Volcanism and volatile recycling on a one-plate planet: Applications to Venus
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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, E04S06, doi:10.1029/2006JE002793, 2007
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Volcanism and volatile recycling on a one-plate planet:
Applications to Venus
L. T. Elkins-Tanton,1,2 S. E. Smrekar,3 P. C. Hess,1 and E. M. Parmentier1
Received 14 July 2006; revised 17 October 2006; accepted 14 November 2006; published 30 March 2007.
[1] The surface of Venus displays volcanic features indicating eruption of lavas with a
wide range of viscosities. We present numerical experiments showing that lithospheric
gravitational instabilities can produce lavas with compositions consistent with the range of
volcanic forms seen on Venus. The presence of incompatible elements and their oxides
(specifically, water, carbon dioxide, and alkali elements) in trace- to percent-level
concentrations in the Venusian mantle allows the formation of a variety of magmatic
source regions. The pressure and temperature paths that the dense lithospheric materials
travel as they sink into the Venusian mantle indicate that the lithospheric material may
devolatilize as it sinks, enriching the surrounding upper mantle, or it may itself melt.
These processes can produce magmas with a variety of compositions and viscosities,
potentially consistent with the range of Venusian volcanic forms. These processes also
suggest that Venus may recycle incompatible elements internally. Indeed, if Venus
began with an internal volatile content, then no amount of partial melting can make it
entirely volatile-free even in the absence of recycling into the interior. These models
therefore suggest geodynamic processes that can produce a range of magmatic activity and
retain some interior volatiles on a one-plate planet.
Citation: Elkins-Tanton, L. T., S. E. Smrekar, P. C. Hess, and E. M. Parmentier (2007), Volcanism and volatile recycling on a one-
plate planet: Applications to Venus, J. Geophys. Res., 112, E04S06, doi:10.1029/2006JE002793.
1. Introduction: Evidence for Widely Varying subsequent delamination or thinning through gravitational
Lava Viscosities instabilities, allowing further mantle melting. Alternatively,
a mantle downwelling causes the crust to thicken into a
[2] Venus has an apparently unmoving lithosphere and a plateau [Bindschadler and Parmentier, 1990; Lenardic et
young surface indicative of volcanic resurfacing. Despite al., 1995]. The downwelling lithosphere and mantle are
the apparent absence of plate tectonics, Venus has a wealth candidates for remelting as they heat conductively. The
of tectonic features, including 100,000 small shield volca- location of one of Venus’ three festoon features on the
noes as well as the descriptively named pancakes, ticks, and tessera plateau Ovda Regio [Head et al., 1991] suggests that
arachnoids [Dupeyrat and Sotin, 1995]. Most features are remelting may have occurred.
believed to be formed by mantle upwelling, lithospheric [4] Downwelling may also contribute to the formation of
downwelling, or a combination of the two. coronae. Coronae are quasicircular volcanotectonic features
[3] Perhaps the most dramatic tectonic features on Venus unique to Venus. There are over 500 such features, which
are the tessera plateaus. There are 6 such plateaus on Venus, range in diameter from 50 to 2,600 km. The 2,600 km
each 1000 – 2000 km in diameter with elevations of 0.5– diameter Atemis Corona is anomalously large. If it is not
4 km above the surrounding plains. Their surfaces are included, coronae have a mean diameter of 275 km [Glaze
intensely deformed by multiple fracture sets. In one hypoth- et al., 2002]. The most unusual feature of coronae is the
esis, the plateau forms above an upwelling mantle plume that large variation in their topographic morphology. Coronae
spreads out beneath the lithosphere. The plateau shape is have raised interiors and depressed interiors in roughly
maintained after the thermal plume dissipates by crustal equal numbers [Stofan et al., 2000]. Some have perimeter
thickening generated by pressure release melting [Grimm troughs, some have rims, some are plateaus, and others are
and Phillips, 1991; Phillips et al., 1991]. In this scenario, the domes. All have associated volcanism [Smrekar and Stofan,
thick, hot crust and lithosphere may be susceptible to 1997]. Although most models have described the formation
of coronae via mantle upwelling [e.g., Stofan et al., 1991],
1 to produce the interior depressions others have required
Department of Geological Sciences, Brown University, Providence,
Rhode Island, USA. lithospheric thinning via gravitational instabilities with
2
Now at Department of Earth, Atmospheric, and Planetary Sciences, [Smrekar and Stofan, 1997] or without [Hoogenboom and
Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
3
Houseman, 2005] a central upwelling. In the scenario where
Jet Propulsion Laboratory, Pasadena, California, USA. coronae form purely as result of downwelling, remelting is
required to produce the observed volcanism.
Copyright 2007 by the American Geophysical Union.
0148-0227/07/2006JE002793$09.00
E04S06 1 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
Figure 1. Pancake domes about 65 km in diameter and less than 1 km in height at 12.3N, 8.3E in the
Eistla region of Venus (NASA/JPL/Magellan).
[5] Steep-sided or ‘‘pancake’’ domes are associated with had viscosities low enough to allow fluid flow for hundreds
coronae [e.g., Head et al., 1991; Pavri et al., 1992] (Figure 1) of kilometers, creating channels reminiscent of water rivers
and appear to consist of more viscous magma, perhaps on Earth; these may be created by carbonatites [e.g., Sill,
emplaced episodically [Pavri et al., 1992; Fink et al., 1984; Kargel et al., 1994].
1993]. They can be up to 3 km in height and have volumes [7] The wide range of apparent magmatic viscosities
from 30 to 3,000 km3 (calculated from data of Smith demonstrated by these disparate volcanic forms is supported
[1996]); hundreds dot the planet [Pavri et al., 1992; Smith, by data from Soviet landers indicating compositional vari-
1996; Ivanov and Head, 1999]. Several hypotheses have ability in Venusian magmas. Rocks analyzed by the Venera 9
been presented for the composition of pancake domes: and 10 and Vega 1 and 2 landers have K less than 1 wt% and
Ivanov and Head [1999] suggests they may have silicic U less than 1 ppm, while rocks at the Venera 8 landing
compositions created by remelting basaltic crust; Bridges site have K contents as high as 4 ± 1.2 wt% and U as high
[1997] and Stofan et al. [2000] state that the shapes of as 2.2 ± 0.7 ppm [Surkov, 1990; Nikolaeva and Ariskin,
pancake domes are most consistent with basaltic composi- 1999]. Nikolaeva and Ariskin [1999] suggest that the
tions, but hotter surface conditions would allow domes Venera 8 composition may be the result of melting an
made of rhyolite; Pavri et al. [1992] suggest they are eclogite, while the other magmas may be mantle melts.
formed of either silicic magma or vesiculated basaltic The high alkali content of some Venusian compositions
magma. Plaut et al. [2004] demonstrated that though the may also be the product of fractionation in magma
morphology of steep-sided domes might support silicic chambers [Bazilevsky, 1997]. Kargel et al. [1993] sug-
compositions, the radar properties did not. Bridges [1997] gested that the enhanced alkali compositions may be the
compared magma compositions in subaerial and subaque- result of increased carbon dioxide and decreased water
ous terrestrial conditions to Venusian conditions and vol- activity in the melting source; this hypothesis may be
canic forms. Though he concluded that the pancake domes supported by the work presented here.
were likely to be basaltic, the Venusian festooned flows, [8] The compositions of Venusian lavas and the processes
some extending 400 km [Manley, 1993] may be more silicic, that create them on an apparently one-plate planet remain
perhaps rhyolitic [Moore, 1987; Manley, 1993]. McKenzie et open questions. On the Earth, the best-understood volcanic
al. [1992] further suggested that magmas consistent with processes operate at mid-ocean ridges and at volcanic arcs,
pancake domes may be created by wet melting at depth. both of which are the result of Earth’s apparently unique
[6] In addition to their association with coronae, pancake plate tectonics. On Venus, a similar or even larger range of
domes are associated with shield volcanoes effusing pos- magmatic viscosities appears to be produced in the absence
sibly basaltic magmas [Smith, 1996; Ivanov and Head, of plate tectonics. On Earth, the closest analog is volcanism
1999] with apparently low viscosities. Some flows spread on stable cratons, such as is seen in Siberia in the form of
widely and form sheets (Figure 2), apparently emplaced as flood basalts, kimberlites, and carbonatite complexes [e.g.,
a series of thin flows [Byrnes and Crown, 2002]. These Fedorenko and Czamanske, 1997; Boyd et al., 1997].
flows extend up to 1,000 km from their inferred sources [9] Parmentier and Hess [1992] suggest that Venus has
[e.g., Roberts et al., 1992], and may be emplaced in stages undergone cyclic catastrophic crustal recycling through
over hundreds of years [Zimbelman, 1998]. Other magmas gravitational instability. Both Dupeyrat and Sotin [1995]
2 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
Figure 2. Large volcanic flows appear on the left side of this Magellan radar image centered at 1S, 37E.
The image covers 440 by 350 km (NASA/JPL/Magellan).
and Hoogenboom and Houseman [2005] suggest that eclo- 1998; Reese et al., 1999; Solomatov and Moresi, 2000].
gitization of the lower lithosphere can be a driving force for Such a regime may be unstable and produce episodic
gravitational instabilities sinking from the lithosphere, a resurfacing of the planet under certain circumstances, such
process that has been invoked on Earth to create distinctive as particular values of lithospheric strength. This mantle
surface topography and magmatism [Kay and Kay, 1993; heating and episodic breakup has been proposed to resurface
Schott and Schmeling, 1998; Elkins Tanton and Hager, Venus on intervals of 700 Myr [Parmentier and Hess,
2000]. Instabilities may also be coupled with rising plumes 1992; Reese et al., 1999].
[Parmentier and Hess, 1992; Dupeyrat and Sotin, 1995; [12] The gravity and topography data are the only avail-
Smrekar and Stofan, 1997; Hoogenboom and Houseman, able information to constrain lithospheric thickness on
2005]. Venus. Numerous regional gravity and topography studies
[10] Here we present models showing that lithospheric have estimated the elastic thickness, yielding values ranging
gravitational instabilities can produce melting in a range of from 0 to 100 km [Phillips et al., 1997; McKenzie and
source compositions in the absence of plate tectonics, Nimmo, 1997; Simons et al., 1997; Smrekar and Stofan,
creating both basaltic magmas and magmas with higher 1999; Barnett et al., 2000, 2002; Hoogenboom et al., 2004;
levels of incompatible elements, including alkalis and low Anderson and Smrekar, 2006]. Estimates of elastic thick-
amounts of volatiles (consistent with the suggestions of ness from plate curvature studies yield a similar range
McKenzie et al. [1992]). This is a candidate process to [Johnson and Sandwell, 1992; Sandwell and Schubert,
create a variety of compositions and viscosities of magmas 1992]. Elastic thickness can be used to estimate the thermal
in the absence of subduction. The magma compositions gradient in the lithosphere, taking into account the litho-
predicted from source compositions and melting conditions spheric rheology and curvature of the deflected elastic plate
indicated by models of gravitational instabilities are consis- [McNutt, 1984]. In addition to estimates of elastic and
tent with the range of volcanic forms seen on Venus. crustal thickness, apparent depths of compensation in the
range of 100 –300 km have been interpreted as the depth to
2. Venusian Lithosphere the base of the thermal lithosphere [Herrick and Phillips,
1990; Grimm and Phillips, 1992]. Again, different methods
[11] Analysis of the topography and radar imaging data tend to favor smaller or larger depths. Additional estimates
indicates that Venus does not have a terrestrial-style system of the thermal lithospheric thickness come from models of
of plate tectonics [e.g., Solomon et al., 1992]. The leading large-scale mantle upwellings, analogous to terrestrial hot
hypothesis to describe the overall state of mantle-lithospheric spots. Estimates of thermal lithospheric thickness that pre-
dynamics is that Venus is in a stagnant lid regime. In this dict melt volumes comparable to the observed large volca-
state, the interior is actively convecting, but the lithosphere noes for mantle temperatures of 1300°C and plume
is too strong to break up into plates [Moresi and Solomatov, temperatures of 1500°C are in the range of 100 – 150 km
3 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
[Smrekar and Parmentier, 1996; Nimmo and McKenzie, on the basis of its similar position to the Earth’s in the
1996]. Higher mantle temperatures allow thicker lithosphere. protoplanetary disk (though non-peridotitic mantle compo-
[13] A recent study of global variations of elastic and sitions have been suggested [see, e.g., Fegley, 2003]).
crustal thickness variations [Anderson and Smrekar, 2006] Density anomalies in the Venusian lithosphere conducive
shows that in many regions lithospheric properties vary on to producing gravitational instabilities could be caused by
relatively small scales (250 –1000 km), even in regions such mafic minerals remaining in magma chambers after erup-
as the plains where there are not conspicuous variations in tion, by eclogitization of basalt injected into the lower
surface geology. Such variations may reflect lower litho- lithosphere from mantle melting [Elkins Tanton and Hager,
spheric processes, such as delamination or lithospheric loss 2000; Jull and Kelemen, 2001], or by eclogitization of the
through gravitational instability [Anderson and Smrekar, lower lithosphere as it thickens into the garnet stability zone
2006]. Another important result is that the elastic thickness [Kay and Kay, 1993], either through compressive tectonics
for approximately half of the planet is 20 km or less. Such or by conductive cooling. In the case of any of these driving
small values can be interpreted as indicating high heat flow mechanisms, heterogeneous source regions for later mag-
and thin elastic lithosphere and thus thermal lithosphere. matism have already been created: eclogite differs from
Alternatively, these regions may simply be compensated by peridotite, as do the mafic residues of fractional crystalli-
crustal thickness changes, with little or no flexural compen- zation. The melting temperatures and resulting melt com-
sation, in which case gravity and topography data do not positions of these sources also differ.
constrain elastic thickness. In regions such as tessera [18] The apparent stiffness of the Venusian crust, as
plateaus, it is likely that crustal compensation is the correct evidenced by the topography on Venus [e.g., Grimm and
interpretation. In other areas, the interpretation is ambigu- Solomon, 1988; Bindschadler and Parmentier, 1990; Kiefer
ous, and measurements could reflect high heat flow from a and Hager, 1991], have been used to argue for extreme
mantle long insulated by a stagnant lithosphere. This dryness, which creates exceptionally high viscosity [Nunes
interpretation is consistent with the high mantle temper- et al., 2004; Smrekar and Solomon, 1992]. This dryness may
atures required to produce melting in this and other studies. plausibly be created by baking under the high surface
Additionally, a study of the coronae found along major temperatures of the planet [Mackwell et al., 1998]. The
rifts indicates that those coronae that are stratigraphically quantities of noble gas isotopes in the Venusian atmosphere,
younger have a thin elastic lithosphere, which also supports however, argue for volcanic degassing in the relatively
the high heat flow hypothesis over the isostatic interpretation recent past [Namiki and Solomon, 1998]; water in the
[Hoogenboom et al., 2005]. atmosphere also constrains atmospheric escape and degass-
ing rates [Kasting and Pollack, 1983; Lammer and Bauer,
2.1. Dynamics of a Stable Lid 2003]. The interior of Venus then cannot be completely
[14] Several mechanisms for small-scale convection in and lacking water, and it is equally unlikely to be completely
below the lithosphere may exist on Venus. As in a fluid devoid of carbon dioxide or other incompatible elements
cooled from above, in which small-scale convection develops (throughout we include water, carbon dioxide, and alkalis in
beneath a thickening boundary layer [e.g., Chandrasekhar, the term ‘‘incompatible elements,’’ all of which lower the
1961], small-scale convection occurs beneath a cool upper melting temperature of the silicic source that contains them).
boundary layer of a planet. This process is the least likely to Melts from the interior will carry with them the majority of
produce volcanism or variations in topography, since it is the volatiles and alkalis from the sources, and melts that
driven by the radial temperature gradient in the planetary freeze in the lithosphere will enrich the lithosphere with
lithosphere and therefore tends toward lateral homogeneity. incompatible elements. Volatiles will be held in silicic
[15] On Earth, brittle delamination of basaltic under- magmas according to the composition of the magma and
plating or shallowly dipping oceanic slabs has been its pressure. The lower the silica content of the magma, the
proposed in some regions with anomalous topography or higher its dissolved carbon dioxide content can be (Figure 3)
volcanism [e.g., Oxburgh, 1972; Bird, 1979, 1988], but there [Papale, 1999].
is no specific evidence for subduction or brittle delamination [19] In magmas that freeze at shallow depths or even
on Venus, where it is less likely due to the planet’s thick, stiff erupt onto the Venusian surface, high atmospheric pressure
stagnant lid, high surface temperatures, and lack of oceans. acts to hold water in the crust and mantle. Degassing of lavas
[16] Here we investigate ductile gravitational instabilities is inefficient first because high heat transfer to the dense
from the Venusian lithosphere [Stofan et al., 1991; atmosphere quickly quenches lava, and second because
Dupeyrat and Sotin, 1995; Smrekar and Stofan, 1997; Venus’ atmospheric pressure allows basalt to retain a higher
Hoogenboom and Houseman, 2005] as a process to create water content than the Earth equivalent. Atmospheric pres-
a range of volcanic products on Venus. These instabilities sure on Venus allows basaltic lava to retain on the order of
differ from small-scale lithospheric convection in that they 1 wt% water, while the same basalt at Venus surface
are driven by compositional density anomalies, and there- pressure could contain only about 0.02 wt% of carbon
fore may be distributed heterogeneously in the Venusian dioxide.
lithosphere, both laterally and vertically. This process [20] Incompatible elements in the lithosphere are avail-
requires only a region denser than the material adjacent to able to induce melting in material sinking from the litho-
it, and viscosity low enough to enable flow. sphere in gravitational instabilities. The process of
2.2. Possible Mantle and Lithospheric Compositions gravitational instability itself provides both opportunities
for melting and the possible production of additional,
[17] The Venusian mantle is usually assumed to be compositionally distinct source regions: as the denser lith-
peridotitic, in the absence of evidence to the contrary, and ospheric anomalies sink into the underlying mantle, it is
4 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
[23] The lithosphere is defined here as the depth over
which a conductive temperature profile dominates and the
temperature is below the adiabatic mantle temperature. A
half-space cooling solution starting condition for each
numerical experiment was created by using a complemen-
tary error function cooling law to make a cooled lithosphere
of the desired depth, employing the temperature at the
surface (TS), the temperature of the convecting mantle
(TM), thermal diffusivity (k), and the time period of thermal
diffusion (t) [Turcotte and Schubert, 2002]:
" #
z
T ð zÞ ¼ ðTS TM Þerfc þ TM ð1Þ
2ðkt Þ0:5
to create a mantle lithosphere of either 75 or 150 km
thickness. The modeled mantle lithospheric material
possesses the same temperature dependence of viscosity
and the same thermal diffusivity as the underlying
convecting mantle, though the cooler temperatures in the
lithosphere produce higher viscosities. A sample starting
condition for a numerical experiment is shown in Figure 4.
For a list of values used in all models, see Table 1, and for a
list of all models, see Table 2.
[24] In some models a weak lower crustal layer is added,
which on Earth would be interpreted as a decrease in
Figure 3. Silicate magmas with lower silica content can strength caused by a hot thermal profile causing weakness
contain larger quantities of carbon dioxide. This image, after in the lower crust (a Moho, after example H1 of Ranalli and
Papale [1999], shows that at Venusian surface pressures Murphy [1986]). The lithospheric structure and composition
very low silica magmas can contain as much as 0.2 wt% on Venus is not known well enough to determine whether
CO2. At lithospheric pressures the carbon dioxide solubility such a structure may be present, but it is additionally
is far higher. A trachyte would have 60% to 70% silica, possible that on Venus a viscosity change occurs in the
while a nephelinite would have only 35% to 42% silica. lithosphere where shallow material, baked free of volatiles,
grade into a deeper region where volatiles have been
retained because of greater pressures. When a weak layer
is added in these models, it has an initial viscosity three
efficiently warmed conductively by the underlying upper orders of magnitude lower than the background value.
mantle. If the unstable material contains quantities of [25] Both temperature and composition contribute to
volatiles or incompatible elements even in concentration buoyancy. Thermal buoyancy is determined by the Rayleigh
of less than a percent, these components may be released number, containing terms for density (r), gravity (g),
from the sinking material as its pressure and temperature thermal expansivity (a), temperature range across the model
increase, just as subducting slabs on Earth devolatilize as box (DT), height of the model box (h), reference viscosity
they sink into the mantle. These released incompatible (h), and thermal diffusivity (k):
elements can either cause the sinking material to melt, or
they may be released into the surrounding upper mantle and
rgaDTh3
there trigger melting there, again in analogy to melting in Ra ¼ ¼ 106 : ð2Þ
the mantle wedge of a terrestrial subduction zone. hk
[21] The stability of the sources hypothesized here, and
the paths of possible Venusian lithospheric instabilities [26] The models include a lithosphere with a flat lower
through pressure and temperature space are investigated boundary (no lithospheric root) into which a region of
here using numerical experiments. higher-density material has been injected. This denser
material is an analog of hot magmatic flux that has frozen
as an eclogite, or has left behind dense mafic cumulates.
3. Model Parameters This material is therefore both denser and warmer than the
[22] Numerical experiments have been conducted using a surrounding lithosphere. The denser composition is mod-
spherical axisymmetric version of the two-dimensional eled as a half cosine wave in x with a maximum at the left
finite element code ConMan [King et al., 1990] called side of the axisymmetric model box, falling to zero in the
SSAXC. This code solves conservation equations for heat, positive x direction, and a half cosine wave in z, with a
mass, and momentum (equations given by van Keken et al. maximum at the bottom of the mantle lithosphere, falling to
[1997] and Elkins-Tanton [2007]) using a model box of 128 zero vertically in z. Temperature is also added to the
by 128 nodes, corresponding to a domain of 500 by 500 km lithosphere in the same pattern, bringing the region of
on Venus. intrusion closer to the mantle temperature beneath and
correspondingly lowering its viscosity. As shown in
5 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
Figure 4, density and temperature is added throughout the
thickness of the lithosphere.
[27] The resulting negative buoyancy of the dense lower
lithosphere is measured by the compositional Rayleigh
number,
Drgh3 Dr
Rac ¼ ¼ Ra ¼ 106 ð3Þ
hk raDT
in which Dr is the difference between the densities of the
lower lithospheric composition and the adjoining upper
mantle, and is set to a 3% increase over adjacent mantle
lithosphere. The maximum temperature addition is 10%
above the ambient asthenospheric temperature, consistent
with heats of fusion (a density contrast of 1% is sufficient to
drive a gravitational instability under reasonable terrestrial
lithospheric conditions, shown by Elkins-Tanton [2007]).
[28] Viscosity is calculated in most experiments using the
following Newtonian law:
E þ vz E þ vzo
hNewtonian: ¼ ho exp ; ð4Þ
T þ To 1 þ To
where ho, zo, and To are reference values for viscosity, depth,
and temperature, respectively; E is the activation energy,
and v is the reference volume (Table 1). To avoid numerical
problems, the maximum viscosity is set as 105 times the
background viscosity. One experiment, as noted in Table 2,
includes a stress-dependent viscosity law in which viscosity
is scaled as
s n1
o
hnonNwetonian ¼ hNewtonian : ð5Þ
t
where so is the reference stress, t is the second invariant of
the stress tensor, and n, the power law exponent, is set to 3
in these experiments.
[29] The importance of the temperature dependence of
viscosity is investigated by using values for the activation
energy E equivalent to either 250 or 500 kJ/mol. The
reference mantle temperature To is 1,300°C, and the surface
Figure 4. Starting conditions for numerical experiments.
(top) A two-dimensional cross section through the litho- Table 1. Parameters Used in Models
sphere and mantle, with an axis of symmetry at the left side. Parameter Symbol Value
Temperature is shown in shades of gray, from 460°C at the Height and width of model box h 500 km
surface to the mantle potential temperature in white. Added Number of nodes in each dimension 128
material with density and temperature contrast is shown in of the model box
contours of 10% each, with the maximum addition at the Reference mantle density r 3,300 kg/m3
axis of symmetry on the interface between the mantle and Reference viscosity h0 1020 Pa s
Reference stress for stress-dependent so 106 Pa
lithosphere. The maximum addition in each model corre- viscosity
sponds to a 3% density contrast with the mantle. (bottom) Thermal expansivity a 3 105/°
Temperature and viscosity profiles through model space Thermal diffusivity k 106 m2/s
equivalent to that shown in the top figure. Dashed line: the Rayleigh number Ra 106
Venusian temperature profile. Bold solid line: viscosity with Compositional Rayleigh number Rac 106
Density contrast between altered lower Dr 3%
temperature dependence of viscosity law corresponding to lithosphere and upper mantle
an olivine activation energy of 250 kJ/mol. Medium line: Mantle potential temperature Tp 1,300°C
corresponds to olivine activation energy of 500 kJ/mol. Fine Heat capacity of silicates CP 1256.1 J/°kg
line: viscosity in model with temperature dependence Heat of fusion of silicates Hf 418,700 J/kg
corresponding to 250 kJ/mol but with a temperature profile Fraction of melt produced from nominally 1 wt%/kbar
dry peridotitic upper mantle per kilobar
with 20°C at surface. above solidus
6 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
Table 2. Numerical Experiments
Olivine Activation Energy
Equivalent Lithospheric (Controls Temperature Low-Viscosity
Name Thickness Dependence of Viscosity) Layer? Notes
dV1 150 km 250 kJ/mol no Baseline experiment: Ra = 107 Tp = 1300°C
dV2 150 km 500 kJ/mol no As dV1 but E* differs
dV3 150 km 250 kJ/mol yes As dV1 but low-viscosity layer
dV5 150 km 250 kJ/mol no As dV1 but stress-dependent viscosity
dV6 75 km 250 kJ/mol no As dV1 but thin lithosphere
dV7 75 km 500 kJ/mol no As dV2 but thin lithosphere
temperature 460°C, a significant deviation from Earth Kinzler and Grove [1992] and Langmuir et al. [1992]. The
surface condition, which affects the speed and efficiency expression for the solidus is fitted to experimental data on
of gravitational instabilities by raising the average litho- the continental fertile peridotite KLB-1 from Herzberg et al.
spheric temperature when compared to Earth (Figure 4). [2000] and Takahashi et al. [1993]. Incompatible-element
The top of the model box is a free-slip boundary, and the triggered melting volumes are not estimated.
right-hand and bottom sides have flow-through boundary
conditions. 4. Melting From Possible Sources
[30] Any melt produced by dry adiabatic melting in
convection currents associated with the gravitational insta- [31] All models exhibited gravitational instabilities. Two
bility is calculated with a post-processor routine using the examples of numerical experiments are shown in Figures 5
parameters listed in Table 1. This postprocessor routine uses and 6. Figure 5 shows the baseline experiment, dV1, in
the mantle flow fields to calculate the volume of astheno- which the 150 km lithosphere has a density anomaly with a
spheric material moving above its solidus during each time maximum contrast of 3% with the laterally adjacent litho-
step of the numerical calculations. During adiabat melting sphere and the temperature dependence of viscosity is
of dry upper mantle, melt is produced at a rate of 1% per equivalent to an activation energy of 250 kJ/mol. The dense
kilobar rise above the solidus, consistent with the results of region develops quickly into an instability, which carries
Figure 5. Numerical experiment dV1: cross sections through the crust into the mantle. The left
boundary is an axis of symmetry, passing through the center of the instability. Temperature is shown with
shading, dense compositions are shown in solid contours of 10%, and vectors show velocity. Conductive
lithospheric temperature profile ends at 150 km depth. Instability forms and sinks below 500 km depth in
about 2 Myr, but substantial dense material remains frozen in the lithosphere.
7 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
Figure 6. Numerical experiment dV3. As Figure 5, but a layer with viscosity three orders of magnitude
less than the background is added at midlithosphere depth. The instability forms more rapidly and
removes more dense material from the lithosphere.
much of the dense composition beyond 500 km depth slowly, exiting the model box depth of 500 km in 6 and
within a few million years. The less dense regions of the 12 million years, respectively. The smaller instability are
lithosphere at lower pressures are frozen into place, and will expected because instabilities scale with the thickness of the
not form later instabilities without additional perturbation in dense layer [e.g., Turcotte and Schubert, 2002], and because
composition or temperature. smaller masses will sink more slowly. In all experiments
[32] The second example, in Figure 6, begins with iden- presented in this paper instabilities did form and sink; with
tical conditions but with the addition of a low-viscosity higher viscosity and far lower density contrasts, the dense
layer midway through the lithosphere. This instability falls material can be retained in the lithosphere and formation of
much faster, exiting the model box about one million years the instability prevented.
earlier than the baseline model in Figure 5. The lateral slip [35] During formation and sinking of an instability there
allowed by the low viscosity layer produces less upward are two opportunities to create melt. The first involves
motion in the upper mantle (and therefore limits the melting nominally dry mantle material near the
possibility of dry adiabatic melting), and carries far more lithosphere-upper mantle boundary in convection currents
of the dense material to depth. induced by the sinking instability. The second may occur if
[33] In comparison to the baseline experiment dV1 in the sinking material has incompatible elements, which either
Figure 5, the higher temperature dependence of viscosity may trigger melting in the instability itself as it warms, or
used in experiment dV2 (Table 2) still allows the instability may be lost into surrounding mantle material as the insta-
to form and sink, but the material sinks about twice as bility sinks and heats.
slowly as that in experiment dV1, and more dense material
is left in the lithosphere. The addition of a stress-dependent 4.1. Melting Nominally Anhydrous Mantle Materials
viscosity law (dV5) speeds the sinking by about a half [36] If at the time when the instability accelerates down-
million years and removes more of the dense material, to a ward lateral flow cannot replenish material at the base of the
depth of about 90 km, while the baseline model removes the instability fast enough, the material joining the instability
dense material only to about 105 km depth. With the separates at its edges from the laterally adjacent lithosphere.
distribution of dense material used in these models, approx- The result is an annulus of thinned lithosphere, centered on
imately the lowest third of the dense region is removed in the instability. Asthenospheric material can be drawn up-
most models. ward into this relatively shallow annulus by convection
[34] The two experiments with lithosphere of 75 km (dV6 currents initiated by the moving instability, during which
and dV7) produce smaller instabilities that sink far more process the asthenosphere may melt adiabatically, depending
8 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
Figure 8c. To produce melt through this process on Venus
with a lithosphere 150 km thick, the mantle potential
temperature would have to be close to 1500°C. Possible
magma compositions resulting from this process are
described below.
4.2. Incompatible-Element-Triggered Melting
[39] The second opportunity for melting occurs if the
sinking material contains incompatible elements (in partic-
ular, H2O and CO2). Melting can occur in the instability
itself as it sinks if its temperature rises faster than its
pressure, which may allow the material to pass over its
solidus and begin melting. Examples of these paths are
shown in Figure 8b.
[40] If, in contrast, an instability sinks fast enough that
pressure increases faster than temperature, its path through
pressure-temperature space will either parallel or diverge
from its solidus, and no melting in the instability will occur.
As it sinks, the material may eventually lose volatiles and
alkalis under the effects of pressure and temperature (as a
subducting slab does on Earth [Keppler, 1996]), and trigger
melting in surrounding mantle or in the sinking material
itself if volatiles are concentrated in one region. This
melting can occur because the addition of even small levels
of incompatible elements can trigger melting in silicate
materials below their nominally dry solidi (in the case that
Venus has a non-peridotitic mantle or significantly different
lithospheric or temperature structure, the particulars of these
P-T paths and the solidi of the materials would change, but
Figure 7. Vector field shows upwelling into a shallow the principals remain the same). These processes together
annulus around the instability, where adiabatic melting can create the possibility of melting the material of the instabil-
occur under the correct conditions of temperature and ity itself, of melting the surrounding upper mantle if the
composition. Candidate region for melting is shaded. instability releases incompatible elements, or of enriching
the deeper Venusian mantle with material that neither
melted nor devolatilized.
[41] The initial temperature, conductive temperature
upon the solidus and temperature of the asthenosphere and
increase, and pressure change of the material at the center
the height of the topography in the annulus; the candidate
of each drip can be calculated from numerical experiment
region is marked in Figure 7. This mode occurs in the
results, and are given in Figure 8. The numerical experi-
minority of Venusian models, because it depends on the
ments presented here for the growth of gravitational insta-
lithosphere having sufficient stiffness to resist rapid inward
bilities and the sinking velocity of the unstable material have
flow around the axis of symmetry as the instability accel-
initial viscosities and rheologies that are appropriate for
erates, and it depends upon the mantle potential temperature
nominally dry material. In this process, however, we envi-
being sufficiently high that the small additional decompres-
sion melting in an incompatible-element enriched material.
sion provided by a brief upward flow causes the material to
A volatile-bearing, gravitationally unstable lower lithosphere
cross its solidus and melt.
may begin with a lower viscosity than used in the numerical
[37] Numerical experiments of gravitational instabilities
models here.
on Venus demonstrate less melting through this process than
[42] Material that sinks relatively slowly heats conduc-
do experiments using Earth conditions because the higher
tively to higher temperatures while at lower pressures;
temperature of the lithosphere on Venus produces a litho-
material that sinks quickly retain its initial temperature to
sphere more likely to flow and maintain a flat bottom than
greater depths. These two generalized paths result in
under equivalent Earth conditions. A flat lithospheric
different predictions: material that sinks slowly crosses
bottom removes the possibility of adiabatic rise for the
solidi in pressure-temperature space as it heats, and can
underlying mantle.
move into regions where damp peridotite or eclogite will
[38] In the numerical experiments presented here, only
melt while dry peridotite will not (Figure 8b). The drips that
those with lithosphere 75 km thick created melt through
sink quickly can descend into a region where free hydrous
adiabatic melting of nominally dry peridotite. These experi-
fluid exists. These latter drips therefore may release volatiles
ments produced melt only with a mantle potential temper-
into the surrounding mantle without necessarily melting
ature of 1,400°C, when using a linear solidus equivalent to
themselves (Figure 8c).
Hirschmann [2000] for nominally dry terrestrial peridotite.
[43] If material in a gravitational instability melts when it
The models dV6 and dV7 produce 100 km3 of melt over
is heated by surrounding unmelted upper mantle, it neces-
1 million years; the region of this melting is shown in
sarily must have a distinct composition that allows it to melt
9 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
Figure 8. (a) Solid lines: phase boundaries for peridotite with varying water content. Solidi are shown
for a range of water contents from zero to saturation. Below the solidus stability limits for water-bearing
minerals are shown, as is a shaded region in which no water-bearing minerals are stable, and so water will
be released as a free fluid. Dashed lines show solidi for carbonated eclogite: the composition of Yaxley
and Brey [2004] [YB] contained 15 wt% CO2, and that of Dasgupta et al. [2004] [DH] contained only
5 wt% CO2. The higher CaO content of the Yaxley and Brey [2004] composition may have stabilized
carbonate, effectively raising the solidus temperature. (b) Example paths of material in sinking
instabilities, showing paths in bold that heat sufficiently quickly that, depending upon their
compositions, may cross their solidi and produce melt. The dashed line shows the path of a quickly
sinking instability that will not cross solidi but may devolatilize at depth. (c) The regions covered by
paths of material in instabilities from numerical experiments are shaded. Dashed lines at the top of
these regions show the starting conditions of material in instabilities from 75 km and 150 km
lithospheres. Three example paths are shown in bold. Regions of dry adiabatic melt, incompatible-
enriched melting, and complete devolatilization are shown with bold outlines. Phase boundaries from
Kawamoto [2004], Herzberg et al. [2000], Takahashi et al. [1993], Trønnes and Frost [2002], Schmidt
and Poli [1998]. Dry peridotite solidus: Hirschmann [2000]. 2% water solidus: Litasov and Ohtani
[2003], Ohtani et al. [2004]. Water-saturated solidus: T. L. Grove (unpublished), Mysen and Boettcher
[1975]. Carbonated eclogite solidi: Yaxley and Brey [2004], Dasgupta et al. [2004].
10 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
at a lower temperature than that of upper mantle. The higher
the volatile content or the more fertile the major element
composition, the lower the solidus temperature. Thus where
melting will occur and to what extent it will proceed depend
entirely upon the major element and volatile composition
of the material melting. The calculations of melting with
enrichment of incompatible elements rely entirely on
phase equilibria that have been determined experimentally
(Figure 8) and are not included in the numerical models.
In the absence of incompatible element enrichments,
melting in the sinking, unstable material would be limited
to eclogite.
4.3. Resulting Magma Compositions and Viscosities
[44] Possible melting sources created by this hypothetical
dynamic process thus include nominally dry asthenospheric
peridotite, nominally dry eclogite, and their incompatible-
element enriched analogs (Figure 8). The melting behaviors
of these sources have been investigated experimentally and
have been measured in natural rocks, and some of the
possible magma compositions from partial melting of these
sources are shown in Figure 9. Varying extents of melting
from these sources can produce magmas with Mg#s from 30
to above 80 (where Mg# = 100 times molar Mg/(Mg + Fe)),
can have silica contents from 40 to 60 wt%, and alkali
contents up to several weight percent. Figure 9 also shows
three Venusian compositions measured by Soviet landers
[Surkov, 1990]. In most of their major element composi-
tions these melts fall between eclogitic and peridotitic melt
compositions, with the exception of one composition,
which contains approximately 4 wt% K2O and therefore
represents a composition significantly enriched in incom-
patible elements.
[45] The range of compositions of these magmas would
produce a range of viscosities. Possible viscosities have
been calculated over a range of melting temperatures using
the techniques of Bottinga and Weil [1972] and Shaw
[1972], and are shown in Figure 10. The viscosities range
Figure 9. Melt compositions expected for modeled
sources compared with Venusian compositions. Squares:
eclogite melts. Triangles: peridotite melts. Empty diamonds:
measured Venusian surface compositions. Data from
Klemme et al. [2002]; Pertermann and Hirschmann
[2003]; Pertermann et al. [2004]; Falloon et al. [1999];
Baker and Stolper [1994]; Walter [1998]; Fedorenko and Figure 10. Viscosities of magma compositions from
Czamanske [1997]; Surkov et al. [1983]. Figure 9. Filled symbols: viscosities calculated according
to Shaw [1972] and Bottinga and Weil [1972].
11 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
surrounding solid (2,800 kg/m3 versus 3,300 kg/m3). For
each 100 kg/m3 added to the density of the magma, its
velocity slows by a factor of 0.8. Therefore magma buoyancy
is not the most influential parameter of the model.
[48] Instabilities in the numerical experiments shown here
sink with velocities comparable to subducting slabs on
Earth, and will devolatilize when they pass into a region
in phase space where no volatile-bearing phases are stable,
and so fluids are expelled from solid phases. When stress-
dependence of viscosity is added, the velocity of the sinking
instability is far greater [Elkins-Tanton, 2007], and the most
viscous of magmas may be trapped in a rapidly sinking
instability. These rapidly sinking instabilities can carry
volatiles to depth, as can instabilities that neither melt nor
devolatilize.
5. Discussion and Conclusions
[49] The paradox of Venusian magmatic systems is the
range of apparent viscosities and compositions that are
required to make the landforms, and yet the planet appears
to be currently devoid of plate tectonics. An partial analogy
to Venus is magmatism that occurs on terrestrial continents
in the absence of subduction, for example, the alkalic
basalts that have been erupted on the Tibetan plateau [Bird,
1979; Turner et al., 1996], in the Sierra Nevada [Van Kooten,
1980; Ducea and Saleeby, 1998; Jones and Phinney, 1998;
Manley et al., 2000; Elkins-Tanton and Grove, 2003] as well
as in the vicinities of Rome and Naples, Italy [Conticelli
and Peccerillo, 1992]; the Colorado and Wasatch Plateaus
Figure 11. Fluid rise velocities versus sinking drip [Wannamaker et al., 2000], and western Mexico [Righter,
velocities. Double-ended arrows: velocity ranges of sinking 2000; Carmichael et al., 1996]. These events are widely
instabilities estimated using Stokes’ law. Bold box: thought to be caused by instabilities sinking from the
velocities measured from numerical experiments. Shaded lower crust or mantle lithosphere and allowing hotter
regions: fluid percolation velocities calculated by Darcy’s upper mantle to rise, causing melting [e.g., Kay and Kay,
law for magmas or fluids rising from sinking instabilities. 1993; Ducea and Saleeby, 1998; Farmer et al., 2002;
Magmas and fluids will escape sinking instabilities in Elkins-Tanton and Grove, 2003].
almost all cases. [50] Though the atmosphere of Venus contains only
minute amounts of water, its interior likely retains some
over three orders of magnitude, with the measured Venusian small fraction of water and carbon dioxide, as well as other
compositions lying in the middle of the field. incompatible elements. Any initial volatile content of the
[46] Magmas may be produced in the upper mantle and planet will be partitioned into melt and degassed to build the
may therefore rise either to freeze in the lithosphere or to planet’s dense atmosphere. Some fraction of the initial
erupt. Magmas may also be produced in the sinking insta- volatile content will be retained in the solid mantle, ranging
bility itself, raising the question of the likelihood of their from 100% in regions that have not been melted, to 1 to 2%
escape from the instability. Given the viscosity range of these in regions that have experienced melting depending upon
magmatic compositions and the predicted velocities of the partition coefficient [Bolfan-Casanova and Keppler,
sinking instabilities, the likelihood of escape of liquids from 2000; Koga et al., 2003; Aubaud et al., 2004; Bell et al.,
falling instabilities can be calculated by comparing the Darcy 2004]. The interior of Venus therefore contains some
velocity of the rising magma with the sinking velocity of the fraction of volatiles to the present-day.
instability; these calculations are shown in Figure 11. [51] The lithosphere of Venus consists of magmas, more or
[47] The sinking velocities of instabilities in numerical less processed, that originated from melts of its interior.
models using only temperature- and pressure-dependent Portions of Venus’ lithosphere will therefore be volatile-
viscosity laws is in general slower than the theoretical Stokes bearing if the planetary interior is volatile-bearing. Sinking
flow velocity, because the instability is retarded in its fall by lithospheric material will carry incompatible elements (vola-
a neck of cooler material attaching it to the lithosphere. In tiles and alkalis in particular) back into the mantle. As
these numerical experiments, assuming the range of magma demonstrated by the numerical experiments presented here,
viscosities calculated and shown in Figure 11, all melts and melting in the sinking material or its surrounding upper mantle
liquids will escape sinking instabilities and either reach the may be induced by devolatilization or conductive heating.
surrounding upper mantle or rise up the neck of the insta- [52] Pancake domes have been proposed to consist of
bility to reach the lithosphere. The magma density used in silicic compositions or vesiculated basalts [Pavri et al.,
these calculations is 500 kg/m3 lower than the assumed 1992; Ivanov and Head, 1999] or basaltic compositions
12 of 15E04S06 ELKINS-TANTON ET AL.: VENUSIAN GRAVITATIONAL INSTABILITIES E04S06
perhaps emplaced episodically [Bridges, 1997; Stofan et al., carbon dioxide-rich fluids from a sinking instability, very
2000; Plaut et al., 2004]. Because of the likelihood of low viscosity carbonatite magmas could only be produced
explosive eruptions of silicic compositions, and the diffi- in small volumes through this process. The production of
culty of creating flow of these magmas in the absence of channels requires many hundreds or even thousands of
volatile-driven eruptions, these domes may more likely cubic kilometers of magma. These magmas are therefore
consist of basaltic compositions emplaced at lower temper- far more likely to be produced from a crustal source during
atures and in small volumes. Venusian festooned flows, a global climate change; the surface temperature of Venus is
however, may be more silicic, perhaps rhyolitic [Moore, close enough to the melting temperature of carbonatites that
1987; Manley, 1993]. a relatively small excursion in temperature could sweat
[53] Rocks at the Venera 8 landing site have K contents as carbonatite magmas from large volumes of crust of appro-
high as 4 ± 1.2 wt% and U as high as 2.2 ± 0.7 ppm [Surkov, priate composition [Kargel et al., 1994; Treiman, 1995], but
1990; Nikolaeva and Ariskin, 1999]. Nikolaeva and Ariskin only if sufficient pressure was present to prevent the
[1999] suggest that the Venera 8 composition may be the carbonate from degassing rather than melting.
result of melting an eclogite, while the other magmas may [57] The sinking of compositionally dense lithospheric
be mantle melts. Kargel et al. [1993] suggested that the material into the Venusian mantle provides an almost
enhanced alkali compositions may be the result of increased complete analog process to terrestrial subduction zones.
carbon dioxide and decreased water activity in the melting The sinking material may carry a range of incompatible
source, and McKenzie et al. [1992] suggested that melting elements and may refertilize the mantle with volatiles and
with some degree of water is consistent with the magmas eclogite. Melting these new eclogitic sources may allow the
required to make pancake domes. production of boninites and adakites, distinctive subduction-
[54] The predictions of the numerical experiments pre- related magmas on Earth, in the absence of plate tectonics.
sented here are consistent with these hypotheses based on In the longer term, this process of melting and refertilizing
surface features: the lithospheric instability model predicts could produce material similar to the earliest continental
that both eclogitic and peridotitic melts will be produced, as crust on Earth, the tonalite-trondhjemite-granodiorite prov-
well as melts over a small range of temperatures and with a inces [Bedard, 2006].
range of incompatible elements. Higher viscosity melts
appropriate for festoon flows may be created from eclogitic [58] Acknowledgments. This research was conducted with support
melts from the instability, and melts appropriate for the from the NSF Petrology and Geochemistry program. Constructive reviews
by R. Dasgupta and an anonymous reviewer improved the paper.
creation of pancake domes may originate from source
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