Stagnant Lid Research Articles

Melt propagation and volcanism in mantle convection simulations, with applications for Martian volcanic and atmospheric evolution

Standard models for a warm, wet early Mars require a significant CO2‐H2O atmosphere in the past. The source for these phases is assumed to be volcanic degassing. However, no consistent, dynamical models exist relating volcanic degassing to evolving mantle temperatures. Here we use a range of thermal, geophysical, geological, and petrological constraints from Mars to constrain mantle convection model simulations of Mars' post‐Noachian stagnant lid evolution. We develop a methodology to self‐consistently calculate melt extraction from the mantle source region. Using a dike‐propagation algorithm, we can calculate the rate of volcanism and rate of volcanic degassing from these simulations and compare them with estimates for Mars. We find that Martian melt production rates are satisfied by a 200‐km thick lithosphere (surface heat flow 25 ± 5 mW/m3) for an intermediate Martian solidus. Core‐mantle temperatures cannot exceed ∼1850°C from geodynamo constraints, and the enrichment of heat‐producing elements into the crust is unlikely to exceed 25–50%. For hotter Martian mantle temperatures in the past, we find an evolution in rates of volcanism from >0.17 km3/yr for the early Hesperian to ∼1 × 10−4 km3/yr at present, consistent with geological evidence. During this same interval, CO2 flux would have declined from 8.8 × 107 to 6.7 × 106 kg/yr. If the early Hesperian supported a dense (>1 bar) atmosphere, this implies that the average loss rate of CO2 from the atmosphere was 15 times greater than the maximum influx rate during this time.

Onset of convection in fluids with strongly temperature-dependent, power-law viscosity: 2. Dependence on the initial perturbation

The onset of convection in the power-law creep regime on the silicate and icy planetary bodies requires a finite amplitude initial perturbation. This is a nonlinear problem and thus, both the amplitude and shape of the perturbation are important. We performed numerical simulations of the onset of convection in a two-dimensional layer with a fixed temperature contrast between the boundaries and in the stagnant lid regime of temperature-dependent viscosity convection. The optimal perturbations are located at the bottom of the layer (in the rheological sublayer) and have the wavelength of about twice the thickness of the rheological sublayer. The critical Rayleigh number for the onset of convection by optimal perturbations is calculated for a broad range of viscosity parameters. The results are summarized in terms of simple scaling relationships.

Conditions for the onset of plate tectonics on terrestrial planets and moons

Plate tectonics on Earth is driven by the subduction and stirring of dense oceanic lithosphere into the underlying mantle. For such a regime to exist on any planet, stresses associated with mantle convection must exceed the strength of the lithosphere. This condition is sufficiently restrictive that plate tectonics currently operates only on Earth, and mantle convection in most terrestrial planets and moons is probably in a stagnant lid regime. Convective stresses on the lithosphere depend on the viscosity and velocity of underlying cold downwellings. The lithospheric yield stress is controlled by its friction coefficient and elastic thickness (the depth to the brittle–ductile transition or BDT). Both convective stresses and the plate's yield strength depend critically on the size, thermal state and cooling history of a planet. Accordingly, here we use numerical simulations and scaling theory to identify conditions in which mantle convection leads to lithospheric failure for a range of conditions relevant to the terrestrial planets. Whereas Earth is expected to be in a plate-tectonic regime over its full thermal evolution, the Moon and Mercury are expected to have always remained in a stagnant lid regime. Venus, Io and Europa currently fall on the transition between the two regimes, which is consistent with an episodic style of mantle convection for Venus, a tectonic component to deformation on Io, and the resurfacing history and lithospheric evolution of Europa. Our results suggest that Venus may have been in a plate-tectonic regime in the past. While stagnant now, it is plausible that Mars may have also been in an active-lid regime, depending on whether there was liquid water on the surface.

Thermal cracking and the deep hydration of oceanic lithosphere: A key to the generation of plate tectonics?

The development of transient thermal stress in suboceanic mantle is investigated on the basis of two‐dimensional thermoviscoelastic models incorporating composite rheology appropriate for dry oceanic lithosphere. Thermal stress is shown to be sufficiently high to deeply fracture the coldest part of lithosphere, e.g., to the depth of at least ∼30 km (and possibly down to ∼50 km) in 100‐Ma‐old lithosphere. The release of thermal stress by tension cracking is limited to the vicinity of cracks, and the cascade crack system is suggested to be required given the finite fracture strength of mantle materials. Possible physical and chemical consequences of deep thermal cracking are also discussed. The rheological evolution of oceanic lithosphere is likely to be affected by thermal cracking and subsequent serpentinization, which introduces the localized zones of weakness in the otherwise stiffest part of lithosphere. This localized weakening may help to explain why plate tectonic convection, not stagnant lid convection, operates in Earth's mantle.

Mechanisms for cessation of magmatic resurfacing on Venus

Proposed mechanisms of resurfacing on Venus about 0.3–1 Gyr ago usually involve either some form of tectonic resurfacing in which Venusian lithosphere is recycled mechanically or magmatic resurfacing where essentially immobile lithosphere is covered by lava. The focus of this study is mechanisms of magmatic resurfacing in the stagnant lid regime of mantle convection. Parameterized convection models suggest that cessation of magmatic resurfacing can occur in several ways. (1) The mantle temperature drops sufficiently such that mantle rising adiabatically does not cross the solidus. (2) The molten layer migrates below the solid/melt density inversion at 250–500 km so that no melt can escape. (3) Sublithospheric small‐scale convection stops and conductive thickening of the lid suppresses melting. In each case, inability of magma to penetrate thickened Venusian lithosphere may play a role. The timing of melt cessation and duration of late stage resurfacing depend on various factors such as mantle rheology, degree of mantle depletion, and depth of resurfacing. The models indicate that the waning stages of resurfacing which result in surface age variations can last ∼0.1–1 Gyr. A general trend of recent lithospheric thickening is also predicted. Some cases exhibit a rapid transition from relatively thin to thick lid as suggested by previous authors.

Thermal Diapirism and the Habitability of the Icy Shellof Europa

Europa's chaos and lenticulae features may have originated by thermal diapirs related to convective plumes. Warm ice plumes could be habitable, since their temperature is close to the ice melting temperature. Moreover, thermal plumes intruding into the lower stagnant lid warm several kilometers of country ice above 230 K for periods of 10(5) years, and hundreds of meters above 240 K for periods of 10(4) years. Diapir coalescence generating chaos areas should provide a large zone with temperature above approximately 240 K for thousands of years. A temperature above approximately 230 K is potentially interesting for astrobiology, since it corresponds to the lowest temperature at which microbial metabolic activity in Antarctic ice has been reported. So, the warming by thermal plumes could cause an aureole of biological activation/reactivation in the country ice. Adaptation of life to either high salinity or low temperature is similar: it requires the synthesis of compatible solutes, like trehalose or glycerol, which are efficient cryoprotectants. We therefore propose that the future astrobiological exploration of Europa should include the search for compatible solutes in chaos and lenticulae features.

When and how did plate tectonics begin? Theoretical and empirical considerations

Plate tectonics is the horizontal motion of Earth’s thermal boundary layer (lithosphere) over the convecting mantle (asthenosphere) and is mostly driven by lithosphere sinking in subduction zones. Plate tectonics is an outstanding example of a self organizing, far from equilibrium complex system (SOFFECS), driven by the negative buoyancy of the thermal boundary layer and controlled by dissipation in the bending lithosphere and viscous mantle. Plate tectonics is an unusual way for a silicate planet to lose heat, as it exists on only one of the large five silicate bodies in the inner solar system. It is not known when this mode of tectonic activity and heat loss began on Earth. All silicate planets probably experienced a short-lived magma ocean stage. After this solidified, stagnant lid behavior is the common mode of planetary heat loss, with interior heat being lost by delamination and “hot spot” volcanism and shallow intrusions. Decompression melting in the hotter early Earth generated a different lithosphere than today, with thicker oceanic crust and thinner mantle lithosphere; such lithosphere would take much longer than at present to become negatively buoyant, suggesting that plate tectonics on the early Earth occurred sporadically if at all. Plate tectonics became sustainable (the modern style) when Earth cooled sufficiently that decompression melting beneath spreading ridges made thin oceanic crust, allowing oceanic lithosphere to become negatively buoyant after a few tens of millions of years. Ultimately the question of when plate tectonics began must be answered by information retrieved from the geologic record. Criteria for the operation of plate tectonics includes ophiolites, blueschist and ultra-high pressure metamorphic belts, eclogites, passive margins, transform faults, paleomagnetic demonstration of different motions of different cratons, and the presence of diagnostic geochemical and isotopic indicators in igneous rocks. This record must be interpreted individually; I interpret the record to indicate a progression of tectonic styles from active Archean tectonics and magmatism to something similar to plate tectonics at ∼1.9 Ga to sustained, modern style plate tectonics with deep subduction—and powerful slab pull—beginning in Neoproterozoic time.

Transient mantle convection on Venus: The paradoxical coexistence of highlands and coronae in the BAT region

The coexistence of Venusian highlands, attributed to long-lived axisymmetric mantle plumes, and uncompensated coronae, attributed to transient discrete mantle ‘thermals’, is difficult to reconcile with models of mantle convection under thermally steady-state conditions. However, cratering and geological studies indicate a uniformly young surface age (∼ 700 Myr) as well as a comparable timescale for resurfacing (∼ 100 to 400 Myr), possibly consistent with a recent lithospheric overturn and a transient mantle thermal regime. We use laboratory experiments on free and forced thermal convection at high Rayleigh number ( Ra ∼ 10 7) in a variable viscosity fluid to investigate the steady-state and transient thermal regimes preceding and following such an overturn. From analyses of shadowgraph images and time series of global and local variations in temperature, basal heat flux and viscosity, we establish steady-state stagnant- and active-lid states and characterize two intermediate transient regimes. Flow in steady-state stagnant lid is in the form of intermittent thermals, consistent with published work. During the transition to active-lid convection the stagnant lid is stirred into the interior using a conveyor belt. Spreading of this cold fluid along the hot boundary leads to a transition to a “mixed mode” of flow from the hot boundary: approximately isoviscous thermals rise from the thermal boundary layer ahead of the advancing cold front and low viscosity plumes rise from behind the front, as a result of an enhanced temperature contrast. The longevity of this regime and the timescale for the transient depends on the rate of overturn (Pe) and the aspect ratio of the system (A). The magnitude of local temperature, viscosity and heat flux variations increases with Pe and can exceed steady-state values for active-lid convection. Additional numerical simulations show that the mixed mode regime will occur in the presence of internal heating, and for no- and free-slip boundaries. In contrast, the transition from active-lid to stagnant-lid convection is marked by a change from a flow composed of plumes and large-scale overturning motions to a regime dominated by rising and sinking thermals on a timescale of thermal diffusion. Applied to Venus, our results support a hypothesis that the contemporaneous coexistence of the Atla and Beta highlands regions with interspersed uncompensated coronae is consistent with a transient thermal regime following a lithospheric overturn. It is also expected that such coronae formed > 250 Myr after the uplift of the highlands. Implications of the thermal origin of coronae for Venusian mantle structure are also explored.

Influence of low viscosity asthenosphere on mantle flows

Numerical simulation in recent years has revealed that the cold lithosphere, whose viscosity is three to four orders of magnitude higher than that of the underlying mantle, behaves during mantle convection as a stagnant lid. On the basis of model calculations, this paper shows how convection changes over to this regime with increasing viscosity. Spatially fixed high viscosity inclusions and those moving with the convective flow have fundamentally different effects on the structure of convective flows. The model calculations indicate that anomalously low viscosity asthenospheric regions also lead to a specific regime of convection. With a decrease in the viscosity by more than three orders of magnitude, a further reduction in the viscosity of the region ceases to influence the structure of convection in the outer region. The boundary with this region behaves as a freely permeable boundary. In the low viscosity asthenospheric region itself, autonomous convection can arise under certain conditions.

Stagnant lid convection in the mid-sized icy satellites of Saturn

Thermal history models for the mid-sized saturnian satellites Mimas, Tethys, Dione, Iapetus, and Rhea have been calculated assuming stagnant lid convection in undifferentiated satellites and varying parameter values over broad ranges. Of all five satellites under consideration, only Dione, Rhea and Iapetus do show significant internal activities related to convective overturn for extended periods of time. The interiors of Mimas and Tethys do not convect or do so only for brief periods of time early in their thermal histories. Although we use lower densities than previous models, our calculations suggest higher interior temperatures but also thicker rigid shells above the convecting regions. Temperatures in the stagnant lid will allow melting of ammonia-dihydrate. Dione, Rhea and Iapetus may differentiate early and form early oceans, Iapetus only if ammonia is present. Mimas and Tethys with ammonia may differentiate if they accreted in an optically thick nebula with ambient temperatures around 250 K. Our models suggest that the outer shells of the satellites are largely primordial in composition even if the satellites differentiated. In these cases the deep interior may be layered with a pure ice shell underlain by an ammonia dihydrate layer and a rock core.

Temporal variations in the convective style of planetary mantles

Investigations of mantle convection with temperature- and strain-rate-dependent viscosity have shown the existence of fundamentally different convective styles: By varying e.g. the Rayleigh number, the viscosity contrast or the strain-rate dependency of viscosity, the planform of convection in the asymptotic stationary state changes from the so-called stagnant lid regime to an episodic behaviour and further to a state characterised by a permanently mobilised surface. Our studies suggest that this transition may not only be induced by a change of parameters but also occurs temporally for fixed parameters. We have in fact observed convective systems in the stagnant lid regime that show isolated events of surface mobilisation occurring out of a thermally equilibrated state. We use a 3D numerical mantle convection model to investigate mantle convection and surface dynamics as a coupled fluid dynamical system. Our studies focus on the existence of a transitional regime in which temporal variations between the stagnant lid and the episodic regime occur. We were able to deduce a mobilisation criterion that describes the stability of the stagnant surface, thus allowing for a quantitative analysis of the transition to a (temporarily) mobilised surface. This criterion is also suitable to predict the occurrence of surface mobilisation events.

On convection in ice I shells of outer Solar System bodies, with detailed application to Callisto

It has been argued that the dominant non-Newtonian creep mechanisms of water ice make the ice shell above Callisto's ocean, and by inference all radiogenically heated ice I shells in the outer Solar System, stable against solid-state convective overturn. Conductive heat transport and internal melting (oceans) are therefore predicted to be, or have been, widespread among midsize and larger icy satellites and Kuiper Belt objects. Alternatively, at low stresses (where non-Newtonian viscosities can be arbitrarily large), convective instabilities may arise in the diffusional creep regime for arbitrarily small temperature perturbations. For Callisto, ice viscosities are low enough that convection is expected over most of geologic time above the internal liquid layer for plausible ice grain sizes (⩽a few mm); the alternative for early Callisto, a conducting shell over a very deep ocean (>450 km), is not compatible with Callisto's present partially differentiated state. Moreover, if convection is occurring today, the stagnant lid would be quite thick (∼100 km) and compatible with the lack of active geology. Nevertheless, Callisto's steady-state heat flow may have fallen below the convective minimum for its ice I shell late in Solar System history. In this case convection ends, the ice shell melts back at its base, and the internal ocean widens considerably. The presence of such an ocean, of order 200 km thick, is compatible with Callisto's moment-of-inertia, but its formation would have caused an ∼0.25% radial expansion. The tectonic effects of such a late, slow expansion are not observed, so convection likely persists in Callisto, possibly subcritically. Ganymede, due to its greater size, rock fraction and full differentiation, has a substantially higher heat flow than Callisto and has not reached this tectonic end state. Titan, if differentiated, and Triton should be more similar to Ganymede in this regard. Pluto, like Callisto, may be near the tipping point for convective shutdown, but uncertainties in its size and rock fraction prevent a more definitive assessment.

Low‐degree mantle convection with strongly temperature‐ and depth‐dependent viscosity in a three‐dimensional spherical shell

A series of numerical simulations of thermal convection of Boussinesq fluid with infinite Prandtl number, with Rayleigh number 107, and with the strongly temperature‐ and depth‐dependent viscosity in a three‐dimensional spherical shell is carried out to study the mantle convection of single‐plate terrestrial planets like Venus or Mars without an Earth‐like plate tectonics. The strongly temperature‐dependent viscosity (the viscosity contrast across the shell is ≥ 105) makes the convection under stagnant lid short‐wavelength structures. Numerous, cylindrical upwelling plumes are developed because of the secondary downwelling plumes arising from the bottom of lid. This convection pattern is inconsistent with that inferred from the geodesic observation of the Venus or Mars. Additional effect of the stratified viscosity at the upper/lower mantle (the viscosity contrast is varied from 30 to 300) are investigated. It is found that the combination of the strongly temperature‐ and depth‐dependent viscosity causes long‐wavelength structures of convection in which the spherical harmonic degree ℓ is dominant at 1–4. The geoid anomaly calculated by the simulated convections shows a long‐wavelength structure, which is compared with observations. The degree‐one (ℓ = 1) convection like the Martian mantle is realized in the wide range of viscosity contrast from 30 to 100 when the viscosity is continuously increased with depth at the lower mantle.

Onset of convection in fluids with strongly temperature-dependent, power-law viscosity

The onset of convection in the power-law creep regime on the terrestrial planets and icy satellites is poorly constrained. The major difficulty is that the viscosity of power-law fluids approaches infinity when the perturbation amplitudes approach zero and thus the methods of linear theory are inapplicable. Here, we determine the critical Rayleigh number for the onset of convection by starting in the convective regime and gradually decreasing the Rayleigh number in small increments until the solution collapses to the conductive state. For Newtonian viscosity, this approach constraints the subcritical branch and determines the critical Rayleigh number for the cessation of convection. For power-law viscosity, this gives a perturbation-independent critical Rayleigh number below which no steady-state convection solution can exist. The calculations are performed in the stagnant lid regime of temperature-dependent viscosity convection and for several values of the stress exponent. The results approximately agree with earlier theoretical estimates.

Non-Newtonian stagnant lid convection and the thermal evolution of Ganymede and Callisto

The thermal evolution of Ganymede and Callisto was calculated using a realistic water ice heat flux scaling law. This scaling was derived from numerical studies of thermal convection with a stress and temperature dependent viscosity relationship that is descriptive of dislocation creep of crystalline water ice I. This result is then compared with that determined using a non-Newtonian silicate like rheology, a strongly temperature dependent Newtonian rheology and an isoviscous scaling law. In all cases, the stagnant lid convection models resulted in warmer internal mantle temperatures and thicker conductive lids than the isoviscous scaling law, in agreement with theory. It was found that the isoviscous thermal evolution models for each icy satellite gave cool, frozen models, whilst the stagnant lid scaling laws resulted in warmer satellite interiors. High viscosity models resulted in extensive melting of the icy mantle. The presence of subsurface oceans within the icy Galilean satellites has been inferred from the Galileo data and stagnant lid thermal convection is one mechanism through which a subsurface ocean may form.

Plume heat flow in a numerical model of mantle convection with moving plates

Abstract Self-consistent numerical models are presented for a two-dimensional thermal convection with moving plates to estimate the heat flow transported by hot upwelling plumes in both internally and basally heated mantle. The plume heat flow depends on the internal heating rate and convective regimes but does not exceed 30% of basal heat flow when the plates rigidly move as observed on the Earth; the fraction of plume heat flow to basal heat flow becomes higher when the lithosphere behaves as a stagnant lid or as a mechanically not so strong plate. When estimated from the dynamic topography of plume-swells above hot upwelling plumes, the plume heat flow appears to be only a small fraction of the real plume heat flow. As a whole, the apparent plume heat flow estimated from dynamic topography remains only a few percent of the total heat flow on the surface boundary, the value observed for the Earth, even when the basal heating rate exceeds 50% of the total heating rate. Such a high fraction of basal heating rate is necessary for the amplitude of topography above hot upwelling plumes to become comparable to the value observed for the Earth, too. It is necessary to reexamine the earlier inference that the heat released from the core manifests itself as plume heat flow in the Earth.

Towards a self-consistent plate mantle model that includes elasticity: simple benchmarks and application to basic modes of convection

One of the difficulties with self consistent plate-mantle models capturing multiple physical features, such as elasticity, non-Newtonian flow properties, and temperature dependence, is that the individual behaviours cannot be considered in isolation. For instance, if a viscous mantle convection model is generalized naively to include hypo-elasticity, then problems based on Earth-like Rayleigh numbers exhibit almost insurmountable numerical stability issues due to spurious softening associated with the co-rotational stress terms. If a stress limiter is introduced in the form of a power law rheology or yield criterion these difficulties can be avoided. In this paper, a novel Eulerian finite element formulation for visco-elastic convection is presented and the implementation of the co-rotational stress terms is addressed. The salient dimensionless numbers of visco-elastic plastic flows such as Weissenberg, Deborah and Bingham numbers are discussed in a separate section in the context of Geodynamics. We present an Eulerian formulation for slow temperature dependent, visco-elastic-plastic flows. A consistent tangent (incremental) formulation of the governing equations is derived. Numerical and analytical solutions demonstrating the effect of visco-elasticity, co-rotational terms are first discussed for simplified benchmark problems. For flow around cylinders we identify parameter ranges of predominantly viscous and visco-plastic and transient behavior. The influence of locally high strain rates on the importance of elasticity and non-Newtonian effects is also discussed in this context. For the case of simple shear we investigate in detail the effect of different co-rotational stress rates and the effect of power law creep. The results show that the effect of the co-rotational terms is insignificant if realistic stress levels are considered (e.g. deviatoric invariant smaller than 1/10 of the shear modulus say). We also consider the basic convection modes of stagnant lid, episodic resurfacing and mobile lid convection as applicable to a cooling planet. The simulations show that elasticity does not have a significant effect on global parameters such as the Nusselt number and the qualitative nature of the basic convection pattern. Our simple benchmarks show, however, also that elasticity plays a significant role for instabilities on the local scale of an individual subduction zone.

Thermal convection with a water ice I rheology: Implications for icy satellite evolution

We model stagnant–lid convection for water ice I using a multicomponent rheology, combining grain boundary sliding, dislocation and diffusion creep mechanisms. For the superplastic flow–dislocation creep rheology, dislocation creep ( n = 4 ) dominates the deformation within the actively convecting sublayer whilst superplastic flow ( n = 1.8 ) is the dominant process within the stagnant–lid whilst for the superplastic flow–diffusion creep rheology, superplastic flow is the dominant deformation mechanism within the convecting sublayer while diffusion creep ( n = 1 ) is the dominant deformation process in the stagnant–lid. These results suggest deformation in the actively convecting sublayer is likely to be dominated by the mechanism with the largest stress exponent. We also provide heat flux scaling relationships for the superplastic flow, basal slip, dislocation creep–superplastic flow and superplastic flow–diffusion creep rheologies and provide a simple parameterized convection model of an icy satellite thermal evolution.

EVOLUTION OF THE CONTINENTAL LITHOSPHERE

▪Abstract Stable cratons and stable continental platforms are salient features of the Earth. Mantle xenoliths provide detailed data on deep structure. Cratonal lithosphere is about 200 km thick. It formed in the Archean by processes analogous to modern tectonics and has been stable beneath the larger cratons since that time. Its high viscosity, high yield strength, and chemical buoyancy protected it from being entrained by underlying stagnant lid convection and by subduction. Chemically buoyant mantle does not underlie platforms. Platform lithosphere has gradually thickened with time as convection waned as the Earth's interior cooled. The thermal contraction associated with this thickening causes platforms to subside relative to cratons. At present, the thickness of platform lithosphere is comparable to that of cratonal lithosphere.

Effects of plasticity on convection in an ice shell: Implications for Europa

Europa's surface exhibits numerous pits, uplifts, and disrupted chaos terrains that have been suggested to result from convection in the ice shell. To test this hypothesis, we present numerical simulations of convection in an ice shell including the effects of plasticity, which provides a simple continuum representation for brittle or semibrittle deformation along discrete fractures. Plastic deformation occurs when stresses reach a specified yield stress; at lower stresses, the fluid flow follows a Newtonian, temperature-dependent viscosity. Four distinct modes of behavior can occur. For yield stresses exceeding ∼1 bar, plastic effects are negligible and stagnant-lid convection, with no surface motion and minimal topography, results. At intermediate yield stresses, a stagnant lid forms but deforms plastically, leading to surface velocities up to several millimeters per year. Slightly smaller yield stresses allow episodic, catastrophic overturns of the upper conductive lid, with (transient) stagnant lids forming in between overturn events. The smallest yield stresses allow continual recycling of the upper lid, with simultaneous, gradual ascent of warm ice to the surface and descent of cold, near-surface ice into the interior. The exact yield stresses over which each regime occurs depend on the ice-shell thickness, melting-temperature viscosity, and activation energy for viscous creep. To form hummocky matrix and translate chaos plates by several kilometers, substantial surface strain must accompany chaos formation, and the three plasticity-dominated convection modes described here can provide such deformation. Our simulations suggest that, if yield stresses of ∼0.2–1 bar are relevant to Europa, then convection in Europa's ice shell can produce chaos-like structures at the surface. However, our simulations have difficulty explaining Europa's numerous pits and uplifts. When plasticity forces the upper lid to participate in the convection, dynamic topography of ∼50–100-m amplitude results, but the topographic structures generally have diameters of 30–100 km, an order of magnitude wider than typical pits and uplifts. None of our simulations produced isolated pits or uplifts of any diameter.