Magma ascent pathways associated with large mountains on Io

Icarus 272 (2016) 246–257

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Magma ascent pathways associated with large mountains on Io Patrick J. McGovern a,∗, Michelle R. Kirchoff b, Oliver L. White c, Paul M. Schenk a a

Lunar and Planetary Institute, Universities Space Research Association, 3600 Bay Area Blvd., Houston, TX 77058, United States Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302, United States c NASA Ames Research Center, MS 245-3, Moffett Field, CA 94035-1000, United States b

a r t i c l e

i n f o

Article history: Received 1 July 2015 Revised 2 February 2016 Accepted 23 February 2016 Available online 5 March 2016 Keywords: Io Volcanism Tectonics Satellites, surfaces Jupiter, satellites

a b s t r a c t While Jupiter’s moon Io is the most volcanically active body in the Solar System, the largest mountains seen on Io are created by tectonic forces rather than volcanic construction. Pervasive compression, primarily brought about by subsidence induced by sustained volcanic resurfacing, creates the mountains, but at the same time inhibits magma ascent in vertical conduits (dikes). We superpose stress solutions for subsidence, along with thermal stress, (both from the “crustal conveyor belt” process of resurfacing) in Io’s lithosphere with stresses from Io mountain-sized loads (in a shallow spherical shell solution) in order to evaluate magma ascent pathways. We use stress orientation (least compressive stress horizontal) and stress gradient (compression decreasing upwards) criteria to identify ascent pathways through the lithosphere. There are several configurations for which viable ascent paths transit nearly the entire lithosphere, arriving at the base of the mountain, where magma can be transported through thrust faults or perhaps thermally eroded flank sections. The latter is consistent with observations of some Io paterae in close contact with mountains. © 2016 Elsevier Inc. All rights reserved.

1. Introduction Jupiter’s moon Io is the most volcanically active planetary body in the Solar System, and the only one other than Earth known to be currently erupting silicate magmas (e.g., Lopes and Spencer, 2007; McEwen et al., 2004). Tidal heating of Io’s interior, driven by Jupiter’s gravitational field and the eccentricity of Io’s orbit generates a magmatic flux sufficient to produce the observed hotpsots and volcanic plumes and remove all observable trace of resolvable impact-related structures (e.g., Lopes and Spencer, 2007; McEwen et al., 2004), and perhaps even generate a global magma ocean (Khurana et al., 2011). Thermal observations of Io’s hotspots yield very high temperatures consistent with mafic to ultramafic volcanism (e.g., Carr, 1986; Johnson et al., 1988; McEwen et al., 1998; McEwen et al., 20 0 0; Williams et al., 20 0 0). While these indications of volcanic vigor might conjure visions of a planet studded with grand basaltic edifices like the Tharsis Montes of Mars, in fact most of Io’s volcanic sources are associated with very low-relief paterae or shield structures; only a handful of conical volcanic edifices (of relatively modest width) have been detected (e.g., Schenk et al., 2001; Jaeger et al., 2003; Turtle et al., 2007). Io does indeed have mountains (topographic features with relief greater than a kilometer or two), as unveiled by the close ∗

Corresponding author. Tel.: +1 2814862187; fax: +1 2814862162. E-mail address: [email protected] (P.J. McGovern).

http://dx.doi.org/10.1016/j.icarus.2016.02.035 0019-1035/© 2016 Elsevier Inc. All rights reserved.

encounters of the Voyager and Galileo missions. However, most of them have a characteristic tilted-block morphology that is suggestive of a tectonic (compressional) origin (e.g., Schenk and Bulmer, 1998; Carr et al., 1998; Schenk et al., 2001; Turtle et al., 2001; McEwen et al., 2004). To explain the observed structure of Io’s mountains in the context of a body with high resurfacing rate, Schenk and Bulmer (1998) proposed that burial-induced subsidence would over time produce a compressive stress state due to the reduction in volume with depth inside a spherical shell. Thus, Io’s lithosphere may be essentially a resurfacing “conveyor belt”, generating compression at depth. We perceive a strong sense of contradiction in these characterizations of Io’s behavior. The idea of a compression-dominated lithosphere allowing vigorous ascent of magma through it confounds traditional notions of intrusive ascent pathways (e.g., Anderson, 1951): compression favors trapping of magmas in subhorizontal sills rather than ascent in vertical dikes. Looked at from the perspective of mountain building, this contradiction can be turned on its head: on the most volcanic planetary body of all, the most prominent mountains are produced tectonically and not as volcanically constructed edifices. And yet Io churns along, indifferent to our struggles to understand its enigmatic history. Here we explore the paradox of copious volcanism on a compression-dominated planet via quantitative modeling of the evolution of stresses in and deformation of Io’s lithosphere from two sources: mountain loading and crustal recycling. Model

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inputs for mountain stress calculations are informed by Digital Terrain Models (DTMs) produced via stereogrammetry techniques. The model results constrain scenarios for mountain building and associated volcanic features on Io, while also yielding estimates of the thickness of the crust/lithosphere that are most consistent with the proposed crustal resurfacing/recycling scheme. 2. Measuring heights of mountains on Io Our knowledge of Io’s mountains comes from spacecraft imagery (Voyager and Galileo). Mountains on Io tend to be spatially isolated and are not part of broad-scale mountain belts as seen on Earth and Venus. Morphology of mountains can range from relatively flat, low plateaus and mesas to asymmetric ridges similar to flatirons on Earth to tall peaks. Their heights can be as low as 1–2 km (the lower limit for the classification) to ∼18 km for Boösaule Montes, with an average height of ∼6 km for all identified mountains. Their widths and lengths can range from ∼13 km to ∼570 km, with averages of ∼80 and 160 km, respectively. When combined, these dimensions indicate that about 3% of Io’s surface is covered by mountains (Schenk et al., 2001; McEwen et al., 2004). The mountains have been shown to be anticorrelated at low harmonic degree on a planetary scale with the volcanic sources (Kirchoff et al., 2011; Schenk et al., 2001; McKinnon et al., 2001; Hamilton et al., 2013), although at smaller scales, a fraction (∼40%) of Io mountains have paterae on their margins (Turtle et al., 2001; Jaeger et al., 2003). Our primary tools to characterize mountain shapes and morphology in detail are regional and high-resolution stereo image pairs. We use digital stereogrammetry to produce 3-dimensional topographic maps, or Digital Terrain Models (DTMs) of the surface (e.g., Schenk et al., 2004; Schenk and Bulmer, 1998; White et al., 2014). DTM generation involves refinement of stereo mapping parameters, including scene matching spot size, best-fit equation order, and other parameters designed to optimize the stereo matching procedure. This process is complex on Io due to ongoing volcanism, non-uniform photometric function and the necessity of sometimes using different filter images in a given stereo pair, all of which can potentially change surface feature appearance between exposures. In addition, Io stereo DTMs typically include a significant amount of noisy patches due to the lack of surface contrast, which most commonly exist in the featureless plains interstitial to volcanic centers and mountain ranges. Sunlit portions of mountain ranges themselves are typically less affected by noise as they possess high albedo contrast and strong parallax due to their high relief; shadowed portions of mountain ranges in either image of the stereo pair, however, will create noise in the resulting DTM. Areas of noise will be removed using our noise removal criteria, including height error, pixel shift, correlation coefficient and standard threshold noise filters; if necessary, noise can also be removed manually. The maximum lateral resolution attained by a stereo DTM is governed by the lowest resolution image in the original stereo pair – lateral resolutions of our DTMs typically achieve several hundred meters to more than a kilometer per pixel. The vertical precision of stereo DTMs is a function of the lateral resolution and viewing angles of the separate images in each stereo pair – vertical precisions of our DTMs typically achieve a few hundred to several hundred meters. Finally, our stereo DTMs are controlled using Galileo limb profiles in order that they fit the triaxial ellipsoid of Io as defined by the limb profiles (Thomas et al., 1998). The reader is directed to White et al. (2014) for further details of the stereo and controlling processes. Boösaule Mons (Fig. 1) is the tallest known mountain on Io, reaching about 18 km above the Io datum. The maximum relief on the topographic profiles in Fig. 1b is more than 20 km. The lateral extent of this mountain is 160–180 km. The summit is not located

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Table 1 Locations of mountains and associated paterae on Io, with distances between them. Mountain

Patera

Distance (km)∗

Danube Planum 22.6ºS, 258.1ºW Euboea Montes 48.0ºS, 335.8ºW Euxine Mons 26.3ºN, 126.4ºW Gish Bar Mons 18.5ºN, 89.0ºW

Pele 18.7ºS, 255.3ºW Creidne Patera 53.3ºS, 342.6ºW Unnamed patera 23.8ºN, 125.7ºW Gish Bar Patera 16.2ºN, 90.3ºW Estan Patera 21.5ºN, 87.6ºW Hi’iaka Patera 3.6ºS, 79.5ºW Monan Patera 19.8ºN, 104.8ºW Ah Peku Patera 10.4ºN, 107.0ºW Unnamed patera 63.7ºN, 244.3ºW Ot Patera 1.1ºS, 217.4ºW Rata Patera 35.6ºS, 199.7ºW Tohil Patera 26.3ºS, 158.1ºW Radegast Patera 27.8ºS, 160.0ºW Tvashtar Paterae 62.8ºN, 123.5ºW Zal Patera 40.1ºN, 47.5ºW Nyambe Patera 0.3ºN, 343.2ºW Ülgen Patera 40.7ºS, 287.2ºW Savitr Patera 48.5ºN, 123.2ºW Carancho Patera 1.5ºN, 317.3ºW Tol-Ava Patera 1.8ºN, 322.0ºW

147

Hi’iaka Montes 4.7ºS, 82.0ºW Monan Mons 15.5ºN, 104.2ºW

Nemea Planum 72.3ºS, 265.8ºW Ot Mons 4.3ºN, 215.7ºW Rata Mons 36.4ºS, 201.3ºW Tohil Mons 28.4ºS, 161.6ºW

Tvashtar Mensae 61.6ºN, 120.0ºW Zal Montes 38.4ºN, 77.2ºW Unnamed mons 1.6ºN, 341.3ºW Unnamed mons 38.8ºS, 285.0ºW Unnamed mons 46.0ºN, 126.1ºW Unnamed mons 1.0ºS, 317.3ºW

∗

219 86 84 104 87 138 186 396 180 49 121 49 64 85 72 82 103 81 175

Between center coordinates given for each feature.

at the center of the elevated region but rather is displaced toward the south. Thus, the southern flank is the steepest flank, and it is cut by a topographic discontinuity that may be a flank failure. Tohil Mons (Fig. 2) has a peak elevation of about 10 km above the datum and 11 km maximum relief, with a lateral extent of more than 300 km. The highest elevations form an arcuate ridge surrounding a central depression. A sector of low plains (−1 to −2 km elevation) is embedded in the northeast sector of the edifice, and this sector includes a dark patera (Radegast Patera). Euboea Mons (Fig. 3) has a peak elevation of more than 9 km above the datum and more than 11 km maximum relief. The main edifice is about 275 km in lateral extent, although there are several adjacent mountains to the northwest and northeast. There are also two volcanic shields with central calderas and radiating flows to the northeast of Euboea Mons: at least one of them has positive relief (see profile A–B between 300 and 400 km distance in Fig. 3b). A dark patera (Creidne Patera) lies adjacent to the northwest flank of Euboea Mons. Other mountains on Io also have low-lying paterae in close proximity: examples are listed in Table 1. 3. Magma ascent criteria Our best attempts to understand the crustal/lithospheric dynamics of a planetary body like Io lead to an apparent paradox: pervasive extrusive volcanism at the surface produces a vertical subsidence “conveyor belt” that via mechanical and pos-

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Fig. 1. (a) Digital Terrain Model (DTM) for Boösaule Mons. Elevations are denoted by colors, gray where topography is not resolved. Lateral DTM theoretical resolution is 0.637 km/pixel; vertical DTM precision is 1.175 km. (b) Topographic profiles of Boösaule Mons, corresponding to tracks marked by red solid lines in (a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

sible thermal effects generates a state of horizontal compression in the lithosphere (Schenk and Bulmer, 1998; Kirchoff and McKinnon, 2009; Turtle et al., 2001; Schenk et al., 2001; Jaeger et al., 2003; McEwen et al., 2004). But the well-known criterion of Anderson (1951) indicates that magmatic intrusions will propagate perpendicular to the least compressive principal stress σ 3 ; since the compression-dominated stress state on Io would produce vertical σ 3 , intrusion planes would tend to be horizontal (i.e., sills) rather than the vertical intrusions (dikes) that would be expected to carry voluminous surface volcanism. Thus, when Anderson’s rule is applied as a magma ascent criterion, the most volcanic body in the Solar System fails! We will seek to resolve this paradox, but things will get worse before they get better: there is a second criterion for magma ascent that complicates matters (but that also has a significant and somewhat counter-intuitive “silver lining”). We describe both criteria below, with an ultimate goal of defining where magma ascent might be favored on Io. We employ two stress-based magma ascent criteria to assess potential magmatic pathways through Io’s crust/lithosphere. The first ascent criterion simply states Anderson’s (1951) finding that intrusions tend to form perpendicular to the least compressive principal stress. This “stress orientation” criterion is

is based on pressure balance in vertical dikes. Rubin (1995) summarizes three sources of pressure available to drive magma flow in vertical dikes (his Eq. (7), modified to account for our “extension positive, z positive upward” sign conventions):

σy + σlocal > 0,

where we have incorporated the local excess magma pressure gradient and buoyancy terms into the term PG, and the stress gradient criterion for ascent becomes dσ y /dz + PG > 0. In general, the dominant stress gradient term must be positive for magma ascent, i.e., differential compression must decrease with height; otherwise, by Eq. (4) (neglecting PG for the moment), magma would be forced downward rather than upward.

(1)

where σ y is the differential stress, defined as the difference of horizontal normal stress and vertical normal stress (σ y – σ z ; this is termed the “tectonic” stress by Rubin (1995)), and σ local is a local variation in stress due to factors such as buoyancy and magma chamber overpressure. A second, less well-known ascent criterion

(dP/dz + ρm g) = dσy /dz + dP/dz − ρ g,

(2)

where P is magma pressure, ρ m is magma density, ρ is host rock density ρ r minus magma density ρ m , and P is local excess magma pressure,. The left-hand term in Eq. (2) is a factor in the relation for mean magma flow velocity uz given laminar flow (Eq. (4) of Rubin (1995)):

uz = (1/3η )w2 (dP/dz + ρm g),

(3)

where η is the magma viscosity and w is the dike half-thickness. For z defined positive upward (note: this choice makes g negative), the quantity dP/dz + ρ m g must be positive to obtain magma ascent (flow in the positive z direction). In practice, when flexure is significant (see below) the vertical gradient of tectonic stress (abbreviated VGTS) term dσ y /dz dominates the pressure balance. Substituting Eq. (2) into Eq. (3), we get

uz = (1/3η )w2 (dσy /dz + P G ),

(4)

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Fig. 2. (a) Digital Terrain Model (DTM) for Tohil Mons. Elevations are denoted by colors, gray where topography is not resolved. Lateral DTM theoretical resolution is 0.184– 1.485 km/pixel; vertical DTM precision is 0.061–0.269 km. (b) Topographic profiles of Tohil Mons, corresponding to tracks marked by red solid lines in (a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

We assume that magma will not ascend in a given location unless both of the criteria outlined above are satisfied. Failing to satisfy the stress orientation criterion will tend to result in lateral rather than vertical magma transport, in sills rather than dikes. Failing to satisfy the stress gradient criterion will result in “squeezing off” of potential dikes due to increased compression in their upper regions. 4. Stress calculations We can apply the two magma ascent criteria to models of stress as a function of depth and lateral position in Io’s lithosphere to predict where magma may be more likely to erupt or to stall. We consider superposition of two sources of stress states likely to be prevalent in Io’s lithosphere: loading-related stress from the emplacement of mountains on the lithosphere (which itself is composed of two components, flexural and membrane), and stress due to the “conveyor belt” of crustal recycling. Large loads such as mountains and volcanoes provide a primary source of stress in planetary lithospheres. The vertical and lateral distributions of such stresses depend on variables such as the size and shape of the load and the stiffness and thickness of the lithosphere. These stress states from various forms of lithospheric loading interact with the conditions outlined in Eqs. (1)–( 4) to exert strong control on the ascent of magmas through the lithosphere (e.g., Litherland and McGovern, 2009; Buz and McGovern, 2010; McGovern et al., 2011; McGovern and Litherland 2010, 2011). Lithospheric flexure (the “bending” response) is perhaps the most

familiar type of loading, occurring for regional-scale loads. Flexure solutions are commonly used to interpret topographic and bathymetric profiles and tectonic signatures around rift zones, subduction zones, and ocean island volcanoes on Earth (e.g., Watts, 2001) and similar features on other planets (e.g., Johnson and Sandwell, 1994; McGovern and Solomon, 1997). Flexure creates a characteristic dipole response beneath a volcanic load, for example, with compression in the upper lithosphere and extension in the lower. This response creates a vertical gradient in tectonic stress whose magnitude and sign varies as a function of distance from the load center. These stresses create zones with characteristic tectonic and magmatic responses as functions of horizontal and vertical location, as discussed in Fig. 10 of Jaeger et al. (2003) for Io. A second kind of loading becomes important as the characteristic width of the load approaches a significant fraction of the planetary radius. The membrane (or “stretching”) response induced by planetary curvature is important for regional to large-scale loads such as rises of various scales on Mars, e.g. the Elysium and Tharsis Rises (Turcotte et al., 1981), and of broad mountains on a small planetary body like Io (Turtle et al., 2001). In contrast to flexure, membrane support gives a uniform response as a function of depth: downward deflections create compression and upward ones create extension. The combination of loading modes can create very favored zones of ascent around large loads, because of interaction of favorable flexural stress gradient and membrane extensional bias, e.g., around large mare-filled impact basins on the Moon (McGovern and Litherland, 2010, 2011).

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Fig. 3. (a) Digital Terrain Model (DTM) for Euboea Mons. Elevations are denoted by colors, gray where topography is not resolved. Lateral DTM theoretical resolution is 1.361 km/pixel; Vertical DTM precision is 0.213 km. (b) Topographic profiles of Euboea Mons, corresponding to tracks marked by red solid lines in (a). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

We calculate stresses from mountain loading using the shallow spherical shell formulation of Brotchie (1971), as described in Solomon and Head (1980) and using the correction of Freed et al. (2001). This formulation accounts for both flexural and membrane responses to loading. We calculate two components of horizontal normal stress, the radial stress and the out-of-plane, or “hoop” stress. These components calculated by this method are those in excess of the lithostatic gradient, and therefore fall under the category of “tectonic” stress as defined by Rubin (1995). We choose values for mountain load dimensions radius rm and height hm within the range of values found for Io mountains by the DTM-generating techniques described above (Figs. 1–3). The main parameter controlling the response to loading is the thickness of the elastic lithosphere Te . We calculate stresses in Io’s lithosphere that result from crustal recycling using the formulation of Kirchoff and McKinnon (2009), accounting for thermal, Poisson, and subsidence stresses as a function of depth in the crust. There is one important difference: we assume laterally unconstrained material, i.e., a post-faulting stress state presuming stress release on existing faults (see also Kirchoff and McKinnon, 2006). In practice, the difference amounts to a rightward shift of the Kirchoff and McKinnon (2009) curves such that the upper lithosphere is in extension. We focus on the linear rheology models (power-law exponent n = 1) to allow mathematically legal superposition with the lithospheric loading models described above. These crustal recycling stresses are also “tectonic” by the definition of Rubin (1995). The model parameter β sets the fraction of the total subsidence stress retained by the system, accounting for stress release on preexisting faults that will likely reduce the magnitude of subsidence stress that can build before being released. We consider a nominal β value of 0.2 (the nominal

Table 2 Nominal model parameter values. Parameter

Definition

Value

E

Young’s modulus Poisson’s ratio Crustal density Magma density Gravity Subsidence rate Subsidence stress parameter

6.5 × 1010 Pa 0.25 2900 kg/m3 2800 kg/m3 1.8 m/s2 4.756 × 10−10 m/s 0.2

ν ρc ρm G V

β

value of Kirchoff and McKinnon (2009)) and also a value of 0.1 (to reflect even greater subsidence stress release). A list of parameters adopted for both the mountain loading and crustal recycling stress models is shown in Table 2. The resulting superposed stress states are compared to the stress envelope for frictional sliding along faults according to Byerlee (1978); see Kirchoff and McKinnon (2009). We assume that the final stress states are bounded by the Byerlee envelopes in compression and extension. In practice, this can turn upper lithospheric stress states where both ascent criteria (magnitude and gradient) are satisfied into states where the gradient criterion is violated, due to the negative gradient of the extensional Byerlee envelope. In order to superpose the two types of models, we assume that the lithosphere and crust are co-incident; this assumption is consistent with scenarios for Io’s internal evolution that postulate a mantle with high degrees of partial melting (and consequently, low mechanical strength) as the source for Io’s volcanism (e.g., Keszthelyi and McEwen, 1997; Anderson et al., 2001). Accordingly, we will use the terms “crust” and “lithosphere” interchangeably.

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0 −10

depth, km

−20 −30

25 km 35 km

−40 −50

50 km

−60 −70 −80 −2000

75 km −1500

Compression Extension −1000 −500 Stress, MPa

0

500

Fig. 4. Crustal recycling stress (elastic only; Kirchoff and McKinnon, 2009) with unconfined lateral boundary condition, as function of depth in crusts with thicknesses 25, 35, 50, and 75 km.

5. Results Crustal recycling stress calculations for several different crustal thicknesses (Fig. 4) reveal stress curves with two characteristic sections: moderate changes of stress with depth (i.e., stress gradients) in the upper lithosphere, and significantly larger stress gradients in the lower lithosphere. The sign of the gradients in both cases is positive, that is, the stresses are increasingly extensional with increasing height. The transition from moderate to high stress gradient occurs far closer to the bottom of the lithosphere than the top: the result is a characteristic “hockey stick” pattern, with a long very high-magnitude compressive stress tail (the “blade” of the hockey stick) at the bottom of the crust/lithosphere. For thicker crusts, the crossover from compression to extension occurs in the middle of the moderate gradient zone, or “shaft” of the hockey stick; for thinner crusts, the crossover occurs closer to the transition between “blade” and “shaft”. Increasing the thickness of the crust/lithosphere slightly increases the magnitudes of the minimum and maximum stress at the bottom and top, respectively. Mountain loading stresses, for locations beneath the mountain, show an opposite trend to that of the crustal recycling stresses, with compression at the surface and extension at the bottom of the lithosphere. However, the mountain loading stress gradients are comparable to those in the “shaft” section of the crustal recycling stress profile. The superposition of these two types of stress can therefore tend to cancel out, with low magnitude net stress and stress gradients seen near the surface, although the compressive recycling stress peak at the bottom of the lithosphere still dominates the stress state there (Fig. 5a–c). Mountain loading stress magnitudes decrease with increasing distance from the symmetry axis, resulting in total stress profiles that resemble the recycling stress state far from the axis (Fig. 5d). For nominal “conveyor belt” stress states, the magma ascent criteria (positive stress and stress gradient) are both satisfied only in a narrow (10 km or so), roughly mid-lithosphere band (see, for example, the right sides of Fig. 6a–d showing far-field recyclingdominated stress), bounded on the bottom by the crossover from compression to extension and on the top by the intersection with the Byerlee law in extension. We term this zone the AscentFavorable Zone, or AFZ. For a modest mountain load (radius rm = 150 km, height hm = 5 km), the AFZs for both radial and hoop stress are slightly widened near the symmetry axis, but otherwise

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unaffected (Fig. 6a). Increasing hm to 10 km results in a substantial thickening of the AFZs at the symmetry axis, creating cone-shaped AFZs there (Fig. 6b); this thickening falls short of reaching the lithosphere’s surface, however. Increasing hm yet again to 15 km yields two important changes (Fig. 6c): first, at the symmetry axis the AFZs are narrowed and depressed in depth relative to the farfield cases. Second, at some distance from the symmetry axis the width of the AF zone expands drastically, reaching the surface of the lithosphere; this occurs where the oppositely sloping mountain loading and crustal recycling stress curves essentially cancel out, leaving an approximately constant, slightly positive (extensional) stress profile throughout all but the lowermost lithosphere (see Fig. 5b). The combination of these effects produces characteristic “U”-shaped AFZs. The “U” shapes are maintained upon further increases in edifice height, although the location of the vertical part of the “U” moves outward in radius. Variations in mountain radius also affect the geometries of AFZs. For a mountain with rm = 100 km and hm = 15 km (Fig. 7a), central cone-shaped AFZs are generated, nearly reaching the lithosphere’s surface at the symmetry axis. Increasing rm to 125 km results in the AFZs intersecting the lithosphere surface just beyond the axis: a nascent U-shaped AFZ. A further increase to rm = 150 km yields the full-fledged U-shaped AFZs of Fig. 7c. Going to rm = 175 pushes the vertical sections of the “U” further out in radius (Fig. 7c). Lithosphere thickness Te also plays an important role in controlling AFZ geometry. For Te = 25 km, a mountain with rm = 150 km and hm = 15 km (Fig. 8a) displays several important differences from the Te = 50 km case (Fig. 6c). First, the thickness of the farfield AFZ is greatly reduced compared to the Te = 50 km cases shown above. Second, the vertical part of the “U”-shape for the radial normal stress component is significantly thinner than that of the comparable cases, and does not intersect the surface of the lithosphere (Fig. 8a). Third, the AFZ for the hoop stress component does not display a “U” shape at all, merely a slight depression of the depth of the AFZ near the symmetry axis. Increasing Te to 35 km restores a surface intersection for the radial stress component and the hoop stress component shows a shortened “U”-shape, failing to intersect the surface (Fig. 8b). For Te = 75 km, slight increases in the upper boundary of the AFZs relative to the far-field values are shown, but no U-shaped zones or surface intersections are evident (Fig. 8c). The nature of the lithospheric stress boundary conditions exerts a significant influence on predictions of AFZs. Lithospheric stress states that are completely within the compressive regime, such as those shown in Figs. 8b and 11 of Kirchoff and McKinnon (2009) that are laterally confined and incorporate thermal, Poisson, and subsidence stresses, are generally incapable of producing ascent zones linking the deep lithosphere with the surface when superposed with mountain-loading stresses, because the stress orientation criterion is violated almost everywhere. The same result holds even for an intermediate stress state calculated by translating the “crustal recycling” stress curve leftward (compressionward) by half the magnitude of the stress at the surface. Such a shift moves the transition depth between compression and extension upward and produces greater compression in the lower lithosphere, thereby preventing the formation of AFZs connecting the lower and upper lithospheres. In contrast, an intermediate stress state created by reducing the subsidence stress control parameter β from 0.2 to 0.1 (Fig. 9a) promotes the development of “U”-shaped AFZs that intersect the lithosphere surface at greater radial distances than for nominal model counterparts (compare Fig. 9b to Fig. 6c). Further, at β = 0.1 the “U” shape develops more strongly for narrower and shorter mountains than for the β = 0.2 case (compare Fig. 9c with Fig. 7b and Fig. 9d with 6b).

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Fig. 5. Superposition of crustal recycling stress with mountain loading stress. Te = 50 km, rm = 150 km, hm = 15 km. Shown are crustal recycling stress (green curve), mountain loading (blue curve), superposed stress (dashed blue curve) and Byerlee (1977) failure criteria in compression and extension (black diagonal lines). (a) at r = 1.25 km. (b) at r = 73.5 km. (c) at r = 111.25 km. (d) at r = 148.75 km. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

6. Discussion The models presented above have strong implications for the ascent of magma through Io’s lithosphere near large mountains. There appear to be three main configurations of Ascent-Favorable Zones (AFZs) in Io’s lithosphere resulting from superposition of resurfacing and mountain stress states: (1) a mid-lithosphere band, resembling the baseline “crustal conveyor belt” stress state (Fig. 4), (2) a cone-shaped widening of the AFZ at the symmetry axis (that in one case, Fig. 7b, reaches the surface of the lithosphere), and (3) a “U”-shaped AFZ resulting from a near-axis depression of the AFZ accompanied by a distal widening of the AFZ that often reaches the surface of the lithosphere (Figs. 6c and d, 7c and 8b). The “U”-shaped pathways appear to be the most robust, as they provide for magma transport from very deep in the lithosphere to its surface, albeit beneath some fraction of the mountain topography. Nonetheless, models with “U”-shaped AFZs are consistent with the presence of volcanic sources (e.g., paterae) incised into or

on the margins of Io’s mountains (Table 1), resembling, for example, Tohil Mons (Fig. 2) and Euboea Mons (Fig. 3). Table 1 contains more examples of mountain/patera pairs with spacings consistent with the combination of “U”-shaped AFZs and lateral magma transport along mountain-building faults proposed here. Magma may reach the surface by thermally eroding the mountain flanks from below, perhaps accounting for the apparent incision of Radegast Patera into Tohil Mons (Fig. 2a), and/or by ascending through fractures that extend through the mountain and surrounding terrain, as observed at the volcanic center Pillan (Keszthelyi et al., 2001). Further, magma may be able to exploit the thrust faults that built the mountains as magma conduits to reach the surface at the margins of the mountains, consistent with observations of volcanic eruption in compressional environments like the Andes Mountains on Earth and analogue mechanical models of coupled thrust faulting and magmatic ascent (Galland et al., 2007). Magma conduits are oriented perpendicular to the least compressive principal stress. For the radial normal stress, dikes are

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Fig. 6. Topography (top panel) and magma ascent criteria satisfaction for superposed models of crustal recycling and mountain loading stresses (bottom panels), for Te = 50 km and rm = 150 km. Red areas denote where both stress orientation and tectonic stress gradient ascent criteria are satisfied, blue areas denote where one or more criteria are not satisfied. (a) For hm = 5 km. (b) For hm = 10 km. (c) For hm = 15 km. (d) For hm = 20 km. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

oriented circumferential to the center of the mountain; for the hoop stress, dikes are oriented radial to that center. Although the “U”-shaped AFZs described above connect the lower lithosphere (near the symmetry axis) to the lithosphere’s surface (under the flank of the mountain), AFZs corresponding to the radial normal stress cannot directly transport magma from the former to the latter, because the conduits are strictly circumferential. On the other hand, the AFZs corresponding to the hoop stress can result in transport from the lower lithosphere to the surface, because the conduits have radial orientations. Thus, we consider the hoop stress AFZs (bottom panels in Figs. 6–8 and Fig. 9b–d) to be the primary means of magma transport through the lithosphere. “U”-shaped AFZs are favored in specific regions of the parameter space of these models. A lithosphere thickness Te of 50 km produces the most prominent AFZs in terms of thickness of the vertical part of the “U” and total fraction of Te covered (Figs. 6 and 7). Reducing Te to 35 km greatly reduces the radial thickness of

the surface-intersecting part of the “U” for the radial normal stress component and removes that part entirely from surface contact for the hoop stress component. Further, as noted above, pathways corresponding to the radial stress component are circumferential in orientation and do not provide means of connecting the lower lithosphere with the surface. Therefore, the Te = 35 km case of Fig. 8b does not provide a viable eruption scenario unless the transport pathway is heterogeneous: radial dikes in the lower lithosphere connecting with circumferential dikes in the vertical part of the “U”. For very thin Te (25 km, Fig. 8a), the AFZs are truncated “U” shapes and thin bands for radial and hoop stresses, respectively, making surface eruption very unlikely. For these conditions, high-magnitude compressive stresses from mountain loading in the upper lithosphere present a major obstacle to magma ascent. Bands are also the primary expression of AFZs for thick lithospheres (Te = 75 km, Fig. 8c): for thicker lithospheres, stresses from mountain loading are too low in magnitude to significantly offset crustal recycling stresses. Thus, we conclude that there is a value

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Fig. 7. Topography and magma ascent criteria satisfaction for superposed models of crustal recycling and mountain loading stresses, as in Fig. 6, for Te = 50 km and hm = 15 km. (a) rm = 100 km. (b) rm = 125 km. (c) rm = 175 km.

Fig. 8. Topography and magma ascent criteria satisfaction for superposed models of crustal recycling and mountain loading stresses, as in Fig. 6, for rm = 150 km and hm = 15 m. (a) Te = 25 km. (b) Te = 35 km. (c) Te = 75 km.

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Fig. 9. Stresses, topography, and magma ascent criteria satisfaction for superposed models of crustal recycling and mountain loading stresses, with crustal recycling parameter β = 0.1. (a) Superposition of crustal recycling stress with mountain loading stress, as in Fig. 5, for β = 0.1, Te = 50 km, rm = 150 km, hm = 10 km, at r = 111.25 km. (b) Topography and magma ascent criteria satisfaction for superposed models of crustal recycling and mountain loading stresses, as in Fig. 6, for β = 0.1, Te = 50 km, rm = 150 km and hm = 15 m. (c) As in (b), for rm = 125 km and hm = 15 m. (d) As in (b), for rm = 150 km and hm = 10 m.

of lithosphere thickness Te near 50 km that is optimal for eruption of magmas at centers near mountains. Interestingly, this value is coincident with those reported for Io’s crust and/or lithosphere based on petrological considerations (e.g., Keszthelyi and McEwen, 1997). The tendencies for the superposed stress states to generate intersections of AFZs with the lithosphere surface and robust “U”-shaped AFZs increase with increasing (pre-flexure) mountain height hm and radius rm (Figs. 6 and 7). Values of hm in excess of 10 km and rm in excess of 100 km appear to facilitate these AFZ geometries, although a crustal recycling stress scenario with a lower fraction of subsidence stresses (reduced β , as in Fig. 9) tends to reduce the values of mountain dimensions required to produce the “U”. The ranges of dimensions of the largest Io mountains (e.g., Figs. 1–3) overlap these ranges, taking into account that the final (observed) mountain height will be somewhat less than hm due to the subsidence of the loaded lithosphere (Figs. 6–8). Further, mountains with smaller dimensions might be able to produce comparable AFZs if favorable regional stress perturbations were also superposed. Near-surface stress relief from deep-seated thrust faulting (Bland and McKinnon, 2014) may also contribute to

favorable stress states for magma ascent in the upper lithosphere and mountain flanks, thereby facilitating eruptions. Such stress relief can actually produce extension at the surface (Bland and McKinnon, 2014), perhaps accounting for observations of mountaincutting fractures associated with the eruptive fissures at Pillan (Keszthelyi et al., 2001). Further, only crustal recycling stress models with substantial stress relief (i.e., those with unconfined lateral boundary conditions and values of subsidence stress parameter β comparable to those used here) are capable of producing (when superposed with mountain loading stresses) AFZs connecting the deep crust/lithosphere with the surface. Such crustal recycling models generate significant extension in upper lithosphere that, when superposed with mountain loading stress, produce the “constant but slightly positive” stress profiles (Fig. 5b) that result in viable AFZs. The extreme compression at the base of the lithosphere (e.g., Fig. 5) is the reason why no AFZ in Figs. 6–8 reaches the bottom of the lithosphere. Thus, this compression is the remaining major barrier to magma ascent. Re-melting of the lower crust/lithosphere (the bottom of the “conveyor belt” cycle), enhanced by the increased heating the mountain “root” will experience as it subsides

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into the partially or completely molten (Khurana et al., 2011) upper mantle, would remove this last barrier. Crustal recycling stress profiles with non-linear rheology (power-law exponent n > 1; Kirchoff and McKinnon, 2009) show an additional segment in the lowermost crust, transitioning from a compressional stress maximum to zero. Such stress profiles, even when superposed with mountain loading stresses, violate the stress gradient ascent criterion, preventing formation of AFZs in the lowermost crust/lithosphere. However, the vertical extent of this barrier region is similar to that of the high compressional stress region (violating the stress orientation criterion) in the linear case; thus, the lower crustal remelting mechanism invoked above to remove the barrier applies to the non-linear case as well. In the upper lithosphere the widths of AFZs calculated here are conservative because favorable effects of overpressure (from large supply rates or magmatic volatiles) have not been applied. The interactions of stresses from lithospheric loading and crustal recycling also have implications for broad-scale distributions of volcanic features on Io. Thus far we have considered downward loads on the lithosphere: however, phenomena such as buildup of magma in the upper mantle/asthenosphere produced by tidal heating may create loads that are directed upwards. For such a case, the loading stresses shown in Fig. 5 would be essentially reversed, with extension in the upper lithosphere and compression in the lower lithosphere. This situation would make the difficulty with large compression in the lower lithosphere from crustal recycling stress even worse, thereby making magma ascent very unlikely in the lithosphere directly above an upward load. Instead, the magma would tend to be directed toward the margins of the uplift, where stress conditions would be far less adverse to ascent. Such a finding is consistent with the offset of tidal heating patterns with observed locations of volcanic vents (Kirchoff et al., 2011; Veeder et al., 2012; Hamilton et al., 2013). Thus, we favor a stress-based explanation for the observed offsets. The models and interpretations presented here address volcanism associated with large mountains on Io, a subset of overall volcanic activity on that body. Many volcanic sources on Io are not related to areas with large topographic relief like Io’s mountains. In such settings, considerations of magma buoyancy and volatile (primarily SO2 ) distribution within the crust (e.g., Leone and Wilson, 2001; Leone et al., 2011) may facilitate magma ascent, although the expected high level of compression in the lower crust is still expected to exert primary control on intrusion orientations (Leone et al., 2011). 7. Conclusions We have superposed stress solutions for crustal recycling in Io’s lithosphere with stresses from Io mountain-sized loads in order to evaluate magma ascent pathways near Io’s mountains. For nominal crustal recycling stress states alone, the ascent-favorable zone (AFZ) where both stress orientation and gradient magma ascent criteria are satisfied consists of only a narrow (5 km or so), roughly mid-lithosphere band. When lithospheric stresses from loading of mountains with dimensions comparable to those observed on Io are superposed with the recycling stress solutions, predicted AFZs expand to span nearly the entire vertical extent of the lithosphere. For moderate mountain heights, on a lithosphere with thickness Te = 50 km, the AFZs reach greatest vertical extent under the center of the mountain; as mountain height increases, the form of the AFZ transitions to a “U” shape, deepest beneath the center of the mountain with a vertical segment that intersects the submountain lithosphere surface at some distance from the center. This vertical segment corresponds to a nearly constant and slightly extensional stress profile in the upper and mid-lithosphere that falls under the criterion for brittle failure in extension (the “By-

erlee” curve). The AFZ surface intersection distance (from mountain center) increases with increasing mountain height and radius. Formation of “U”-shaped AFZs is inhibited for lithospheres with elastic thickness Te substantially thinner or thicker than 50 km. “U”-shaped AFZs outline viable magna ascent paths that transit nearly the entire vertical extent of the lithosphere, arriving at the base of the mountain where magma can be transported through thrust faults or perhaps thermally erode flank sections, the latter consistent with observations of paterae in close contact with mountains. The major remaining barrier to ascent in all these scenarios is the extreme value of compressive stress in the lower lithosphere. This will be relieved somewhat by the mountaingenerating faulting. Further, the resurfacing cycle is thought to end at the bottom of the crust/lithosphere by remelting of crust, which would remove the stress trap there, facilitating magma access to the aforementioned pathways in the lithosphere above. This is likely to happen because the root of the mountain, protruding into the zone of melting in the asthenosphere, will experience enhanced heating. Acknowledgments This work was supported by NASA Outer Planets Research Program (OPR) Grant NNX12AM78G. We are grateful for thorough and constructive reviews from Zibi Turtle and Ashley Davies that significantly improved the manuscript. This is LPI Contribution # 1906. References Anderson, E.M., 1951. The Dynamics of Faulting and Dyke Formation with Application to Britain. Oliver and Boyd, Edinburgh. Anderson, J.D., Jacobson, R.A., Lau, E.L., et al., 2001. Io’s gravity field and interior structure. J. Geophys. Res. 106, 32963–32970. Bland, M.T., McKinnon, W.B., 2014. Deep faulting, stress release, and mountain formation on Io. In: Lunar Planet. Sci. XV, Abstract # 2502. Brotchie, J.F., 1971. Flexure of a liquid-filled spherical shell in a radial gravity field. Mod. Geol. 3, 15–23. Buz, J., McGovern, P., 2010. Venusian volcano shapes: Implications for edifice evolution and the internal thermal state of Venus. In: Lunar Planet. Sci. XLI, Abstract # 1482. Byerlee, J., 1978. Friction of rocks. Pure Appl. Geophys. 116, 615–626. Carr, M.H., 1986. Silicate volcanism on Io. J. Geophys. Res. 91, 3521–3532. Carr, M.H., et al., 1998. Mountains and calderas on io: possible implications for lithosphere structure and magma generation. Icarus 135, 146–165. Freed, A.M., Melosh, H.J., Solomon, S.C., 2001. Tectonics of mascon loading: resolution of the strike-slip faulting paradox. J. Geophys. Res. 106 20,603–20,620. Galland, O., Cobbold, P.R., de Bremond d’Ars, J., et al., 2007. Rise and emplacement of magma during horizontal shortening of the brittle crust: Insights from experimental modeling. J. Geophys. Res. 112. doi:10.1029/20 06JB0 04604. Hamilton, C.W., Beggan, C.D., Still, S., et al., 2013. Spatial distribution of volcanoes on Io: Implications for tidal heating and magma ascent. Earth Planet. Sci. Lett. 361, 272–286. Jaeger, W.L., Turtle, E.P., Keszthelyi, L.P., et al., 2003. Orogenic tectonism on Io. J. Geophys. Res. 108, 5093. doi:10.1029/20 02JE0 01946. Johnson, C.L., Sandwell, D.T., 1994. Lithospheric flexure on Venus. Geophys. J. Int. 119, 627–647. Johnson, T.V., Veeder, G.J., Matson, D.L., et al., 1988. Io–evidence for silicate volcanism in 1986. Science 242, 1280–1283. Keszthelyi, L., McEwen, A.S., 1997. Magmatic differentiation of Io. Icarus 130, 437–448. Keszthelyi, L., 2001. Imaging of volcanic activity on Jupiter’s Io by Galileo during the Galileo Europa mission and the Galileo millennium mission. J. Geophys. Res. 106, 33025–33052. Khurana, K.K., Jia, X., Kivelson, M.G., et al., 2011. Evidence of a global magma ocean in Io’s interior. Science 332, 1186–1189. Kirchoff, M.R., McKinnon, W.B., 2006. Mountain building on io - part 2: effects of preexisting faults and pore sulfur on thermal stresses. In: Lunar Planet. Sci. 37, abstract #2120. Kirchoff, M.R., McKinnon, W.B., 2009. Formation of mountains on Io: variable volcanism and thermal stresses. Icarus 201, 598–614. Kirchoff, M.R., McKinnon, W.B., Schenk, P.M., 2011. Global distribution of volcanic centers and mountains on Io: Control by asthenospheric heating and implications for mountain formation. Earth Planet. Sci. Lett. 301, 22–30. Litherland, M.M., McGovern, P.J., 2009. Effects of planetary radius on lithospheric stresses and magma ascent on the terrestrial planets. In: Lunar Planet. Sci. 40, abstract 2201. Leone, G., Wilson, L., 2001. Density structure of Io and the migration of magma through its lithosphere. J. Geophys. Res. 106, 32983–32995.

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