# Hot climate inhibits volcanism on Venus: Constraints from rock deformation experiments and argon isotope geochemistry

Sami Mikhail, Michael Heap

► To cite this version:

Sami Mikhail, Michael Heap. Hot climate inhibits volcanism on Venus: Constraints from rock deformation experiments and argon isotope geochemistry. Physics of the Earth and Planetary Interiors, 2017, 268, pp.18 - 34. 10.1016/j.pepi.2017.05.007. hal-01615055

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1 Hot climate inhibits volcanism on Venus: Constraints from rock deformation experiments and argon isotope geochemistry

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4 Sami Mikhail¹,²* and Michael J. Heap³

5 ¹The School of Earth and Environmental Sciences, The University of St Andrews, U.K.

6 ²St Andrews Centre for Exoplanet Science, The University of St. Andrews, U.K.

7 ³Géophysique Expérimentale, Institut de Physique de Globe de Strasbourg, France.

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9 *Corresponding author: S. Mikhail (sm342@st-andrews.ac.uk)

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11 Abstract

12 The disparate evolution of sibling planets Earth and Venus has left them markedly different. Venus'
13 hot (460 °C) surface is dry and has a hypsometry with a very low standard deviation, whereas
14 Earth's average temperature is 4 °C and the surface is wet and has a pronounced bimodal
15 hypsometry. Counterintuitively, despite the hot Venusian climate, the rate of intraplate volcano
16 formation is an order of magnitude lower than that of Earth. Here we compile and analyse rock
17 deformation and atmospheric argon isotope data to offer an explanation for the relative contrast in
18 volcanic flux between Earth and Venus. By collating high-temperature, high-pressure rock
19 deformation data for basalt, we provide a failure mechanism map to assess the depth of the brittle-
20 ductile transition (BDT). These data suggest that the Venusian BDT likely exists between 2–12 km
21 depth (for a range of thermal gradients), in stark contrast to the BDT for Earth, which we find to be
22 at a depth of ~25-27 km using the same method. The implications for planetary evolution are
23 twofold. First, downflexing and sagging will result in the sinking of high-elevation structures, due
24 to the low flexural rigidity of the predominantly ductile Venusian crust, offering an explanation for
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the curious coronae features on the Venusian surface. Second, magma delivery to the surface—the
most efficient mechanism for which is flow along fractures (dykes; i.e., brittle deformation)—will
be inhibited on Venus. Instead, we infer that magmas must stall and pond in the ductile Venusian
crust. If true, a greater proportion of magmatism on Venus should result in intrusion rather than
extrusion, relative to Earth. This predicted lower volcanic flux on Venus, relative to Earth, is
supported by atmospheric argon isotope data: we argue here that the anomalously unradiogenic
present-day atmospheric $^{40}$Ar/$^{36}$Ar ratio for Venus (compared with Earth) must reflect major
differences in $^{40}$Ar degassing, primarily driven by volcanism. Indeed, these argon data suggest that
the volcanic flux on Venus has been three times lower than that on Earth over its 4.56 billion year
history. We conclude that Venus' hot climate inhibits volcanism.
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# 1 Introduction

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The present-day differences in the expression and intensity of volcanism on the telluric planets serves as a testament to the dynamic nature of planetary evolution (Wilson, 2009). For example, Earth and Venus are colloquially referred to as sibling planets because of their similar mass and bulk composition (i.e., bulk petrology). However, their contrasting atmospheric mass and chemistry (e.g., Gaillard and Scaillet, 2014; Mikhail and Sverjensky, 2014), climate (e.g., Pollack et al., 1980), and geomorphology (e.g., Head and Solomon, 1981; Donahue and Russell, 1997; Basilevsky and Head, 2003; Ghail, 2015) and volcanic character (e.g., Fegley and Prinn, 1989; Head et al., 1992; Wilson, 2009) is striking: Earth is a crucible of life, whereas Venus is a barren wasteland. Suffice to say, then, Earth and Venus are not identical siblings. The major differences between Venus and Earth are discussed in detail below.

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First, the average surface temperatures are 460 and 4 °C on Venus and Earth, respectively. The Earth also has an excess in surface water of about $1.2 \times 10^{21}$ kg compared to Venus, a difference between five and six orders of magnitude (Donahue, 1999; Lécuyer et al., 2000). The high temperature and low water content of the Venusian surface are a combined consequence of the absence of a magnetic field (Donahue and Russell, 1997), the presence of a dense atmosphere dominated by CO$_2$ (at a pressure of 9 MPa), and its proximity to the Sun (with a solar irradiance of 2611 W/m$^2$, compared with 1366 W/m$^2$ on Earth).

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Second, hypsometric data show that >80% of the surface elevation of Venus ranges from -1.0 to +2.5 km; only ~2% of the surface lies >2 km above the median radius (Fig. 1) (Head and Solomon, 1981; Basilevsky and Head, 2003; Taylor and McLennan, 2009). The surface of Earth, by contrast, has a pronounced bimodal hypsometry (i.e., it has continental rises and ocean basins; Fig. 1). The fact that Venus has a hypsometry with a very low standard deviation is not easily attributable to the absence of plate tectonics on Venus, because Mars—a planet that, like Venus, operates a stagnant-lid tectonic regime (Head and Solomon, 1981; Head et al., 1992; Donahue and Russell, 1997; Basilevsky and Head, 2003)—has a surface hypsometry with a very large standard deviation (Fig.
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Third, the way in which volcanism is manifest on Earth and Venus differs substantially (e.g., Wilson and Head, 1983; Wilson, 2009). For example, while the majority (ca. 90%) of Earth's volcanism occurs along curvilinear belts and rift-margins, which collectively define tectonic plate boundaries (Cottrell, 2015), Venus operates a stagnant-lid tectonic regime and is dominated by features interpreted to be related to mantle plumes (e.g., Head et al., 1992). Although Venus is host to volcanic features commonly observed on Earth, such as lava plains, discrete lava flows, shield volcanoes, and shield fields, it is also home to enigmatic, flat landforms such as coronae (Head et al., 1992; Stofan et al., 1992; Squyres et al., 1992; McKenzie et al., 1992; Grosfils and Head, 1994; Addington, 2001; Krassilnikov and Head, 2003; Grindrod and Hoogenboom, 2006; Robin et al., 2007; Wilson, 2009; Krassilnikov et al., 2012; Ivanov and Head, 2013).

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An important difference between volcanism on Earth and Venus is that, by comparing intraplate volcanic fluxes on both Earth and Venus, it is clear that Earth is the most volcanically active of the two planets, possibly by an order of magnitude (Ivanov and Head, 2013). Indeed, while volcanic activity on Earth is evidently abundant, evidence for ongoing, present-day volcanism on Venus is comparatively sparse, although it is thought that the vast majority of the Venusian surface is volcanic in origin (Head et al., 1992; Basilevsky and Head, 2003; Wilson, 2009). However, a number of recent findings suggest that volcanic activity on Venus persists to the present: [1] infrared radiation from three volcanic regions showed some flows to be warmer than their surrounding rocks, implying that these lavas are younger than 2.5 Ma (Smrekar et al., 2010); [2] sporadic atmospheric SO₂ fluctuations have been observed at Venus (Esposito, 1984; Marcq et al., 2011); and [3] thermal spikes have been reported at Ganiki Chasma, a rift valley proximal to Ozza and Maat Montes (Shalygin et al., 2015). In addition, the sulfuric clouds that envelop the entire planet would not persist beyond 1–50 Ma without the replenishment of SO₂, the source of which is presumed to be magmatic (Fegley and Prinn, 1989; Bullock and Grinspoon, 2001).

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To emphasise the difference between volcanic activity on Earth and Venus: while Earth's oceanic
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crust (that covers 60% of Earth's surface) has created >100,000 individual volcanoes (including
seamounts) in <100 Ma (e.g., Wessel et al., 2001 and references therein), Venus' entire surface has
produced roughly 70,000 individual volcanoes in <700 Ma (Head et al. 1992). The difference in the
rate of volcano production is therefore about an order of magnitude greater on Earth than on Venus.

We further note that, because >70% of all extrusive volcanism on Earth occurs beneath ocean
depths >1000 m under pressures >9 MPa, the presence coronae, a landform unique to the surface of
Venus, cannot simply be explained by the high Venusian atmospheric pressure (Smith, 1996). To
wit, Earth's ocean basins are not littered with coronae, but with well-formed stratovolcanoes (i.e.,
seamounts).

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The principal goal of this contribution is to explore the reasons as to why Earth hosts vastly more
intraplate volcanoes than Venus. To do so, we formulate a conceptual model that combines data
from rock deformation experiments on basalts, which inform on the mechanical behaviour of the
crust and therefore the depth of the brittle-ductile transition (BDT) on both planets, with
atmospheric noble gas isotope data from Earth and Venus, which inform on planetary volcanic flux.

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Additionally, our model also offers an explanation as to why volcanoes on Venus are
morphologically distinct from those on Earth.

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## 2 The deformation mode of the Terran and Venusian crusts

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The depth of the BDT on Venus has been estimated numerous times. For example, first-order
morphological differences between fold and thrust belts on Earth and Venus can be explained by a
shallow BDT on Venus relative to Earth (Williams et al., 1994). Spacing between adjacent
extensional structures may match the spacing between linear bands seen in the mountains of Ishtar
Terra on Venus if the surficial brittle layer is no more than a few km in thickness (Solomon and
Head, 1984). Preservation of substantial crater topographic relief on Venus is likely the result of a
thin (<10 km) brittle crust (Grimm and Solomon, 1988). Further, surface features within tesserae
(e.g., ribbons, long-wavelength folds, and grabens) offer a wealth of information as to the depth and
114 evolution of the BDT on Venus (Phillips and Hanson, 1998). For example, ribbons within tesserae
115 (Hansen and Willis, 1996) suggest a BDT as shallow as ~1 km during their formation (Hansen and
116 Willis, 1998; Ghent and Hansen, 1999; Ruiz, 2007). Of interest, long-wavelength folds and graben
117 are thought to reflect a deepening of the BDT over time (Phillips and Hanson, 1998)—but the depth
118 of the BDT during the formation of long-wavelength folds is estimated at only ~6 km depth (Brown
119 and Grimm, 1997; Ghent and Hansen, 1999). The pervasive deformation of the plateau highland
120 tesserae, the oldest preserved terrain, requires a weak, thin lithosphere (Brown and Grimm, 1999).
121 However, the presence of highland regions and large shield volcanoes (e.g., Crumpler et al., 1986;
122 Smrekar and Soloman, 1992; McGovern et al., 2014) implies localised crustal domains where the
123 BDT is deep enough to provide support for these structures. Nonetheless, these studies suggest that,
124 on average, the BDT on Venus is shallower than that on Earth.
125 We use here an experimental rock deformation approach to provide an alternate assessment for the
126 depth of the present-day BDT on Venus and Earth (see also Heap et al., 2017), which we interpret
127 here as a purely mechanical boundary between brittle and ductile behaviour. To do so, we compiled
128 experimental rock deformation data on basaltic (and diabase) samples deformed over a range of
129 confining pressures (analogous to depth) and temperatures (Table 1). We used these data to
130 construct a failure mode map that highlights the pressures and temperatures at which basaltic (and
131 diabase) rocks behave either in a brittle or a ductile manner in response to applied stress. We then
132 used this map to assess the position (depth) of the BDT on Earth and Venus. We first review some
133 important considerations for our experimental approach.

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135 *2.1 Considerations for our experimental approach*

136 2.1.1 Composition of the Venusian crust

137 There is a dearth of *in-situ* quantitative geochemical data for Venusian surface rocks, and the
138 planet's thick CO₂-dominated atmosphere makes optical geological observations from orbit or
Earth-based telescopes impossible. The only available *in-situ* geochemical data from Venus are the major element composition of surface rocks, measured using gamma-ray and X-ray fluorescence spectroscopy. The three localities measured show basaltic compositions with SiO₂, FeO, MnO, and MgO abundances similar to mid-ocean ridge basalts on Earth (summarised in Bougher et al., 1997). Furthermore, the data from Venera 13 and 14 (Fe/Mg, Mg/Mn, K/U, and U/Th ratios) suggest Venus and Earth are made of the same chondritic material and have a similar internal structure, and that Venusian basalts are the product of similar degrees of partial (peridotite) mantle melting as those on Earth (Treiman, 2007; Hess and Head, 1990). Combined with the geomorphological data of Venus from radar imagery (i.e., reflectance spectra), it appears that most of the Venusian surface is volcanic in origin. This means the vast majority of the Venusian and Terran crusts are basaltic in their bulk composition (Basilevsky and Head, 2003). Therefore, we consider the deformation mode (i.e., brittle or ductile) of basaltic rocks collected on Earth to be analogous to the deformation mode of those on Venus.

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## 2.1.2 Hydration of the Venusian crust

The Venusian atmosphere is extremely arid, with 150 times less H₂O compared with Earth's exosphere (Donahue and Russell, 1997). However, the lack of water in Venus' atmosphere and on its surface does not necessarily imply a desiccated crust. We suggest that the degree of hydration for Venusian crust and mantle (e.g., Kaula, 1990; Nimmo and McKenzie, 1996; Mackwell et al., 2008) requires re-examination. Note, the degassing of water is extremely inefficient for one-plate planets such as Venus or Mars. For example, it has been modelled that 90-95% of Mars' primordial water reserves should be retained in the mantle following accretion (Hunten, 1993), and recent data show the Martian mantle to be as 'wet' as the Terran mantle (McCubbin et al., 2012).

Combined, these studies conclude that substantial aqueous fluids can remain within planetary interiors, irrespective of the plate tectonic regime and without correlation to the degree of surface desiccation. For instance, if one were to distribute all of the water in the Earth's oceans into the
Venusian mantle, the water abundance (distributed in nominally anhydrous minerals) would not exceed the storage capacity of a peridotitic mantle (Bell and Rossman, 1992; Kohlstedt et al., 1996; Bolfan-Casanova et al., 2000; Lécuyer et al., 2000; Hirschmann, 2006; Smyth et al., 2006). Furthermore, the Martian surface and atmosphere are both very water poor, but we know that the crust on Mars is hydrated (Carr and Head, 2010; 2015). A volatile-rich interior on Venus (or at least a hydrated mantle) could result in explosive volcanism (Thornhill, 1993; Fagents and Wilson, 1995; Glaze et al., 2011; Airey et al., 2015), and some workers have proposed that some morphological units on the Venusian surface are pyroclastic deposits (Campbell and Rogers, 1994; McGill, 2000; Grosfils et al., 2011; Ghail and Wilson, 2013). Therefore, it is difficult to definitively conclude whether the crust and upper mantle on Venus is desiccated or hydrous, and only future missions to Venus can resolve this question. Because of this ambiguity, we contend that the consideration of all of the available experimental rock deformation data for basalt and diabase (including the ultra-dry diabase data from Mackwell et al., 1998) is an effective approach to investigate the failure mode of rock within the Venusian crust. We also note that the majority of the basalts deformed in these studies only contain a subordinate glass phase, if any. As a result, the impact of a glass phase, hydrated or otherwise, should only play a very minor role in dictating the rheological behaviour of a given sample (Smith et al., 2011; Violay et al., 2012; 2015).

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## 2.2 Determining the depth of the brittle-ductile transitions for Earth and Venus

### 2.2.1 Essential nomenclature: brittle and ductile

Before interpreting the collated experimental rock deformation data it is important to outline some essential nomenclature. The terms ‘brittle’ and ‘ductile’ are sometimes interpreted differently across disciplines, which can cause confusion. To avoid such confusion, we define how we use these terms.

Here, we use ‘brittle’ and ‘ductile’ to describe the failure mode of a rock sample on the lengthscale
of that sample (typically between 10 and 100 mm). Brittle behaviour is characterized by localised
deformation, typically manifest as axial splits or shear fractures. During a deformation experiment,
it is typical to observe an increase in porosity of a sample as the peak stress is approached. This
increase in porosity is the result of the growth and formation of dilatant microcracks. Following a
peak stress, a brittle experiment involves a stress drop (i.e., strain softening). This stress drop marks
the point at which a macroscopic (i.e., across the lengthscale of the sample) fracture is forming or
has formed—the hallmark of a brittle failure mode (see Hoek and Bieniawski, 1965; Brace et al.,
1966; Scholz, 1968). We note that, in the case of highly porous samples, brittle deformation can be
associated with a net decrease in porosity. In these cases, inspection of the post-deformation sample
is required to verify the presence of axial splits or shear fractures.

We use the term ductility as per the definition of Rutter (1986), who described it as simply the
capacity of a material to accommodate qualitatively substantial strain without the tendency to
localise the flow into faults—localisation does not occur on the sample lengthscale. The concept of
ductility is not dependent on the mechanism of deformation (Rutter, 1986). Although brittle
behaviour is always the result of cracking on the microscale, ductile behaviour can be the product of
a number of micromechanisms. For example, the micromechanism behind low-temperature, high-
pressure cataclastic flow (i.e., ductile behaviour) is microcracking (Menéndez et al., 1996; Wong et
al., 1997). Ductile behaviour typically involves the loss of porosity. We note that ductile behaviour
can be associated with strain localization in certain circumstances: ductile behaviour in porous
rocks can involve the formation of compaction bands (e.g., Baud et al., 2004) or bands of collapsed
pores (e.g., Heap et al., 2015). The formation of such features is also associated with small stress
drops in the mechanical data. In ambiguous cases, inspection of the post-deformation sample is
required to verify the absence of axial splits or shear fractures, features synonymous with a brittle
failure mode. Mechanical behaviour for two experiments is shown in Fig. 2, a typical brittle test and
a typical ductile test (Violay et al., 2012; Heap et al., 2017).
216 2.2.2 Data selection

217 In the context of our study, we are interested in the transition between brittle behaviour and ductile
218 behaviour as a result of viscous flow (i.e., the change in micromechanism from microcracking to
219 viscous flow). We interpret viscous flow as non-recoverable viscoelastic deformation; this type of
220 deformation is referred to as ‘plastic’ by some authors, but this term is sometimes also used to
221 describe non-recoverable deformation in the brittle field. Since we are interested in the change in
222 deformation micromechanism, we are not concerned here with low-temperature ductility driven by
223 microcracking or cataclastic pore collapse, although very few studies exist on this topic for basaltic
224 rocks (e.g., Shimada, 1986; Shimada et al., 1989; Adelinet et al., 2013; Zhu et al., 2016). We
225 included all available experimental rock deformation data for basalt and diabase into our analysis
226 (Table 1), with the exception of room-temperature experiments under uniaxial conditions (e.g., Al-
227 Harthi et al., 1999; Heap et al., 2009; Schaefer et al., 2015), because they are of little use for
228 determining the BDT, and those triaxial experiments that yielded non-viscous ductile behaviour
229 such as cataclastic pore collapse (e.g., Shimada, 1986; Shimada et al., 1989; Adelinet et al., 2013;
230 Zhu et al., 2016).

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232 2.2.3 Limitations to our approach

233 One obvious limitation of our collation approach is that typical laboratory strain rates (~10⁻⁵ s⁻¹) are
234 much faster than tectonic strain rates (e.g., Grimm, 1994). However, we recognise that [1]
235 experiments already classified as ductile at laboratory strain rates will remain ductile at lower (i.e.,
236 natural) strain rates, and [2] lowering the strain rate at low experimental pressures and temperatures
237 will reduce rock strength—because of the increased time available for subcritical crack growth (see
238 Brantut et al., 2013 for a review)—but may not promote ductile deformation *per se*. For example,
239 the experiments of Heap et al. (2011) showed that basalt can still fail in a brittle manner at a low
240 laboratory strain rate of 10⁻⁹ s⁻¹. Although our approach utilises experiments conducted at high
strain rates, and so should be considered with this caveat in mind, our method does not assume a representative basalt for the Venusian crust (see section 2.1 above).

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## 2.2.4 Calculating depth

Each published experimental datum was assigned a failure mode: brittle or ductile, defined above. Where necessary, and when possible, our definitions supersede those outlined in the studies from which these data were collated. The effective pressure under which each experiment was performed were converted to a depth with the relation $P = \rho \cdot g \cdot h$, where P is lithospheric or hydrostatic pressure and g is surface gravitational acceleration, taken as 9.807 and 8.87 m/s² for Earth and Venus, respectively. This approach allowed us to determine the lithostatic pressure gradients for Earth and Venus. The bulk rock density, $\rho$, was determined with the following relation (Wilson and Head, 1994):

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$$ \rho(h) = \frac{\rho_{\infty}}{[1 + \{V_0 - (1 - V_0)\} \exp(-\lambda \rho_{\infty} gz)]} \quad (1) $$

where $\rho_{\infty}$ (the density of porosity-free rock) was taken as 2900 kg/m³, $V_0$ is the void space fraction (i.e., total porosity) at the surface (assumed here to be 0.25; see Wilson and Head, 1994), and the constant $\lambda$ was assumed to be $1.18 \times 10^{-8}$ Pa⁻¹ (Head and Wilson, 1992). Because of the very high atmospheric pressure of Venus, the lithostatic pressure at the surface was taken as 9 MPa. The hydrostatic pressure gradient for Earth was calculated using a constant water density of 1,000 kg/m³ (yielding a pore pressure gradient of ~9.8 MPa/km). We note that the density of water does not vary considerably at the pressures and temperatures relevant for the Earth's crust.

However, the nature of the pore fluid, and therefore the pore pressure gradient, for Venus is enigmatic. The behavior of CO₂ at the atmospheric pressure and temperature of Venus is that of a
supercritical fluid and, if one assumes that supercritical CO₂ is a plausible pore fluid for Venus, the density will vary with pressure and temperature. For example, the density of CO₂ at the surface of Venus (at a pressure of 9 MPa and a temperature of 460 °C) is 65 kg/m³. CO₂ density increases to 457 kg/m³ at a pressure of 100 MPa and a temperature of 600 °C. Because of the relatively broad parameter space for pore fluid behaviour (and composition) on Venus, we considered three scenarios that likely capture the range of possible pore fluid densities within the Venusian crust. In one, the pore fluid had a constant density of 1,000 kg/m³ (i.e., the same as on Earth, yielding a pore pressure gradient of ~8.9 MPa/km); in the second scenario, pore fluid had a density of 500 kg/m³ and so a pore pressure gradient of ~4.4 MPa/km. In the third scenario, pore fluid density was 100 kg/m³, giving a pore pressure gradient of ~0.89 MPa/km. In all cases, the pore pressure at the surface was taken as 9 MPa. In our analysis, we interpreted the pressure within the crust as the lithostatic pressure minus the pore fluid pressure.

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278 2.2.5 Thermal gradients

Because we are discussing planetary-scale processes, we have opted to constrain the BDT on Earth using an average Terran geothermal gradient of 25 °C/km and an average surface temperature of 4 °C. Due to the lack of heat-flux measurements on Venus, all of the published thermal gradients are inferred. Importantly, as a result of the greenhouse effect imposed by an average atmospheric pressure of 9 MPa and a permanent cloud cover on Venus (Pollack et al., 1980), there is no meaningful difference in average surface temperature across the Venusian day-night cycle (where one Venusian day is equal to 116 Earth days) or with changes in latitude from the equator. In addition, since Venus has a hypsometry with a very low standard deviation (Fig. 1) there is an insignificant effect of altitude on the surface temperature when one considers a global average. Therefore, a representative surface temperature for Venus should have a small standard deviation from the assumed average value of 460 °C. To account for the uncertainty in the Venusian thermal gradient, we have used a selection of values from 5–40 °C/km (e.g., Sclater et al., 1980; Solomon
291 and Head, 1982; 1984; Grimm and Solomon, 1988; Burt and Head, 1992; Turcotte, 1993; 1995;
292 Solomatov and Moresi, 1996; Turcotte et al., 1999; Leitner and Firneis, 2006).

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294 2.2.6 BDT estimates for Venus and Earth using experimental data

295 Once the effective pressure of each experiment was converted to a depth, these data were plotted
296 against the experimental temperature to examine the predicted depth of the present-day brittle-
297 ductile transition on Earth (Fig. 3) and Venus (Fig. 4). The majority of experiments performed with
298 basaltic rock samples were conducted under pressures equating to depths from 0 km (i.e., the
299 surface) to 7 km (Shimada and Yukutake, 1982; Caristan, 1982; Bauer and Handin, 1983; Shimada,
300 1986; Duclos and Paquet, 1991; Schultz, 1993; Rocchi et al., 2004; Apuani et al., 2005; Benson et
301 al., 2007; Ougier-Simonin et al., 2010; Heap et al., 2011, Violay et al., 2012; Adelinet et al., 2013;
302 Violay et al., 2015; Schaefer et al., 2015; Zhu et al., 2016); few studies were performed under
303 pressures corresponding to depths of up to 40 km (Griggs et al., 1960; Caristan, 1982; Hacker and
304 Christie, 1991; Mackwell et al., 1998; Violay et al., 2012; 2015). In all cases, ductile behaviour was
305 not observed below temperatures of 500 °C, even under an effective pressure of 500 MPa (e.g.,
306 Griggs et al., 1960). As expected, ductile behaviour is more commonly observed under combined
307 high pressure and high temperature. Surprisingly, ductile behaviour was observed under room
308 pressure (i.e., 0.1 MPa) at 800 °C (Figs. 3 and 4), which was likely the result of the presence of a
309 melt phase; therefore, although these samples were of a basaltic bulk composition, they may not
310 typify basaltic rocks. However, we prefer to retain all data for rocks of a basaltic composition in our
311 analysis, for two reasons: first, not all of the experimental studies offer a detailed microstructural
312 and compositional breakdown of their basaltic samples; second, we do not want to remove data
313 based on our interpretation of what constitutes a basaltic rock typical of Venus or Earth.

314 Our analysis predicts that the BDT for the oceanic crust of Earth occurs at a depth of ~25-27 km
315 (Fig. 3), consistent with the broad temperature-dependent (i.e., ~10-40 km depth) brittle-ductile
316 transition predicted for a predominantly basaltic oceanic crust on Earth (Kohlstedt et al., 1995).
Assuming a pore fluid pressure gradient on Venus of ~8.7 MPa/km (Fig. 4a), we find that most of the thermal gradients for Venus (i.e., 5–40°C/km) pass through a zone (from ~5 to ~18 km depth) characterised by both brittle and ductile deformation. The difference in failure mode over this depth interval arises from differences in rock properties such as composition, crystal size and content, and porosity, as well as in factors such as strain rate (although we note that typically laboratory strain rates rarely deviate from 10⁻⁵ s⁻¹). We interpret this depth interval on Venus as a failure mode ‘transitional’ zone. Below a depth of ~20 km, our collated experimental data predict exclusively ductile behaviour when the thermal gradient is 15 °C/km or above for a pore pressure gradient of ~8.7 MPa/km (Fig. 4a). However, this failure mode transitional zone is much shallower in the (arguably more plausible) scenarios under which the Venusian pore pressure gradient is lower (Figs. 4b and 4c). The failure mode transition zone on Venus exists at a depth of ~4–14 km (Fig. 4b) or ~2–12 km (Fig. 4c) for pore pressure gradients of ~4.4 or ~0.89 MPa/km, respectively.

Based on these collated experimental data, we conclude that the BDT occurs at a substantially shallower depth on Venus than on Earth (when one considers global averages) (Figs. 3 and 4).

Therefore, these data show that although much of the crust on Earth behaves in a brittle manner, the majority by volume of the Venusian crust should respond to stress in a ductile manner.

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## 3 Implications of a dominantly ductile crust on Venus

### 3.1 Implications for volcano morphology

The tallest volcanoes on Earth, Venus, and Mars are intraplate volcanoes fed by deep-seated mantle plumes (Head and Solomon, 1981; Donahue and Russell, 1997; Herrick et al., 2005; Wilson, 2009): Mauna Loa on Earth (17.2 km of relief), Maat Mons on Venus (9 km of relief; Mouginis-Mark, 2016), and Olympus Mons on Mars (21.9 km of relief; Plescia, 2004), respectively. However, shield volcanoes on Earth and Venus are dramatically different in terms of morphology: those on Venus are, on average, wider and of lower elevation than those on Earth (700 km wide and 1.5 km
relief vs. 120 km wide and 8 km relief, respectively) (Head and Solomon, 1981; Head et al., 1992; Herrick et al., 2005; Wilson, 2009). Because the loci of intraplate volcanism on Earth vary as tectonic plates move across fixed mantle plumes, the maximum elevation of a volcano is therefore not only supply limited, but is also constrained by the velocity of the plate (Morgan, 1971). By contrast, Venus' stagnant-lid tectonic regime enables a volcano to grow for as long as the magma source persists. Note, although it is debateable if plumes on Earth and Venus are geometrically similar (Schubert et al., 1990; Stofan et al., 1995; Smrekar and Stofan, 1997; Jellinek et al., 2002; Johnson and Richards, 2003; Ernst et al., 2007; Robin et al., 2007), the large shield volcanoes observed on the Venusian surface are taken as evidence for long-lived mantle plumes in the Venusian interior (Head and Solomon, 1981; Head et al., 1992; Herrick et al., 2005; Wilson, 2009).
With all else being equal, the average relief of shield volcanoes on Venus should therefore be greater than their Terran counterparts (Wilson, 2009). But, other than some rare if notable exceptions (e.g., Maat and Skadi Montes), Venusian volcanoes are not higher in relief than their Terran counterparts. To explore this discrepancy we assess here three first-order variables that we consider important in controlling the elevation of a volcanic construct: [1] surface gravity, [2] the viscosity of extruded lavas, and [3] the flexural response of the lithosphere to geological loads.

### 3.1.1 Surface gravity

Mars is host to the largest volcanoes in the Solar System. This is, in part, because high-relief structures are easier to build and retain on Mars because of its relatively low surface gravity (i.e., 3.71 m/s², compared with 9.81 m/s² and 8.81 m/s² on Earth and Venus, respectively) (Heap et al., 2017). However, the surface gravitational acceleration on Venus is very similar to that of Earth meaning that, if all else were equal, both planets should extrude lava flows of a similar thickness and build shield volcanoes of a similar size over a given timescale. Large basaltic flows on Earth are typically <30 m thick, and—again, because of the comparable surface gravitational accelerations of Earth and Venus—the same should be true for Venus. This inference is consistent
368 with radar imaging of Venus that shows that flows rarely exceed the vertical resolution of the
369 Magellan topographic data (which has a height resolution of 5-50 m; e.g., Pettengill et al., 1991;
370 Roberts et al., 1992; Wilson, 2009). We conclude therefore that the minor difference in surface
371 gravity between Earth and Venus cannot explain the considerable contrast in volcano relief.

372

373 3.1.2 Viscosity of extruded lava flows

374 On Earth, high-viscosity lavas are better able to construct a tall volcanic edifice than low-viscosity
375 lavas, which tend to travel much greater distances from the vent (e.g., Harris and Rowland, 2009).

376 Although the bulk composition of Earth and Venus are similar (Bougher et al., 1997), the
377 substantial influence of water content on the viscosity of melts (e.g., Dingwell et al., 1996) means
378 that if Venusian melts are anhydrous (dry) then the lavas erupted onto its surface should have a
379 higher viscosity than their Terran counterparts. It is possible that the Venusian mantle is about an
380 order of magnitude more viscous than that of Earth, based on the assumption that Venusian melts
381 are anhydrous and derived from an anhydrous mantle (Kaula, 1990; Nimmo and McKenzie, 1996;
382 Mackwell et al., 1998). However, and as outlined above, recent data that suggest a hydrated Martian
383 mantle (McCubbin et al., 2012) demand a reappraisal of the assumption that the Venusian mantle is
384 anhydrous. Indeed, the vast majority of basaltic lava flows on the Venusian surface are of a similar
385 spatial magnitude and thickness to the flows observed in basaltic large igneous provinces (LIPs) on
386 Earth (e.g., Columbia River and Deccan Traps; Wilson, 2009); this similarity, together with the
387 similar surface gravity of Earth and Venus, implies a similar basaltic flow viscosity. We also note
388 that an increase in temperature results in a decrease in melt viscosity (Hess and Dingwell, 1996;
389 Giordano et al., 2008), even for anhydrous melts (Hess et al., 2001). Therefore, if Venusian lavas
390 are indeed anhydrous, the high temperature of the Venusian surface may decrease their nominal
391 eruptive viscosity to a value closer to lavas extruded on Earth. We conclude, therefore, that the
392 difference in viscosity of erupted lavas cannot explain the difference in morphology between the
393 volcanoes on Earth and Venus.
394

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### 3.1.3 Response of the lithosphere to geological loads

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An additional parameter that controls the height of a volcanic structure is the mechanical rigidity of the basement upon which the volcano is situated (Watts, 2001). The flexural rigidity of the lithosphere depends on its rheology such that a strong and brittle lithosphere is better adapted to support high-elevation structures than a weak and ductile lithosphere (Watts, 2001). Indeed, a thick and predominantly brittle crust has been used to explain the presence of the ultra-high-elevation volcanoes on Mars (Turcotte et al., 1981; Heap et al., 2017), with the mechanical response of the Martian crust even influencing the eruptive behaviour of these shield volcanoes (Byrne et al., 2013).

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We contend that the experimental rock deformation data collated in Figs. 3 and 4 provide a simple explanation as to why Venus hosts volcanoes that, although perhaps as voluminous, are wider and of lower elevation than those on Earth. On a global scale, high-elevation structures cannot be supported on Venus to the same extent as they are on Earth due to the dominantly ductile Venusian crust. Recent analogue modelling by Byrne et al. (2013) aligns with this conclusion. This prediction further suggests that the volcanic topographic highs on Venus (e.g., Maat Skadi Montes) may be relatively young, because our model predicts that high-elevation structures on Venus will force the underlying lithosphere to yield over geological timescales (according to the models presented by Byrne et al. (2013); see also Smrekar and Solomon (1992) and Herrick et al. (2005)). Large volcanoes may even evolve into corona-like structures over time, evidenced by the number of volcano-corona 'hybrids' on the Venusian surface (e.g., Atai Mons; Grindrod et al., 2006). We also note that the downflexing of the lithosphere beneath a volcano imposes a constrictional strain upon the edifice, manifest as imbricate shortening structures arrayed around its flanks (Byrne et al., 2009; 2013). Unfortunately, the flanks of Venusian volcanoes are not sufficiently resolved with currently available data to test this hypothesis (full resolution Magellan topographic imagery has a resolution of about 100 m; Herrick et al., 2005).

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420 3.2 Implications for volcanic character

421 The dominant mode of magma migration through Earth's crust (in terms of volume) is via fractures
422 (e.g., Gudmundsson, 2006). The experimental data collated here suggest that, on Venus, faulting
423 could be restricted to shallow depths (i.e., 2–12 km) (Fig. 4). Similar to Earth (Burov and Gerya,
424 2014), a rising mantle-derived melt on Venus will pond and spread laterally, underplating the crust
425 at depths greater than that of the BDT (as shown in Fig. 5 a-c for Venus). However, based on our
426 depth estimates for the BDT on Venus (Fig. 4), the mechanism by which magmas on Venus can
427 continue to migrate towards the BDT is through buoyancy-driven diapirism. Importantly, however,
428 the lengthscale for magma migration by diapirism is considerably shorter than migration through
429 dykes (Rubin, 1995; Gudmundsson, 2002; Petford, 2003; Gudmundsson, 2006; 2011) and diapirs
430 will inevitably pond and create sills due to a stress-related equilibrium when the forces driving
431 ascent are equal (or less than) the forces acting against ascent (i.e., crystallisation increasing
432 viscosity) – unless more magma is added to further drive ascent via buoyancy-driven diapirism.

433 Therefore, if magma transport through the lower to middle Venusian crust is dominated by
434 diapirism, then a lower fraction of crust-situated melt can reach the surface and erupt, relative to
435 Earth. Occasionally however, a sill may form that is large enough to generate enough uplift to
436 initiate faulting in the brittle crust, creating a set of concentric vertical faults (see Galgana et al.,
437 2013). If the magma reaches these faults (or vice versa) then melts can propagate upwards, forming
438 ring-dikes or arachnoids (Head et al., 1992; Donahue and Russell, 1997; Basilevsky and Head,
439 2003; Wilson, 2009). Should it reach the surface, this melt will erupt as lava, and we conceptually
440 show how this can result in the formation of the curious coronae features on Venus in Fig. 5.

441 A combination of lateral flow and dyke-facilitated volcanism will cause the sill (magma chamber)
442 to contract vertically, and this can cut off the magma supply to the surface as the collapsing brittle
443 crust closes the fracture network. This may result in subsidence beneath the forming or formed
444 coronae with either negative or positive relief (both of which are commonly observed on Venus:
445 Head et al., 1992; Donahue and Russell, 1997; Basilevsky and Head, 2003; Herrick et al., 2005;
Wilson, 2009), which we argue is the result of variable ratios of the erupted lava to the amount of subsidence. If the magma supply from the plume to the crust is large enough and is active over sufficient timescales, then a shallow-flanked shield volcano could form (e.g., Maat Mons), the vertical growth of which is likely tempered by the inability of the predominantly ductile Venusian crust to support high-elevation structures (due to its low flexural rigidity). However, if the magma chamber (sill) cannot connect with the faults, because the sill has stalled below the BDT, then surface eruption will not ensue. In this eventuality, grabens (*fossae* and *lineae*), fractures, scarps (*rupes*), or troughs will form, tectonic landforms common to the Venusian surface (Head et al., 1992; Donahue and Russell, 1997; Basilevsky and Head, 2003; Wilson, 2009).

Most volcanic systems on Earth show complex magmatic plumbing with several reservoirs situated at different depths. However, most primary mantle melts that reach the Earth's crust form sill-like magma chambers at the base of the crust (defined as primary magma chambers) and are typically found at depths considerably greater than 10 km (Kelley and Barton, 2008; Stroncik et al., 2009; Becerril et al., 2013). Therefore, on Earth, most shallow magma chambers are connected to a deeper primary magma chamber at depths of >10 km (Hill et al., 2009; Michon et al., 2015). This magma system architecture suggests that magma ponds at the crust–mantle boundary on Earth. Therefore, if Venusian melts form magma chambers at similar depth, or at a similar depth with respect to the stratigraphy of the crust (i.e., the crust–mantle boundary), as predicted for shallow magma chambers (Wilson and Head, 1994), then those chambers will be hosted below the BDT (predicted to occur between 2 and 12 km on Venus: see Fig. 4a-c), restricting magma mobility to the short lengthscales typical of diapirism (Rubin, 1995; Gudmundsson, 2002; Petford, 2003; Gudmundsson, 2006; 2011).

We can therefore predict, albeit qualitatively, that a greater proportion of magmatism on Venus does not result in volcanism, but instead results in plutonism, than on Earth. Indeed, lava flow unit thickness estimates from Magellan topographic data suggest that coronae are probably underlain by large magma bodies that are not emptied during eruption (Grindrod et al., 2010). Any crustal
thickening in areas of high magmatic activity should thus be compensated by delamination back into the mantle with or without crustal uplift (Smrekar and Stofan, 1997; Ghail, 2015). To test the hypothesis that plutonism is favoured over volcanism on Venus (relative to Earth), we will now compare differences in volcanic flux on Earth and Venus with the available geochemical data.

476

## 4 Measuring the volcanic eruptive flux of Venus and Earth

Finding a suitable metric to compare the eruptive fluxes of Venus and Earth is challenging. For example, there is a large uncertainty for both the longevity and frequency of Venusian volcanism due to the lack of reliable chronostratigraphic or radiogenic isotopic data for the Venusian surface (Head et al., 1992; Basilevsky et al., 2003; Kreslavsky et al., 2015). However, there is evidence that Venus has experienced some voluminous volcanism in the past, coined 'global resurfacing events'. The model for catastrophic volcanic resurfacing is based on the relatively few (ca. 1,000) impact craters, and is thought to have occurred between 300 Ma and 1 Ga (e.g., McKinnon et al., 1997). Assuming a frequency of resurfacing episodes that declined with the rate of heat generation (based on K-Th-U systematics of the mantle), Kaula (1991) proposed that there could have been eight resurfacing events over Venus' 4.56 Ga history. Volcanism on Venus appears to be mostly quiescent between these resurfacing events, which are either random or occurring roughly once every 0.5 Ga (Kaula, 1991). If in fact magmatism during these largely passive periods does not result in extrusive volcanism, then by our inference it may instead be manifest as massive magmatic underplating of basaltic melts at the base of the crust and subsequent plutonism in the crust, possibly followed by delamination back into the mantle (Smrekar and Stofan, 1997).

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An important and poorly constrained parameter is the thermal structure of the Venusian interior. Nimmo and McKenzie (1997; 1998) cite the composition (specifically the FeO abundance) of the basaltic rocks analysed by the Venera and Vega landers to argue that the potential temperature of the Venusian mantle was similar to the Earth's during the emplacement of these rocks. Note, the FeO data used by Nimmo and McKenzie (1997; 1998) are by no means absolute or accurate (they
have large uncertainties), but this is the only data presently available and future missions are required to provide an improved insight. Nevertheless, they do provide a quantitative model with which to demonstrate the point. Since these basalts are between 300–800 Ma one must calculate the mantle temperature for the present day; this is because resurfacing events would have cooled the Venusian upper mantle, which would have been followed by an increase in temperature due to U–Th–K decay and thermal insulation by the crust. Nimmo and McKenzie (1997, 1998) concluded that it is unlikely that the Venusian mantle increased in temperature by more than 200 °C over 800 Ma. Hence, these workers proposed an upper limit of 1500 °C for the potential temperature of the present-day Venusian mantle (Nimmo and McKenzie, 1998). This temperature is below the solidus for water-undersaturated peridotite (Kohlstedt et al., 1996; Hirschmann, 2006), and so melt production would be restricted to adiabatic melting of thermochemical plumes rising through the mantle (e.g., such as the Hawaiian plume on Earth; Morgan, 1971).

A key feature of the conceptual model presented here is that, all else being equal, the volcanic eruptive flux of Venus should be lower than that of Earth. Since we cannot rely on estimates of volcanic flux from chronostratigraphic methods, we must look elsewhere. For example, the chemistry of a planet's atmosphere is a passive recorder of surface and subsurface processes – including volcanism (e.g., Mather, 2008; Gaillard and Scaillet, 2014; Mikhail and Sverjensky, 2014). Therefore, if Venus has experienced a relatively retarded volcanic eruptive flux (relative to Earth) over its geological history then this will have left a geochemical fingerprint in the chemistry of the Venusian atmosphere. Herein therefore we focus on the stable isotopes of argon, principally $ ^{36}Ar, ^{38}Ar, $ and $ ^{40}Ar, $ as useful tools for investigating the origin of volatiles (with $ ^{38}Ar/^{36}Ar $) and the degassing history (with $ ^{40}Ar/^{36}Ar $) of Venus. This is because [1] there are data for the $ ^{40}Ar/^{36}Ar $ and $ ^{38}Ar/^{36}Ar $ ratios for the atmospheres of Earth, Mars, Venus, and solar wind (Porcelli and Pepin, 2002), and [2] $ ^{36}Ar $ and $ ^{38}Ar $ are primordial isotopes whereas $ ^{40}Ar $ is produced from the decay of $ ^{40}K, $ with a half-life of 1.25 Ga, meaning that $ ^{40}Ar $ in planetary atmospheres can be used to derive information regarding the degassing of planetary interiors (e.g., Halliday, 2013).
## 5 Validating the model: argon isotope data

Despite the dearth of missions into and below the Venusian atmosphere over the past 40 years, there are valuable data for the major and minor element geochemistry of the Venusian atmosphere, including argon isotope ratios. Indeed, argon isotopes have been previously used to inform on the evolution of Venus (e.g., Istomin et al., 1980; Hoffman et al., 1980a, b; Turcotte and Schubert, 1988; Kaula, 1990; 1991; Namiki and Solomon, 1998; Porcelli and Pepin, 2002; Mikhail and Sverjensky, 2014; Halliday, 2013; O'Rourke and Korenaga, 2015).

In December 1978, seven gas analysers (four mass spectrometers and two gas chromatographers) provided in-situ measurements of the Venus atmospheric chemical and isotopic composition (summarised by Hoffman et al., 1980a). The Soviet Union's Venera 11 and 12 landers (Istomin et al., 1979) and the United States Pioneer Venus entry probe (Hoffman et al., 1980a) determined the argon isotope composition of the lower Venusian atmosphere (below the altitude limit of isotopic homogenisation). Importantly, these two independent measurements provided a ³⁸Ar/³²Ar ratio within error of one another (summarised by Hoffman et al., 1980b). The similarity for the ³⁸Ar/³²Ar ratios for Earth and Venus is indicative of a shared source of volatile elements (Fig. 6). We consider that the most surprising result of these measurements was that the ratio of radiogenic to primordial argon in the Venusian atmosphere was shown to be highly unradiogenic, with a ⁴⁰Ar/³²Ar ratio of only 1.03 ± 0.04. For comparison, most argon in the atmospheres of Earth and Mars is strongly radiogenic, with ⁴⁰Ar/³²Ar ratios of 298.56 and 1900 ± 300, respectively (Fig. 6). Below, we outline why atmospheric loss, Venus being a K-deficient planet, and diffusive degassing cannot explain the difference between the ⁴⁰Ar/³²Ar ratios of Earth and Venus. We then finish by proposing a solution (that leans on the notion of a shallow BDT for Venus), where we conclude that this discrepancy can be explained by a relatively low volcanic eruptive flux for Venus (compared to Earth).
549 **5.1 The case against atmospheric loss to explain the unradiogenic argon**

550 One of the principle mechanisms leading to stable isotope fractionation of atmosphere-forming
551 elements is low-temperature atmospheric loss (i.e., hydrodynamic escape). This process induces
552 mass dependant stable isotope fractionation, and therefore preferentially removes the lighter
553 isotopes over the heavy isotopes (e.g., ³⁶Ar over ³⁸Ar, and ³⁸Ar over ⁴⁰Ar). This, in turn, means that
554 the ³⁸Ar/³⁶Ar ratio would reflect substantial stable isotope fractionation if atmosphere loss to space
555 were the sole reason for the unradiogenic ⁴⁰Ar/³⁶Ar ratio in the Venusian atmosphere. Note, this is
556 not the case for the Venusian and Terran datasets (Fig. 6). Hydrodynamic escape of ³⁶Ar cannot
557 explain the low ⁴⁰Ar/³⁶Ar ratio of the Venusian atmosphere, because the ³⁶Ar/³⁸Ar data for the
558 Venusian and Terran datasets are almost identical (i.e., 5.5 vs. 5.3; see Fig. 6), and Earth and Venus
559 have very similar escape velocities for argon (ca. 12 and 13 km/s, respectively). Because Earth and
560 Venus both show primordial ³⁶Ar/³⁸Ar ratios, both planets appear to share identical (isotopic) source
561 materials (i.e., both are similar to their initial value recorded by solar wind: Porcelli and Pepin,
562 2002; Halliday, 2013). This in turn implies that both Earth and Venus had the same initial
563 atmospheric ⁴⁰Ar/³⁶Ar ratio. A conundrum thus ensues: where is the missing ⁴⁰Ar in the Venusian
564 atmosphere?

565

566 **5.2 The case against Venus being a K-deficient planet**

567 The unradiogenic ⁴⁰Ar/³⁶Ar ratio for the Venusian atmosphere also cannot be explained by
568 proposing Venus to be a K-deficient planet, because the average observed K/U ratio in rocks on the
569 Venusian surface is 7,220 (akin to mid-ocean ridge basalts on Earth). Therefore, assuming an initial
570 K/U and ³⁸Ar/³⁶Ar ratio for Earth and Venus, the present-day ⁴⁰Ar/³⁶Ar ratio of the Venusian
571 atmosphere is not a reflection of the overall K abundance, but would therefore reflect either the flux
572 of ⁴⁰Ar diffused or degassed out of the mantle and/or crust.
573

573
574 **5.3 The case against efficient, diffusive degassing**

575 The efficient transport of <sup>40</sup>Ar from the interior of a planet into its atmosphere can be, conceptually,
576 achieved by diffusion. The entire Venusian crust is at a temperature above the closure temperature
577 for argon in most silicate systems (Kelley and Wartho, 2000). However, efficient (or total) diffusion
578 of <sup>40</sup>Ar through the crust cannot be proposed, because the Venusian atmosphere is strongly
579 unradiogenic (for argon). This indicates that the Venusian crust has retained considerable <sup>40</sup>Ar
580 produced continually over the age of the planet (4.56 Ga). The BSV must therefore be saturated in
581 <sup>40</sup>Ar. The lack of <sup>40</sup>Ar-diffusion at high Venusian surface temperatures can be explained by the lack
582 of a chemical gradient. A buildup of <sup>40</sup>Ar in the crust above the closure temperature does not
583 necessarily mobilize the <sup>40</sup>Ar into the atmosphere. Buoyancy drives ascent, but pathways and
584 mobilising agents are also required (note, gravity and physical inhibition are also acting as opposing
585 forces). The lack of <sup>40</sup>Ar transport can be explained by a system that rapidly reaches equilibrium
586 with the intergranular medium, despite diffusion coefficients great enough to model efficient
587 mobilisation, conceptually (Cassata et al., 2011), Furthermore, mass-transfer along the grain
588 boundary of silicates and oxides is limited to a very thin layer (ca. 1 nm; Joesten, 1991), so the bulk
589 diffusivity should be reduced by the ratio of the thickness of the grain boundary to the diameter of
590 the grain (Faver and Yund, 1992). For a grain diameter of 0.1 to 1 mm, the diffusive lengthscales of
591 argon is <1.2 km in 1 Ga. Since the lengthscale is less than the likely thickness of the Venusian
592 crust (which is most certainly >1.2 km), the nominal diffusive flux of <sup>40</sup>Ar to the atmosphere is
593 effectively zero over 1 Ga (Namiki and Solomon, 1998). Therefore, the nominal diffusive flux of
594 <sup>40</sup>Ar to the atmosphere will be negligible over 4.5 Ga.

595
596 **5.4 The case for a low volcanic eruptive flux on Venus relative to Earth**

597 We propose volcanism is the main liberating agent for transporting <sup>40</sup>Ar to the Venusian
598 atmosphere. During mantle melting on Earth and Venus, <sup>40</sup>K and <sup>40</sup>Ar are mobilised in melts,
599 because they are both incompatible elements in primary mantle silicates, e.g., olivine (Chamorro et
al., 2002; Brooker et al., 2003). This degassing implies that the strongly unradiogenic low $^{40}$Ar/$^{36}$Ar ratio in the Venusian atmosphere is mirrored by a higher crustal excess of $^{40}$Ar than is observed for the crust on Earth (which is known to contain excess $^{40}$Ar: Allègre et al., 1996; Kelley, 2002). We argue that most of the $^{40}$Ar transported in melts from the Venusian mantle is locked in plutons and stored within the Venusian crust, implying that there is a large excess of $^{40}$Ar in the BSV. Our contention that a dominantly ductile Venusian crust (Fig. 4a-c) inhibits volcanism but results in abundant plutonism (relative to Earth; Fig. 7) forms a testable hypothesis: Venus should have degassed less $^{40}$Ar, relative to Earth. Mars, for example, has a highly fractionated $^{36}$Ar/$^{38}$Ar ratio of 4.1 (Porcelli and Pepin, 2003; Halliday, 2013), which reflects a substantial low-temperature loss of its atmosphere (Porcelli and Pepin, 2003; Halliday, 2013) (Fig. 6). Consequently, their present-day atmospheric $^{40}$Ar/$^{36}$Ar ratios will reflect their relative efficiencies in $^{40}$Ar degassing. The present-day Venusian atmosphere has a strongly unradiogenic $^{40}$Ar/$^{36}$Ar ratio of 1.03 ± 0.04, compared with 298.56 for Earth (Kaula, 1991; Porcelli and Pepin, 2003; Halliday, 2013). However, the Venusian atmosphere also contains roughly two orders of magnitude more $^{36}$Ar relative to Earth's atmosphere (Porcelli and Pepin, 2003). If we correct the $^{40}$Ar/$^{36}$Ar ratio for Venus then the $^{40}$Ar/$^{36}$Ar ratio of the Venusian atmosphere would be approximately 103, meaning Earth has degassed three times more $^{40}$Ar than Venus. We view this implication here as a consequence of a higher rate of volcanism on Earth than on Venus. This is because the majority of Earth's volcanism is directly related to Earth's mobile-lid plate tectonic regime (Cottrell, 2015), but we argue that the high surface temperature and dearth of deep crustal faults on Venus also plays an important role. Therefore plutonism, rather than volcanism, is the dominant mode of magmatic activity on Venus (Fig. 7) and this is reflected in the unusually unradiogenic $^{40}$Ar/$^{36}$Ar ratio observed in the Venusian atmosphere (Fig. 6).

622

## 6 Concluding remarks

We present here an experimentally-constrained and isotopically-supported conceptual model that predicts Venus to have been less volcanically active relative to Earth by a factor of three, in terms
of eruptive flux. Since the volume of magma erupted cannot be directly discussed, we focus here on the degassing flux constrained by argon isotopes, which show that Earth has degassed three times more $ ^{40}Ar $ than Venus. We conclude that the reduced eruptive flux on Venus, compared to Earth, is the result of the hot Venusian climate, a factor that greatly impacts the dominant failure mode of, and therefore the method by which magma can travel up through, the Venusian crust. The higher rate of intraplate volcanic activity on Earth is exemplified by the observation that Earth's relatively young oceanic crust has seen the development of <100,000 individual volcanoes (i.e., seamounts) in <100 Ma, whereas Venus has only produced ca. 70,000 individual volcanoes over a much longer time period (700-1000 Ma) – a difference of an order of magnitude.

An interrogation of high pressure, high temperature experimental rock deformation data suggests that the unrelenting high temperature (460 °C) of the Venusian surface modifies the rheology of the Venusian crust such that the dominant failure mode within the Venusian crust is ductile. These data highlight that the BDT on Venus could be as shallow as 2–12 km (Fig. 4), while the same method yields a realistic estimate for the BDT on Earth of ~25-27 km (Fig. 3). The implications of a dominantly ductile Venusian crust are twofold. First, the flexural rigidity of the Venusian lithosphere will be low, inhibiting the formation of high-relief volcanoes (via lithospheric flexure). We further note that the low flexural rigidity of the Venusian lithosphere may not just impact volcano morphology, but also the global hypsometric profile of Venus (Fig. 1). We therefore speculate that the low standard deviation of the Venusian surface is also the consequence of its hot climate. Second, magma delivery to the surface through fractures (i.e., dykes)—the dominant transport mechanism of magma to shallow crustal levels on the telluric planets (e.g., Wilson and Head, 1994; Gudmundsson, 2006)—will be impeded on Venus. Our conceptual model therefore predicts that most magma on Venus will stall in the crust as sills, rather than be erupted at the surface: plutonism, rather than volcanism, is the dominant mode of magmatic activity on Venus (Fig. 7). Importantly, these implications are supported by the atmospheric argon isotope ratios for Earth and Venus, which indicate that volcanic degassing, and therefore volcanic flux, has been three
652 times lower on Venus than on Earth over the past 4.5 Ga (Fig. 6).

653 Our conceptual model falls short in describing, for example, the formation histories for the
654 Venusian continents, Aphrodite Terra and Ishtar Terra (which, speculatively, could be the result of
655 isostatic rebound before the global resurfacing event, or crustal delamination of the lower
656 lithosphere back into the mantle, or a presently unknown mechanism; Smrekar and Stofan, 1997;
657 Ghail, 2015). We also highlight that our conceptual model assumes various similarities between
658 Earth and Venus, such as similar mantle convective regimes, which may not be strictly true (e.g.,
659 Johnson and Richards, 2003; Robin et al., 2007). Nevertheless, our model offers a viable
660 explanation for the difference in volcano morphology between Earth and Venus (i.e., the presence
661 of coronae) and the relative quiescence of volcanism on Venus compared to Earth (i.e., the order of
662 magnitude difference in the rate of intraplate volcano formation between Earth and Venus).
663 Furthermore, a Venusian BDT as shallow as predicted here also implies that faulting through the
664 vertical lengthscale of the crust is hindered. Therefore, the hot climate of Venus may also inhibit the
665 formation of the plate tectonic boundaries that sub-divide the crust (Foley et al., 2012; Bercovici
666 and Ricard, 2014). Our study highlights another example of the complex interplay between climate
667 and geodynamics.

668

669 Acknowledgements

670 We acknowledge stimulating discussions on argon geochemistry with Simon Kelley, Chris
671 Ballentine, Colin Jackson, and Peter Barry, and with Richard Ghail on the tectonic history of
672 Venus. We also acknowledge critical comments by Nicolas Le Corvec, Paul Byrne, two anonymous
673 reviewers, and the editorial handling of Mark Jellinek that enabled us to improve this manuscript.
674 M.J. Heap acknowledges funding from an Initiative d'Excellence (IDEX) "Attractivité" grant
675 (VOLPERM), funded by the University of Strasbourg. All of the data used in this manuscript are
676 cited in the reference list.
<figure><img src="image_2.png" /><figcaption>**Fig. 1:** Hypsography of Venus, Earth, and Mars (Head and Solomon, 1981; Basilevsky and Head, 2003; Taylor and McLennan, 2009). Dashed lines mark the mean surface elevation for each planet.</figcaption></figure>

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681
<figure><img src="image_3.png" /><figcaption>**Fig. 2:** The mechanical behaviour of rock in compression (from Heap et al., 2017). Examples of brittle and ductile stress-strain curves for basalt deformed at a confining pressure of 300 MPa and a temperature of 650 °C (brittle test) and 850 °C (ductile test) (data from Violay et al., 2012). Inset shows cartoons depicting post-failure samples typical of brittle (throughgoing shear fracture) and ductile (distributed deformation) deformation.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Fig. 3:** Failure mode map (brittle or ductile) for Earth assuming a pore pressure gradient of ~9.8 MPa/km, a surface gravity of 9.807 m/s², an average thermal gradient of 25 °C/km, and an average surface temperature of 4 °C. See text for details.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4: Failure mode maps (brittle or ductile) for Venus assuming a surface gravity of 8.87 m/s² and an average surface temperature of 460 °C. Due to the uncertainty in the pore pressure gradient we provide three scenarios. (a) That the pore fluid has a constant density of 1000 kg/m³ (i.e. the same as Earth; yielding a pore pressure gradient of ~8.9 MPa/km). (b) That the pore fluid has a constant density of 500 kg/m³ (yielding a pore pressure gradient of ~4.4 MPa/km). (c) That the pore fluid has a constant density of 100 kg/m³ (yielding a pore pressure gradient of ~0.89 MPa/km). Due to the</figcaption></figure>
699

uncertainty in the thermal gradient we provide a range from 5 to 40 °C/km. See text for details.

<figure><img src="image_6.png" /></figure>

700

701

702

703

704

705

**Fig. 5:** The formation of coronae on Venus. This cartoon depicts sill emplacement and growth, followed by uplift and faulting of the crust above the brittle-ductile transition (BDT). The schematic also shows how this only leads to volcanism after the magma chamber makes physical contact with faults (see text for more details; not to scale). Arrows indicate directions of main differential stresses.
<figure><img src="image_7.png" /><figcaption>**Fig. 6:** The atmospheric argon isotope composition of Earth, Mars, and Venus (data from Istomin et al., 1979; Hoffman et al., 1980b; Porcelli and Pepin, 2002; Mahaffy et al., 2013).</figcaption></figure>

<figure><img src="image_8.png" /></figure>

706

707

708

709
Fig. 7: Schematic illustration showing the relative differences for magma transport within the lithosphere on Earth and Venus. The cartoon shows that primary magma chambers on Venus rely on diapirism to move towards the surface, leading to stagnation and crystallisation (on average). Conversely for Earth, primary magma chambers can force dyking in the overlying (brittle) lithosphere and initiate volcanism.

715

Table caption

<table><thead><tr><th>Reference</th><th>Pc (MPa)</th><th>Pp (MPa)</th><th>Peff (MPa)</th><th>T (°C)</th><th>σp (MPa)</th><th>Failure mode</th><th>Notes</th></tr></thead><tbody><tr><td>Griggs et al. 1960</td><td>500</td><td>0</td><td>500</td><td>25</td><td>1668</td><td>Brittle</td><td>Basalt</td></tr><tr><td>Griggs et al. 1960</td><td>500</td><td>0</td><td>500</td><td>300</td><td>1390</td><td>Brittle</td><td>Basalt</td></tr><tr><td>Griggs et al. 1960</td><td>500</td><td>0</td><td>500</td><td>500</td><td>1080</td><td>Brittle</td><td>Basalt</td></tr><tr><td>Griggs et al. 1960</td><td>500</td><td>0</td><td>500</td><td>700</td><td>-</td><td>Ductile</td><td>Basalt</td></tr><tr><td>Griggs et al. 1960</td><td>500</td><td>0</td><td>500</td><td>800</td><td>-</td><td>Ductile</td><td>Basalt</td></tr><tr><td>Caristan 1982</td><td>0</td><td>0</td><td>0</td><td>950</td><td>199</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-3</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>0</td><td>0</td><td>0</td><td>970</td><td>223</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>0</td><td>0</td><td>0</td><td>995</td><td>193</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-3</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>30</td><td>0</td><td>30</td><td>1000</td><td>370</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-3</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>50</td><td>0</td><td>50</td><td>1000</td><td>440</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-3</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>150</td><td>0</td><td>150</td><td>810</td><td>780</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>150</td><td>0</td><td>150</td><td>970</td><td>385</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>150</td><td>0</td><td>150</td><td>994</td><td>535</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-3</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>150</td><td>0</td><td>150</td><td>1000</td><td>566</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>150</td><td>0</td><td>150</td><td>1000</td><td>561</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>150</td><td>0</td><td>150</td><td>1000</td><td>573</td><td>Brittle</td><td>Maryland diabase; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>350</td><td>0</td><td>350</td><td>1000</td><td>-</td><td>Ductile</td><td>Maryland diabase; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>400</td><td>0</td><td>400</td><td>1000</td><td>-</td><td>Ductile</td><td>Maryland diabase; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>425</td><td>0</td><td>425</td><td>1000</td><td>-</td><td>Ductile</td><td>Maryland diabase; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>425</td><td>0</td><td>425</td><td>1000</td><td>-</td><td>Ductile</td><td>Maryland diabase; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>425</td><td>0</td><td>425</td><td>1000</td><td>-</td><td>Ductile</td><td>Maryland diabase; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td></tr><tr><td>Caristan 1982</td><td>450</td><td>0</td><td>450</td><td>1000</td><td>-</td><td>Ductile</td><td>Maryland diabase; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Shimada and Yukutake 1982</td><td>57</td><td>0</td><td>57</td><td>25</td><td>400</td><td>Brittle</td><td>Yakuno basalt; Porosity = 0.07; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Shimada and Yukutake 1982</td><td>107</td><td>0</td><td>107</td><td>25</td><td>415</td><td>Brittle</td><td>Yakuno basalt; Porosity = 0.07; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Bauer et al. 1981</td><td>50</td><td>0</td><td>50</td><td>25</td><td>540</td><td>Brittle</td><td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td></tr></tbody></table>
<table>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>25</td>
    <td>400</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>600</td>
    <td>300</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>600</td>
    <td>340</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>700</td>
    <td>300</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>940</td>
    <td>125</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>940</td>
    <td>200</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>1000</td>
    <td>100</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>700</td>
    <td>465</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>900</td>
    <td>240</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>950</td>
    <td>110</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>1000</td>
    <td>180</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Bauer et al. 1981</td>
    <td>100</td>
    <td>50</td>
    <td>50</td>
    <td>820</td>
    <td>180</td>
    <td>Brittle</td>
    <td>Cuerbio basalt; Porosity = 0.05-0.08; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Shimada 1986</td>
    <td>57</td>
    <td>0</td>
    <td>57</td>
    <td>25</td>
    <td>410</td>
    <td>Brittle</td>
    <td>Yakuno basalt; Porosity = 0.07; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Duclos and Paquet 1991</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>300</td>
    <td>399</td>
    <td>Brittle</td>
    <td>Alkaline basalt; partially glassy; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Duclos and Paquet 1991</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>600</td>
    <td>430</td>
    <td>Brittle</td>
    <td>Alkaline basalt; partially glassy; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Duclos and Paquet 1991</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>700</td>
    <td>445</td>
    <td>Brittle</td>
    <td>Alkaline basalt; partially glassy; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Duclos and Paquet 1991</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>750</td>
    <td>430</td>
    <td>Brittle</td>
    <td>Alkaline basalt; partially glassy; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Duclos and Paquet 1991</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>800</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Alkaline basalt; partially glassy; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Duclos and Paquet 1991</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>900</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Alkaline basalt; partially glassy; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Duclos and Paquet 1991</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>1000</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Alkaline basalt; partially glassy; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Hacker and Christie 1991</td>
    <td>1000</td>
    <td>0</td>
    <td>1000</td>
    <td>675</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Tholeiitic basalt; partially glassy; 0.5 wt.% water added; strain rate = 10<sup>-4</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Hacker and Christie 1991</td>
    <td>1000</td>
    <td>0</td>
    <td>1000</td>
    <td>725</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Tholeiitic basalt; partially glassy; 0.5 wt.% water added; strain rate = 10<sup>-4</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Hacker and Christie 1991</td>
    <td>1000</td>
    <td>0</td>
    <td>1000</td>
    <td>775</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Tholeiitic basalt; partially glassy; 0.5 wt.% water added; strain rate = 10<sup>-4</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Hacker and Christie 1991</td>
    <td>1000</td>
    <td>0</td>
    <td>1000</td>
    <td>825</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Tholeiitic basalt; partially glassy; 0.5 wt.% water added; strain rate = 10<sup>-4</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Hacker and Christie 1991</td>
    <td>1000</td>
    <td>0</td>
    <td>1000</td>
    <td>875</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Tholeiitic basalt; partially glassy; 0.5 wt.% water added; strain rate = 10<sup>-4</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schultz 1993</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>450</td>
    <td>210</td>
    <td>Brittle</td>
    <td>Estimated strength value taken as 80% of the average uniaxial compressive strength for basalt; see Schultz (1993) for details</td>
  </tr>
  <tr>
    <td>Mackwell et al. 1998</td>
    <td>400</td>
    <td>0</td>
    <td>400</td>
    <td>1000</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Dehydrated Maryland and Columbia diabase; creep test; strain rate = 10<sup>-5</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Mackwell et al. 1998</td>
    <td>400</td>
    <td>0</td>
    <td>400</td>
    <td>1050</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Dehydrated Maryland and Columbia diabase; creep test; strain rate = 10<sup>-5</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Mackwell et al. 1998</td>
    <td>400</td>
    <td>0</td>
    <td>400</td>
    <td>1050</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Dehydrated Maryland and Columbia diabase; creep test; strain rate = 10<sup>-5</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Mackwell et al. 1998</td>
    <td>450</td>
    <td>0</td>
    <td>450</td>
    <td>970</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Dehydrated Maryland and Columbia diabase; creep test; strain rate = 10<sup>-5</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Mackwell et al. 1998</td>
    <td>450</td>
    <td>0</td>
    <td>450</td>
    <td>1000</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Dehydrated Maryland and Columbia diabase; creep test; strain rate = 10<sup>-5</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Mackwell et al. 1998</td>
    <td>450</td>
    <td>0</td>
    <td>450</td>
    <td>1050</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Dehydrated Maryland and Columbia diabase; creep test; strain rate = 10<sup>-5</sup> - 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
</table>
<table><tr><td>Mackwell et al. 1998</td><td>500</td><td>0</td><td>500</td><td>1000</td><td>-</td><td>Ductile</td><td>Dehydrated Maryland and Columbia diabase; creep test; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>300</td><td>89</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>300</td><td>104</td><td>Brittle</td><td>Etna "core" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>300</td><td>35</td><td>Brittle</td><td>Etna "crust" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>600</td><td>96</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>600</td><td>105</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>600</td><td>103</td><td>Brittle</td><td>Etna "core" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>600</td><td>181</td><td>Brittle</td><td>Etna "core" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>600</td><td>40.5</td><td>Brittle</td><td>Etna "crust" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>700</td><td>33</td><td>Brittle</td><td>Etna "crust" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>800</td><td>42</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>800</td><td>43</td><td>Brittle</td><td>Etna "core" basalt; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>800</td><td>25</td><td>Brittle</td><td>Etna "core" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>800</td><td>17</td><td>Brittle</td><td>Etna "core" basalt; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>800</td><td>20</td><td>Brittle</td><td>Etna "crust" basalt; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>900</td><td>50</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-4</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>900</td><td>38</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>900</td><td>29</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>0</td><td>0</td><td>0</td><td>900</td><td>31</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>5</td><td>0</td><td>5</td><td>25</td><td>108</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>10</td><td>0</td><td>10</td><td>25</td><td>104</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>10</td><td>0</td><td>10</td><td>300</td><td>101</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>10</td><td>0</td><td>10</td><td>300</td><td>88</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>10</td><td>0</td><td>10</td><td>600</td><td>116</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>10</td><td>0</td><td>10</td><td>916</td><td>62</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>12</td><td>0</td><td>12</td><td>25</td><td>93</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>15</td><td>0</td><td>15</td><td>25</td><td>101</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>17</td><td>0</td><td>17</td><td>25</td><td>100</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>20</td><td>0</td><td>20</td><td>25</td><td>109</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>20</td><td>0</td><td>20</td><td>300</td><td>95</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>20</td><td>0</td><td>20</td><td>300</td><td>91</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>20</td><td>0</td><td>20</td><td>600</td><td>118</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>30</td><td>0</td><td>30</td><td>25</td><td>112</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>30</td><td>0</td><td>30</td><td>25</td><td>103</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>30</td><td>0</td><td>30</td><td>300</td><td>105</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>30</td><td>0</td><td>30</td><td>300</td><td>87</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>30</td><td>0</td><td>30</td><td>600</td><td>104</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Rocchi et al. 2004</td><td>30</td><td>0</td><td>30</td><td>604</td><td>79</td><td>Brittle</td><td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr></table>
<table>
  <tr>
    <td>Rocchi et al. 2004</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>900</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Etna "crust" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Rocchi et al. 2004</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>912</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Etna "core" basalt; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Rocchi et al. 2004</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>1001</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Vesuvius basalt; Porosity = 0.08-0.10; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>4</td>
    <td>0</td>
    <td>4</td>
    <td>25</td>
    <td>98</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>4</td>
    <td>0</td>
    <td>4</td>
    <td>25</td>
    <td>72</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>4</td>
    <td>0</td>
    <td>4</td>
    <td>25</td>
    <td>67</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>8</td>
    <td>0</td>
    <td>8</td>
    <td>25</td>
    <td>88</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>8</td>
    <td>0</td>
    <td>8</td>
    <td>25</td>
    <td>99</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>12</td>
    <td>0</td>
    <td>12</td>
    <td>25</td>
    <td>104</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>12</td>
    <td>0</td>
    <td>12</td>
    <td>25</td>
    <td>109</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>16</td>
    <td>0</td>
    <td>16</td>
    <td>25</td>
    <td>54</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>16</td>
    <td>0</td>
    <td>16</td>
    <td>25</td>
    <td>62</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>16</td>
    <td>0</td>
    <td>16</td>
    <td>25</td>
    <td>87</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>16</td>
    <td>0</td>
    <td>16</td>
    <td>25</td>
    <td>94</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>20</td>
    <td>0</td>
    <td>20</td>
    <td>25</td>
    <td>56</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>20</td>
    <td>0</td>
    <td>20</td>
    <td>25</td>
    <td>109</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Apuani et al. 2005</td>
    <td>20</td>
    <td>0</td>
    <td>20</td>
    <td>25</td>
    <td>178</td>
    <td>Brittle</td>
    <td>Vigna Vecchia basalt (Stromboli)</td>
  </tr>
  <tr>
    <td>Benson et al. 2007</td>
    <td>60</td>
    <td>20</td>
    <td>40</td>
    <td>25</td>
    <td>475</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.04; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Ougier-Simonin et al. 2010</td>
    <td>15</td>
    <td>0</td>
    <td>15</td>
    <td>25</td>
    <td>370</td>
    <td>Brittle</td>
    <td>Seljadur basalt; porosity = 0.05; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Heap et al. 2011</td>
    <td>30</td>
    <td>20</td>
    <td>10</td>
    <td>25</td>
    <td>291</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.4; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Heap et al. 2011</td>
    <td>50</td>
    <td>20</td>
    <td>30</td>
    <td>25</td>
    <td>287</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.4; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Heap et al. 2011</td>
    <td>70</td>
    <td>20</td>
    <td>50</td>
    <td>25</td>
    <td>504</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.4; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Heap et al. 2011</td>
    <td>50</td>
    <td>20</td>
    <td>30</td>
    <td>25</td>
    <td>375</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.4; creep test; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Heap et al. 2011</td>
    <td>50</td>
    <td>20</td>
    <td>30</td>
    <td>25</td>
    <td>357</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.4; creep test; strain rate = 10<sup>-7</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Heap et al. 2011</td>
    <td>50</td>
    <td>20</td>
    <td>30</td>
    <td>25</td>
    <td>329</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.4; creep test; strain rate = 10<sup>-8</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Heap et al. 2011</td>
    <td>50</td>
    <td>20</td>
    <td>30</td>
    <td>25</td>
    <td>304</td>
    <td>Brittle</td>
    <td>Etna basalt; porosity = 0.4; creep test; strain rate = 10<sup>-9</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>400</td>
    <td>1002</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>400</td>
    <td>902</td>
    <td>Brittle</td>
    <td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>600</td>
    <td>854</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>700</td>
    <td>508</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>800</td>
    <td>462</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>800</td>
    <td>446</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>100</td>
    <td>0</td>
    <td>100</td>
    <td>900</td>
    <td>355</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>300</td>
    <td>0</td>
    <td>300</td>
    <td>600</td>
    <td>749</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>300</td>
    <td>0</td>
    <td>300</td>
    <td>700</td>
    <td>755</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>300</td>
    <td>0</td>
    <td>300</td>
    <td>800</td>
    <td>518</td>
    <td>Brittle</td>
    <td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Violay et al. 2012</td>
    <td>50</td>
    <td>0</td>
    <td>50</td>
    <td>600</td>
    <td>-</td>
    <td>Ductile</td>
    <td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
</table>
<table><tr><td>Violay et al. 2012</td><td>70</td><td>0</td><td>70</td><td>600</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>500</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>600</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>600</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>700</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>800</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>800</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>800</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>900</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>100</td><td>0</td><td>100</td><td>900</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>250</td><td>0</td><td>250</td><td>650</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>600</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>700</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>750</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>800</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>800</td><td>-</td><td>Ductile</td><td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>850</td><td>-</td><td>Ductile</td><td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>900</td><td>-</td><td>Ductile</td><td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>900</td><td>-</td><td>Ductile</td><td>Porphyritic basalt; partially glassy; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2012</td><td>300</td><td>0</td><td>300</td><td>950</td><td>-</td><td>Ductile</td><td>Aphanitic basalt; porosity = 0.02; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Adelinet et al. 2013</td><td>10</td><td>5</td><td>5</td><td>25</td><td>120</td><td>Brittle</td><td>Reykjanes basalt; porosity = 0.08; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td></tr><tr><td>Adelinet et al. 2013</td><td>80</td><td>76</td><td>4</td><td>25</td><td>118</td><td>Brittle</td><td>Reykjanes basalt; porosity = 0.08; strain rate = 10<sup>-6</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2015</td><td>130</td><td>30</td><td>100</td><td>600</td><td>877</td><td>Brittle</td><td>Aphanitic basalt; porosity = 0.03; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2015</td><td>130</td><td>30</td><td>100</td><td>650</td><td>834</td><td>Brittle</td><td>Aphanitic basalt; porosity = 0.03; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2015</td><td>130</td><td>30</td><td>100</td><td>700</td><td>792</td><td>Brittle</td><td>Aphanitic basalt; porosity = 0.03; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2015</td><td>130</td><td>30</td><td>100</td><td>750</td><td>699</td><td>Brittle</td><td>Aphanitic basalt; porosity = 0.03; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2015</td><td>130</td><td>30</td><td>100</td><td>800</td><td>717</td><td>Brittle</td><td>Aphanitic basalt; porosity = 0.03; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2015</td><td>130</td><td>30</td><td>100</td><td>900</td><td>382</td><td>Brittle</td><td>Aphanitic basalt; porosity = 0.03; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Violay et al. 2015</td><td>130</td><td>30</td><td>100</td><td>1050</td><td>-</td><td>Ductile</td><td>Aphanitic basalt; porosity = 0.03; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr></table>
<table>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>167</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.02; strain rate = 10<sup>-1</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>162</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.05; strain rate = 10<sup>-1</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>126</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.06; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>59</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.19; strain rate = 10<sup>-1</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>49</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.16; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaeffer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>93</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.19; strain rate = 10<sup>-1</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>44</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.19; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>75</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.23; strain rate = 10<sup>-1</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>64</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.21; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>28</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.32; strain rate = 10<sup>-1</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Schaefer et al. 2015</td>
    <td>0</td>
    <td>0</td>
    <td>0</td>
    <td>935</td>
    <td>16</td>
    <td>Brittle</td>
    <td>Pacaya (Guatemala) basalt; porosity = 0.31; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>20</td>
    <td>10</td>
    <td>10</td>
    <td>25</td>
    <td>281</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>20</td>
    <td>10</td>
    <td>10</td>
    <td>25</td>
    <td>240</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>20</td>
    <td>10</td>
    <td>10</td>
    <td>25</td>
    <td>221</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>20</td>
    <td>10</td>
    <td>10</td>
    <td>25</td>
    <td>327</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>30</td>
    <td>10</td>
    <td>20</td>
    <td>25</td>
    <td>329</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>30</td>
    <td>10</td>
    <td>20</td>
    <td>25</td>
    <td>361</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>40</td>
    <td>10</td>
    <td>30</td>
    <td>25</td>
    <td>399</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>50</td>
    <td>10</td>
    <td>40</td>
    <td>25</td>
    <td>403</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>60</td>
    <td>10</td>
    <td>50</td>
    <td>25</td>
    <td>500</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>60</td>
    <td>10</td>
    <td>50</td>
    <td>25</td>
    <td>493</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>60</td>
    <td>10</td>
    <td>50</td>
    <td>25</td>
    <td>561</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>80</td>
    <td>10</td>
    <td>70</td>
    <td>25</td>
    <td>563</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>90</td>
    <td>10</td>
    <td>80</td>
    <td>25</td>
    <td>560</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>90</td>
    <td>10</td>
    <td>80</td>
    <td>25</td>
    <td>574</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>90</td>
    <td>10</td>
    <td>80</td>
    <td>25</td>
    <td>655</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>110</td>
    <td>10</td>
    <td>100</td>
    <td>25</td>
    <td>658</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.04; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>160</td>
    <td>10</td>
    <td>150</td>
    <td>25</td>
    <td>753</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_I); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>60</td>
    <td>10</td>
    <td>50</td>
    <td>25</td>
    <td>365</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_II); porosity = 0.08; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>90</td>
    <td>10</td>
    <td>80</td>
    <td>25</td>
    <td>349</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_II); porosity = 0.08; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>20</td>
    <td>10</td>
    <td>10</td>
    <td>25</td>
    <td>224</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_III); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>60</td>
    <td>10</td>
    <td>50</td>
    <td>25</td>
    <td>434</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_III); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
  <tr>
    <td>Zhu et al. 2016</td>
    <td>90</td>
    <td>10</td>
    <td>80</td>
    <td>25</td>
    <td>543</td>
    <td>Brittle</td>
    <td>Etna basalt (EB_III); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td>
  </tr>
</table>
<table><tr><td>Zhu et al. 2016</td><td>110</td><td>10</td><td>100</td><td>25</td><td>640</td><td>Brittle</td><td>Etna basalt (EB_III); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr><tr><td>Zhu et al. 2016</td><td>160</td><td>10</td><td>150</td><td>25</td><td>798</td><td>Brittle</td><td>Etna basalt (EB_III); porosity = 0.05; strain rate = 10<sup>-5</sup> s<sup>-1</sup></td></tr></table>

717

718

719

720

721

722

723

724

725

**Table 1:** Summary of the experimental conditions for the rock deformation experiments used in this study (for the construction of Figs. 3, 4, and 5) (see also Heap et al., 2017). *Pc* = confining pressure; *Pp* = pore fluid pressure; *Peff* = effective pressure; *T* = experimental temperature; *σ*<sub>p</sub> = peak differential stress (see Figure 1). In some cases, failure mode classification differs from that stated in the original publication. Data not included in this compilation are uniaxial experiments conducted at room temperature and instances of non-viscous ductile deformation (see text for details).
726 References

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732 Al-Harthi, A.A., Al-Amri, R.M., and Shehata, W.M. 1999. The porosity and engineering properties of vesicular basalt in Saudi Arabia. *Engineering Geology*, 54, 313-320.

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736 Apuani, T., Corazzato, C., Cancelli, A., Tibaldi, A. 2005. Physical and mechanical properties of rock masses at Stromboli: a dataset for volcano instability evaluation. *Bulletin of Engineering Geology and the Environment*, 64, 419-431.

739 Basilevsky, A. T., Head, J. W. 2003. The surface of Venus. *Reports on Progress in Physics*, 66, 1699-1734.

740 Basilevsky, A. T., Head, J. W., Schaber, G. G., Strom, R. G. 1997. In *Venus II* (eds. S. W. Bougher, D. M. Hunten, and R. J. Phillips). *University of Arizona Press, Tucson, pp. 1047-1087*.

742 Baud, P., Klein, E., Wong, T.-F. 2004. Compaction localization in porous sandstones: Spatial evolution of damage and acoustic emission activity. *Journal of Structural Geology* 26 (4), 603-624.

744 Bauer, S.J., and Handin, J. 1983. Thermal expansion and cracking of three confined water-saturated igneous rocks to 800 °C. *Rock Mechanics and Rock Engineering*, 16, 181-198.

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