference between the results of
625
these simulations and our nominal simulations is the magnitude of the strain that is accom-
626
modated. For example, for conditions analogous to those shown in Fig. 17, a similar state
627
is reached in these simulations after 8-9% extension rather than 5% extension. Despite the
629
630
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similarity in surface deformation, it is notable that the boundary between the ice lithosphere and asthenosphere is much flatter than in our nominal cases. These simulations indicate that our basic results are qualitatively insensitive to thermodynamic effects, at least for the 2
Viscous relaxation in Fig. 17 is faster than thermal adjustment to steady state: 1% extension occurs in
3000 yrs, whereas the thermal diffusion time for the 2-km thick lithosphere is about twice as long.
26
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631
lithospheric thicknesses we have modeled.
632
4.4
Effect of ice shell properties
The simulations discussed above have explored a range of physical parameters, focused
634
primarily on the heat flux and surface temperature. In addition, the properties of the ice
635
shell are likely critical to understanding the formation of Ganymede’s grooved terrain. The
636
simulations described here assume a cohesion of 1 MPa, consistent with laboratory data
637
(Beeman et al., 1988). However, it’s possible that at geologic scales the effective strength of
638
an ice lithosphere is much lower. The formation of cycloids on Europa, for example, seem
639
to require a relatively weak ice shell (Rhoden and Hurford, 2013), and models of mobile lid
640
convection in an ice shell generally must assume a low yield stress (Barr, 2008; Han et al.,
641
2012). Former numerical models of groove formation had to assume a high cohesion (high
642
strength contrast with deeper warm ice) in order to produce significant amplitude growth
643
(Bland et al., 2007, 2010); however the introduction of more realistic non-associated plasticity
644
in recent models has removed this requirement (Bland and McKinnon, 2015).
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To assess how the assumed strength of the lithosphere affects groove formation in the
646
presence of large-amplitude initial topography, we repeated all of the simulations described
647
above using a cohesion of 100 kPa (one order of magnitude lower than our nominal model).
648
Figure 20 compares these low cohesion simulations to those that used our nominal value of
649
1 MPa for the case where dark terrain is used as the initial topography. In general, the
650
simulations that used a lower cohesion result in lower growth of the necking (or localizing)
651
instability. This also results in a reduction in the localization of strain within individual
653
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troughs. Simulations with cold and intermediate lithospheric temperatures (Ts =70 K and 100 K) still result in deep troughs that dominate the deformation. In contrast, the simula-
654
tion with a warm lithosphere (Ts =120 K) results in semi-periodic structures of relatively
655
consistent amplitude. This deformation is consistent with Ganymede’s grooves.
656
Critically, the groove-like deformation in this simulation (Fig. 20C) does not result from
657
substantial changes in the amplitude of the initial topography. With a warm surface temper27
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658
ature and weak brittle ice shell, instability growth is limited (the strength contrast between
659
the lithosphere and deeper ice is reduced). Growth rates are large enough for a “dominant”
660
wavelength to develop, but insufficient to produce large-amplitude structures. These simula-
661
tions suggest that a weaker ice shell might assist tectonic resurfacing of Ganymede, although
662
the cohesion assumed is relatively unimportant for the cold polar regions. Reducing the cohesion also does not have an appreciable effect on the tectonic resurfacing
664
of relatively fresh, deep craters, and the qualitative results described in section 4.3 hold
665
whether a cohesion of 1 MPa or 100 kPa is used. In these cases, the depth of the trough
666
that results from extension is reduced when a lower cohesion is used, but the difference is
667
not substantial enough to allow direct resurfacing. Even when high heat fluxes are used,
668
reducing the cohesion of the lithosphere does not enable periodic structures to form from
669
preexisting cratered terrain.
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In summary, assuming a low cohesion for Ganymede’s ice lithosphere does not further en-
671
able widespread tectonic resurfacing on Ganymede. However, a lower cohesion may prevent
672
strain from strongly localizing within a narrow trough. It therefore may play an impor-
673
tant role in resurfacing terrain that has already been “smoothed” by viscous relaxation or
674
cryovolcanism.
675
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The role of small-scale faulting
The tectonic resurfacing mechanism depends critically on the development of numerous
677
imbricated faults and subsequent rotation of fault blocks (Head et al., 1997). The block
678
rotation exposes brighter subsurface ice, and contributes to the complete erasure of preex-
680
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isting structures like crater rims. Our numerical simulations result in strong localization of plastic strain into narrow, linear, fault-like structures (see Bland and McKinnon, 2015,
681
for details). The width and spacing of these faults is limited, however, by the resolution
682
of our simulations, which in the examples shown here is 167 m. Any discrete, smaller-scale
683
faulting cannot be captured by our simulations. Despite this, fault-like slip along planes of
684
elements does occur, only limited by the resolution of the mesh (see discussion in Bland and 28
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McKinnon (2015). A full “test” of the tectonic resurfacing mechanism should include a more realistic im-
687
plementation of true fault-like behavior, perhaps by combining increased resolution with a
688
strain- or strain-rate-dependent reduction in brittle strength (e.g., Buck et al., 2005; Bland
689
et al., 2010). These concerns are somewhat mitigated, however, by physical analog mod-
690
els of the extension of ice lithospheres. As described above, these models provide much
691
insight into fault processes on Ganymede, and reproduce many of the fault geometries (in-
692
cluding rotation) observed (Sims et al., 2014). Despite the development of these geometries,
693
faulting and block rotation apparently does not erase preexisting impact crater topography
694
(Wyrick, 2012). These models are therefore in broad agreement with our numerical simula-
695
tions. The analog models, however, do not include viscous deformation, and it may be that
696
a combination of viscous flow that reduces long-wavelength topography (crater bowls), and
697
small-scale faulting and fracturing that removes short-wavelength topography (e.g., crater
698
rims), is necessary to completely resurface preexisting terrain. We therefore conclude that
699
our simulations may underestimate the degree to which short wavelength topography can
700
be disrupted by fracturing and faulting, but they provide a relatively realistic depiction of
701
lithospheric behavior at longer wavelengths.
702
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PT
Localization in three-dimensions
In our two-dimensional simulations, strain localizes relatively easily within topographic
704
lows or thin regions of the lithosphere. These are regions of high stress and thus increased
705
plastic (brittle) strain, which readily localizes via non-associated plasticity. As described
707
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above, this localization often results in isolated troughs rather than widespread deformation, and thus inhibits tectonic resurfacing. Strain localization in three-dimensions is likely more
708
complex. For example, the two-dimensional cross section of an impact crater is essentially
709
a trough, which easily localizes strain. In reality, a crater is an isolated depression, and
710
although it may be a locally thin region of the lithosphere, the regions adjacent to the crater
711
are not. Thus, whereas the crater may be a locus of brittle failure (see, e.g., Fig. 4), fail29
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ure must propagate laterally to form a continuous trough. Normal faults generally form by
713
linkage of smaller-scale fractures and faults (e.g., Peacock and Sanderson, 1991; Anders and
714
Schlische, 1994; Dawers and Anders, 1995; Mansfield and Cartwright, 2001; Wyrick et al.,
715
2011; Cartwright et al., 2016). If fault linkage is inhibited, periodic necking (a viscous insta-
716
bility) may dominate and prevent strain from localizing within a single crater. It is therefore
717
plausible that such strain localization is less efficient in three dimensions, more readily per-
718
mitting the development of periodic structures even when the preexisting topography is large.
719
How strain localizes in three-dimensions to produce grooves that are continuous along strike
720
for hundred of kilometers has not yet been addressed, and a complete understanding of the
721
resurfacing of Ganymede will not be achieved until the three-dimensional nature of groove
722
terrain formation is understood. Fully three-dimensional simulations (Bland and Wyrick,
723
2017) and more robust analog modeling (Wyrick et al., 2017) are warranted.
724
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A new scenario for resurfacing Ganymede Collectively, the simulations described in section 4 suggest several modifications may be
726
necessary to the prevailing picture of resurfacing on Ganymede. Our simulations with large-
727
amplitude initial topography, whether synthetically produced or derived from Ganymede’s
728
dark terrain, fail to produce distributed, periodic surface deformation. This is particularly
729
true when the preexisting surface includes impact craters hundreds of meters or kilometers
730
deep. Creating archetypical grooved terrain directly from Ganymede’s dark terrain therefore
731
appears challenging. Forming periodic ridges and troughs is much easier if the preexisting to-
732
pography is low-amplitude, either due to cryovolcanic resurfacing or viscous relaxation. This
734
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does not imply, however, that tectonic imbrication, block rotation, and pervasive fracturing does not play a critical role in disrupting older bright terrains. There is good observational
735
evidence that such processes occur (Head et al., 1997; Prockter et al., 2000; Pappalardo and
736
Collins, 2005, and see Fig. 3). Rather, we suggest that tectonic resurfacing is a critical
737
resurfacing process on Ganymede, but is likely enabled by viscous relaxation either before or
30
ACCEPTED MANUSCRIPT
738
during extension. As noted above, the heat fluxes commonly associated with the formation
739
of grooved terrain will necessarily result in viscous relaxation of long-wavelength topography
740
(e.g., craters). Based on these results, we propose that Ganymede’s resurfacing has occurred in several
742
stages. Models of grooved terrain formation (Dombard and McKinnon, 2001; Bland and
743
Showman, 2007), viscous relaxation of impact craters (Bland et al., 2017), and Ganymede’s
744
interior evolution (Showman et al., 1997; Bland et al., 2009) all indicate that the global expan-
745
sion associated with resurfacing was accompanied by substantial warming of the lithosphere.
746
This warming may have been associated with incipient mobile lid convection (Hammond and
747
Barr, 2014), resulting in a non-uniform distribution of heat flux and surface strain. That is,
748
regions of high heat flux and high strain are correlated and localized (Hammond and Barr,
749
2014). Where heat fluxes were highest, long wavelength surface topography – principally
750
impact craters – likely underwent rapid viscous relaxation, reducing the amplitude of the
751
pre-existing topography. The subsequent onset of extensional strain within these regions
752
of high-heat flow resulted in the formation of the periodic, distributed deformation associ-
753
ated with the grooved terrain. Where heat flow was especially highly localized, complete
754
separation of the thin lithosphere might have occurred, resulting in band formation (e.g.,
755
Head et al., 2002). Differences in preexisting dark-terrain topography (e.g., predominant
756
topographic wavelengths – affecting viscous relaxation rates) may have also contributed to
757
differences in the style of dark-terrain breakup.
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Away from the regions of localized extension and high heat fluxes, the dark terrain
759
would remain intact. These regions might correspond to convective down-wellings in the
760
mobile-lid model of Hammond and Barr (2014). Between these more quiescent regions and
762
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758
the highly deforming regions (e.g., around the edges of a convective plume) transitional geologic units would be expected to develop with a variety of morphologies. Regions that
763
experienced relatively high strains, but comparatively low heat fluxes might develop heavily
764
tectonized but marginally intact impact craters, such as those shown in Fig. 3B and D,
765
and the simulation shown in Fig. 16. Unlike the now-gone craters that might have existed
31
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before bright terrain formation, these impact craters were preserved (though disrupted)
767
because heat fluxes were insufficient (or too short lived) to permit viscous relaxation before
768
or during extension. Extensional strain localized within these craters, rather than producing
769
the distributed strain patterns (and surface brighting) associated with the grooved terrain.
770
Where only moderate surface strain occurred, tectonism might have proceeded without fully
771
disrupting the dark surface lag deposits to produce surface brightening, resulting in the
772
formation of dark lineated terrains. In contrast, where surface strains were low but heat
773
fluxes were elevated, widespread viscous relaxation would be expected without tectonism.
774
Such widespread viscous relaxation is observed in regions such as northern Marius Regio
775
(Singer et al., 2017), which is situated adjacent to expansive regions of grooved and smooth
776
bright terrain.
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The scenario described above depends only upon regional differences in heat flow and
778
surface strain. Mobile lid convection, as suggested by Hammond and Barr (2014), is one
779
mechanism to achieve such differences, but is not explicitly required. Mobile lid convection
780
implies large surface strains: extensional in the bright terrain and contractional in the dark
781
terrain. The former are not required by our simulations of groove formation, and little, if
782
any, evidence is observed for the latter. We do not dismiss the possibility of mobile lid
783
convection, but the mechanism, and its implications for Ganymede’s resurfacing, require
784
further investigation (e.g., with convection models that include plastic rheology).
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The above discussion does not preclude a significant role for cryovolcanism during resur-
786
facing. The high heat flow and extension would have been conducive to the production of
787
melt, which could have been locally driven to the surface by exsolved gases (Crawford and
788
Stevenson, 1988) or topographic gradients (Showman et al., 2004). This is particularly true
790
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789
CE
785
if Ganymede’s ice shell was thin during the epoch of resurfacing (Bland et al., 2009). Cryovolcanism could have occurred at any point during the resurfacing process. If (or where)
791
it proceeded extension, it would have provided a bright, “clean canvas” for the formation of
792
periodic ridges and troughs (as demonstrated by the simulations shown in Fig. 14). This
793
might have been the case for regions such as Bubastis Sulcus, where the swaths of grooved
32
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terrain are broad, the ridges and troughs are both high-amplitude and strongly periodic,
795
evidence of embayment by smooth material is observed (Allison and Clifford, 1987), and the
796
cold temperatures make resurfacing by tectonism alone difficult even if viscous relaxation
797
occurred. In these regions, the tectonism that followed cryovolcanic resurfacing may have
798
erased most evidence of vents. In contrast, if (or where) cryovolcanism occurred either after
799
extension was complete, or where surface strain was limited, smooth bright terrain would
800
result. There, resurfacing would have occurred predominately by cryovolcanism alone, ei-
801
ther by covering the recently formed grooved swath in the former case, or low-lying dark
802
terrain in the latter. In these regions, we expect vent structures to be preserved, such as the
803
caldera-like features in the Mumma Sulci and elsewhere (Schenk et al., 2001).
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This discussion also does not preclude a significant role for band formation as an agent
805
of resurfacing. Although not a focus of this paper, bands on Ganymede resemble pull-apart
806
bands on Europa (Prockter et al., 2002; Prockter and Patterson, 2009), and formation of
807
relatively smooth terrain during rifting and separation of preexisting dark and grooved ter-
808
rain blocks (e.g., Fig. 4) would clearly provide the subdued topography that would allow
809
full development of ridges and troughs (i.e., grooves) via extensional instability (Sec. 4.2).
810
Bands form with subdued tectonic or cryovolcanic fabrics along strike to begin with, but
811
high-amplitude grooves (Tiamat Sulcus, Fig. 1C, may be an example) as well as complex
812
grooved domain patterns (e.g., Uruk Sulcus, (Golombek and Allison, 1981)) require addi-
813
tional extension.
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804
In summary, resurfacing on Ganymede was likely the result of a complex interplay be-
815
tween tectonism, viscous relaxation, band formation, and cryovolcanism. In broad terms,
816
each terrain type observed on Ganymede may simply reflect which process locally dominated
818
AC
817
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814
the evolution, with the dominant process determined by local heat flux and surface strain. Ganymede’s dark terrain clearly experienced the lowest heat fluxes and limited strain. Tec-
819
tonism and evidence for high heat fluxes there date to an early epoch of Ganymede’s history
820
(e.g., Prockter et al., 1998). On the other end of the spectrum, the bright grooved ter-
821
rain likely experienced heat fluxes high enough to viscously relax preexisting impact craters,
33
ACCEPTED MANUSCRIPT
enabling concomitant or subsequent extension to result in broadly distributed lithospheric
823
deformation and tectonic resurfacing. Between these extremes, the relative amount of strain
824
and heating resulted in dark lineated terrain, localized tectonic disruption of craters, and
825
viscous relaxation without tectonism. Throughout the process, cryovolcanism both enabled
826
groove terrain formation, and resurfaced both dark terrain and newly formed grooved swaths.
827
The end result is the complex patchwork of bright and dark, tectonized and smooth, old and
828
young terrains observed on Ganymede today. Despite the new insight provided by these sim-
829
ulations, the relative importance of tectonic resurfacing, cryovolcanism, and band formation
830
in resurfacing Ganymede will remain an open question until new data, including imaging,
831
altimetry, and radar sounding are acquired (e.g., by ESA’s JUICE mission).
832
Acknowledgments
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This work was supported by NASA’s Outer Planets research program (NNH14AY69I to
834
MTB) and NASA’s Planetary Geology and Geophysics program (NNX11AP16G to WBM).
835
DTMs were generously provided by Paul Schenk. Comments from Chris Okubo, Francis
836
Nimmo, Geoff Collins, and an anonymous reviewer strengthened and clarified this work.
837
Any use of trade, firm, or product names is for descriptive purposes only and does not imply
838
endorsement by the U.S. Government.
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Figure 1: Several of the basic terrain types identified on Ganymede. A. Dark terrain in Nicholson Regio. B. Dark lineated terrain near Harpagia Sulcus. C. A swath of bright
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grooved terrain (Tiamat Sulcus) disrupting the dark terrain of Marius Regio. D. Bright smooth terrains of Nippur Sulcus and Elam Sulci. A and B after Patterson et al. (2010),
which describes these and other terrain types in detail.
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Figure 2: Examples of possible cryovolcanic resurfacing on Ganymede. A. Voyager 2 mosaic
of a portion of Bubastis Sulci (near the south pole) showing smooth bright terrain interspersed with archetypal grooved terrain. Portions of the smooth material appears to embay adjacent ridges and troughs (white arrows). B. Portion of Sippar Sulcus showing a lane of
smooth material that embays adjacent reticulate terrain (white arrows). After Schenk et al. (2001), who also showed that the smooth material generally stands lower than adjacent terrain.
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Figure 3: Examples of possible tectonic resurfacing on Ganymede. A. The intersection of bright grooved terrain in Nippur Sulcus and Philus Sulcus, dark terrain in Marius Regio,
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and smooth terrain in Elam Sulci. The edges of both the dark and smooth terrain appear to be disrupted by imbricated faulting. An enlarged view of such imbrication is shown in B. C. A disrupted crater in Nicholson Regio (lower left). Whereas the crater is still obvious, its center (including its rim) are completely disrupted by a set of parallel, closely spaced fractures. If the bright scarps are interpreted as normal faults they imply the fracture set is down-dropped by several hundred meters relative to the crater floor. D. A pervasively faulted and fractured crater in Nicholson Regio (17 km in diameter, 9◦ N, 18.5◦ E). Only the bright crater rim is visible (white arrows). The image location is indicated in Fig. 4. C 48 and D are modified from Pappalardo and Collins (2005).
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Figure 4: Galileo image mosaic of Arbela Sulcus. Head et al. (2002) suggest Arbela (the north-south trending lane of smooth material) formed as a Europa-like band, involving complete separation of the lithosphere and emplacement of warm, clean ice from below. The white box indicates the location of Fig. 3D.
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Figure 5: Comparison of the initial and final surface deformation from our “successful” model
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(A and B, respectively, with Ts =70 K, F =100 mW m−2 , ε˙ =10−13 s−1 , 10% extension), and typical dark terrain and grooved terrain topography (C and D, respectively). The
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enlarged view) is inconsistent with (not a good match to) the dark terrain (C).
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Figure 6: The surface deformation (right column) that results from extension of a model ice lithosphere initialized with topography of varying initial amplitude (left column). Each simulation used Ts =100 K, F =100 mW m−2 , a strain rate of 10−13 s−1 , and a cohesion of 1 MPa. The form of the initial topography used is identical in each case, only the total amplitude of the relief is changed. From top to bottom: 1 m, 10 m, 25 m, 50 m, 100 m, 150 m, 200 m. Note the difference in scale between left and right columns.
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Figure 7: Power spectrum of the final deformation after 10% extension produced by simu-
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lations with initial topographic relief of 1 m (dark blue), 25 m (light blue), 100 m, (green), and 200 m (red) as labeled (simulations are those shown in Fig. 6). The black curve shows
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the spectrum of the initial topography, which is also shown in the inset for clarity. Note that spectral resolution decreases with increasing wavelength (power at long wavelengths becomes “smeared” out).
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Figure 8: Illustration of the differences in the development of surface deformation for two identical simulations (Ts =100 K, F =100 mW m−2 ) with different initial topographic relief
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(25 m in A and C; 200 m in B and D). A and B show the surface deformation as a function of strain. The top curve is the initial topography and each subsequent curve is
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shown at increments of 1% extension. The red curve indicates 10% extension. C and D show the distribution of strain (lower plot) and deformation of the surface (upper plot) at 10% extension (identical to red curves in A and B).
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Figure 9: Comparison of the surface deformation produced by simulations with initial topographic relief of 25 m (left column, initial topography shown in A) and 150 m (right
column, initial topography shown in B). The pairs of simulations used identical parameters (except where noted here, other parameters were identical to those used in Fig. 6): C and
D, Ts =70 K; E and F, Ts =120 K; G and H, Ts =70 K and F =150 mW m−2 ; I and J a strain rate of 10−14 s−1 . All simulations are shown after 10% extension except F, which is shown after 9%. 54
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Figure 10: Digital terrain model (see text for details) of the northern portion of Marius
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Regio. The topographic profiles illustrate typical dark terrain, but intentionally avoid deep, fresh craters. Portions of profile 1 and profile 3 were used in the finite element simulations
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described here. In the DTM, blue is low and red is high. The total dynamic range is ∼1 km.
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Figure 11: The initial topography (top), final topography (middle), and final lithospheric
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topography shown in profile 1 (A) and profile 3 (B) of Fig. 10.
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Figure 12: The effect of changing the surface temperature and heat flux on the resulting surface deformation for simulations initialized with dark terrain topography (top panel -
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profile 1 of Fig. 10). Each curve shows the deformation after 10% extension, and are offset for clarity. Red: Ts = 70 K, F = 100 mW m−2 ; gold: Ts = 100 K, F = 70 mW m−2 ;
teal: Ts = 100 K, F = 100 mW m−2 (identical to the simulation shown in Fig. 11A); blue: Ts = 100 K, F = 150 mW m−2 ; violet: Ts = 120 K, F = 100 mW m−2 .
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Figure 13: DTM and topographic profiles of Ganymede’s smooth terrain. The DTM is the same as that shown in Fig. 10, but profiles were extracted from Nippur Sulcus and Elam Sulci. Note the difference in vertical scale between the profiles shown here and those in Fig. 10.
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Figure 14: Forming grooves from smooth initial topography. A. The initial topography (a portion of profile 1 in Fig. 13, but with the long wavelength slope removed), B. Ts =100 K,
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Figure 15: DTM (as in Fig. 10) showing the locations where crater topography was extracted for both the fresh and viscously relaxed cases. The simulations shown in Figs. 16, 17, and 18 used a portion of profile c1. The simulations shown in Fig. 19 used a portion of profile r3.
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Figure 16: The initial topography (top), final topography (middle), and final lithospheric deformation (bottom) for a simulations with a relatively cold and thick lithosphere (Ts = 70 K,
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Figure 17: The topography (top) and lithospheric deformation (bottom) for a simulation
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with a relatively warm lithosphere (Ts = 100 K, and F = 100 mW m−2 ) after 0% (A), 1% (B), 3% (C), and 5% (D) extension. The initial topography was derived from profile c1 in
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Fig. 15, and is the same as that in Fig. 16. After 1% extension most of the initial crater topography is removed by viscous relaxation, but a residual zone of weakened lithosphere
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Figure 18: The initial topography (top), final topography (middle), and final lithospheric
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deformation (bottom) for simulations with a warm and thin lithosphere. A. Ts = 100 K, and F = 150 mW m−2 after 2% extension. B. As in A but after 8% extension. C. Ts = 120 K,
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and F = 150 mW m−2 after 1% extension. D. As in C but after 5% extension. In all cases, the initial topography was derived from profile c1 in Fig. 15 and is the same as that in Fig. 16 and Fig. 17A. Note the rapid removal of crater topography in A and C.
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Figure 19: The initial topography (top), final topography (middle), and final lithospheric deformation (bottom) for simulations initialized with topography derived from a viscously
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Figure 20: Comparison of the final surface deformation after 10% extension for pairs of simulations of dark terrain extension that used a cohesion of 1 MPa (black curves) and 100 kPa (grey curves), but were otherwise identical. A. Ts = 70 K, and F = 150 mW m−2 ;
B. Ts = 100 K, and F = 100 mW m−2 ; C. Ts = 120 K, and F = 100 mW m−2 . Compare with Fig. 11.
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