Scaling laws for stagnant-lid convection with a buoyant crust

SUMMARY Stagnant-lid convection, where subduction and surface plate motion is absent, is common among the rocky planets and moons in our solar system, and likely among rocky exoplanets as well. How stagnant-lid planets thermally evolve is an important issue, dictating not just their interior evolution but also the evolution of their atmospheres via volcanic degassing. On stagnant-lid planets, the crust is not recycled by subduction and can potentially grow thick enough to significantly impact convection beneath the stagnant lid. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a buoyant crustal layer. We systematically vary the crustal layer thickness, crustal layer density, Rayleigh number and Frank–Kamenetskii parameter for viscosity to map out system behaviour and determine the new scaling laws. We find two end-member regimes of behaviour: a ‘thin crust limit’, where convection is largely unaffected by the presence of the crust, and the thickness of the lithosphere is approximately the same as it would be if the crust were absent; and a ‘thick crust limit’, where the crustal thickness itself determines the lithospheric thickness and heat flux. Scaling laws for both limits are developed and fit the numerical model results well. Applying these scaling laws to rocky stagnant-lid planets, we find that the crustal thickness needed for convection to enter the thick crust limit decreases with increasing mantle temperature and decreasing mantle reference viscosity. Moreover, if crustal thickness is limited by the formation of dense eclogite, and foundering of this dense lower crust, then smaller planets are more likely to enter the thick crust limit because their crusts can grow thicker before reaching the pressure where eclogite forms. When convection is in the thick crust limit, mantle heat flux is suppressed. As a result, mantle temperatures can be elevated by 100 s of degrees K for up to a few Gyr in comparison to a planet with a thin crust. Whether convection enters the thick crust limit during a planet’s thermal evolution also depends on the initial mantle temperature, so a thick, buoyant crust additionally acts to preserve the influence of initial conditions on stagnant-lid planets for far longer than previous thermal evolution models, which ignore the effects of a thick crust, have found.

Melt volume at Atlantic volcanic rifted margins controlled by depth-dependent extension and mantle temperature

Breakup volcanism along rifted passive margins is highly variable in time and space. The factors controlling magmatic activity during continental rifting and breakup are not resolved and controversial. Here we use numerical models to investigate melt generation at rifted margins with contrasting rifting styles corresponding to those observed in natural systems. Our results demonstrate a surprising correlation of enhanced magmatism with margin width. This relationship is explained by depth-dependent extension, during which the lithospheric mantle ruptures earlier than the crust, and is confirmed by a semi-analytical prediction of melt volume over margin width. The results presented here show that the effect of increased mantle temperature at wide volcanic margins is likely over-estimated, and demonstrate that the large volumes of magmatism at volcanic rifted margin can be explained by depth-dependent extension and very moderate excess mantle potential temperature in the order of 50–80 °C, significantly smaller than previously suggested.

Continental basalts track secular cooling of the mantle and the onset of modern plate tectonics

The temperature of the convecting mantle exerts a first-order control on the tectonic behaviour of Earth’s lithosphere. Although the mantle has likely been cooling since the Archaean eon (4.0–2.5 billion years ago), how mantle temperature evolved thereafter is poorly understood. Here, we apply a statistical analysis to secular changes in the alkali index (A.I. = whole-rock (Na2O + K2O)2/(SiO2 – 38) as weight%) of intracontinental basalts globally to constrain the evolution of mantle potential temperature (Tp) over the past billion years. During the early Neoproterozoic, Tp remained relatively constant at ~1450 °C until the Cryogenian (720 to 635 million years ago), when mantle temperature dropped by ~50 °C over <180 million years. This remarkable episode of cooling records the onset of modern-style plate tectonics, which has been suggested to have been triggered by a dramatic increase in the supply of sediments to lubricate trenches during the thawing of the Snowball Earth.

Global influence of mantle temperature and plate thickness on intraplate volcanism

The thermochemical structure of lithospheric and asthenospheric mantle exert primary controls on surface topography and volcanic activity. Volcanic rock compositions and mantle seismic velocities provide indirect observations of this structure. Here, we compile and analyze a global database of the distribution and composition of Neogene-Quaternary intraplate volcanic rocks. By integrating this database with seismic tomographic models, we show that intraplate volcanism is concentrated in regions characterized by slow upper mantle shear-wave velocities and by thin lithosphere (i.e. <100 km). We observe a negative correlation between shear-wave velocities at depths of 125–175 km and melt fractions inferred from volcanic rock compositions. Furthermore, mantle temperature and lithospheric thickness estimates obtained by geochemical modeling broadly agree with values determined from tomographic models that have been converted into temperature. Intraplate volcanism often occurs in regions where uplifted (but undeformed) marine sedimentary rocks are exposed. Regional elevation of these rocks can be generated by a combination of hotter asthenosphere and lithospheric thinning. Therefore, the distribution and composition of intraplate volcanic rocks through geologic time will help to probe past mantle conditions and surface processes.

Towards constraining Mars' thermal evolution using machine learning

&lt;p&gt;The thermal evolution of terrestrial planets depends strongly on several parameters and initial conditions that are poorly constrained. Often, direct or indirect observables from planetary missions such as elastic lithospheric thickness, crustal thickness and duration of volcanism are inverted to infer the unknown parameter values and initial conditions. The non-uniqueness and non-linearity of this inversion necessitates a probabilistic inversion framework. However, due to the expensive nature of forward dynamic simulations of thermal convection , Markov Chain Monte Carlo methods are rarely used. To address this shortcoming, some studies have recently shown the effectiveness of Mixture Density Networks (MDN) (Bishop 1995) in being able to approximate the posterior probability using only the dataset of simulations run prior to the inversion (Meier et al. 2007, de Wit et al. 2013, K&amp;#228;ufl et al. 2016, Atkins et al. 2016).&lt;/p&gt;&lt;p&gt;Using MDNs, we systematically isolate the degree to which a parameter can be constrained using different &amp;#8220;present-day&amp;#8221; synthetic observables from 6130 simulations for a Mars-like planet. The dataset &amp;#8211; generated using the mantle convection code GAIA (H&amp;#252;ttig et al. 2013)- is the same as that used by Agarwal et al. (2020) for a surrogate modelling study.&lt;/p&gt;&lt;p&gt;The loss function used to optimize the MDN (log-likelihood) provides a single robust quantity that can be used to measure how well a parameter can be constrained. We test different numbers and combinations of observables (heat flux at the surface and core-mantle boundary, radial contraction, melt produced, elastic lithospheric thickness, and duration of volcanism) to constrain the following parameters: reference viscosity, activation energy and activation volume of the diffusion creep rheology, an enrichment factor for radiogenic elements in the crust, and initial mantle temperature. If all observables are available, reference viscosity can be constrained to within 32% of its entire range (10&lt;sup&gt;19&lt;/sup&gt;&amp;#8722;10&lt;sup&gt;22&lt;/sup&gt; Pa s), crustal enrichment factor (1&amp;#8722;50) to within 15%, activation energy (10&lt;sup&gt;5&lt;/sup&gt;&amp;#8722;5&amp;#215;10&lt;sup&gt;5&lt;/sup&gt; J mol-1 ) to within 80%, and initial mantle temperature (1600&amp;#8722;1800K) to within 39%. The additional availability of the full present-day temperature profile or parts of it as an observable tightens the constraints further. The activation volume (4&amp;#215;10&lt;sup&gt;-6&lt;/sup&gt; &amp;#8722;10&amp;#215;10&lt;sup&gt;-6&lt;/sup&gt;&amp;#160; m&lt;sup&gt;3&lt;/sup&gt; mol&lt;sup&gt;-1&lt;/sup&gt;) cannot be constrained and requires research into new observables in space and time, as well as fields other than just temperature. Testing different levels of uncertainty (simulated using Gaussian noise) in the observables, we found that constraints on different parameters loosen at different rates, with initial temperature being the most sensitive. Finally, we present how the marginal MDN proposed by Bishop (1995) can be modified to model the joint probability for all parameters, so that&amp;#160; the inter-parameter correlations and the associated degeneracy can be capture, thereby providing a more comprehensive picture of all the evolution scenarios that fit given observational constraints.&lt;/p&gt;

Using Volcanic Geochemistry and Seismic Tomography to Refine Global Models of Mantle Temperature and Plate Thickness

&lt;p&gt;The thermochemical structure of lithospheric and asthenospheric mantle exert primary controls on surface topography and volcanic activity. Volcanic rock compositions and mantle seismic velocities provide indirect observations of this structure. Here, we compile and analyze a global database of the distribution and composition of Neogene-Quaternary intraplate volcanic rocks. By integrating this database with seismic tomographic models, we show that intraplate volcanism is concentrated in regions characterized by slow upper mantle shear-wave velocities and by thin lithosphere (i.e. &lt; 100 km). We observe a negative correlation between shear-wave velocities at depths of 125-175 km and melt fractions inferred from volcanic rock compositions. Furthermore, mantle temperature and lithospheric thickness estimates obtained by geochemical modeling broadly agree with values determined from tomographic models that have been converted into temperature. Intraplate volcanism often occurs in regions where uplifted (but undeformed) marine sedimentary rocks are exposed. Regional elevation of these rocks can be generated by a combination of hotter asthenosphere and lithospheric thinning. Therefore, the distribution and composition of intraplate volcanic rocks through geologic time will help to probe past mantle conditions and surface processes.&lt;/p&gt;

What led to episodic subduction during the Archean?

&lt;p&gt;The tectonic regime of the early Earth is crucial to understand how interior and exterior elements of the Earth interacted to make our planet habitable (Cawood et al., 2018). Our understanding of the processes involved is far from complete, particularly about how the switch between non-plate tectonic and plate tectonic regimes may have happened during the Archean. In this study, we investigate how Archean subduction events (albeit isolated and intermittent) may have evolved within/from a stagnant-lid regime. We perform 2D numerical modelling of mantle convection (using Underworld2) under a range of conditions appropriate for the early-to-mid Archean Earth including hotter mantle potential temperature and internal heat production. Using the models, we evaluate how the mantle temperature and viscosity, buoyancy force, surface heat flow and surface velocity may have evolved over a duration of ~800-1000 million years.&lt;/p&gt;&lt;p&gt;Our models indicate that lithospheric drips are an efficient way of releasing a large amount of heat from the Earth&amp;#8217;s surface over a short period of time. Repeated occurrences of dripping events result in average mantle temperature gradually decreasing. Concomitant with this thermal evolution, the drip dimensions grew to form large, symmetrical drips as well as occasional, asymmetric subduction type events. The subduction events lead to large-scale resurfacing of the lithosphere. We surmise that the decreasing of average mantle temperature: (1) increases the temperature dependent viscosity of the mantle, and 2) decreases the buoyancy forces of mantle convection. Both these factors lower the convective vigour and increases the lithospheric (the upper thermal boundary layer) thickness via decreasing the effective Rayleigh number. These changes in the lithosphere-asthenosphere system facilitate the transition from a dripping dominated regime to a mix of large-dripping and intermittent subduction regime over a period of ~1 billon years. This change in tectonic setting is predicted to alter surface velocity patterns, surface heat flux and production rate of felsic magmas, which allows the modelling results can be tested against the rock record.&lt;/p&gt;&lt;p&gt;Reference&lt;/p&gt;&lt;p&gt;Cawood, P. A., Hawkesworth, C. J., Pisarevsky, S. A., Dhuime, B., Capitanio, F. A., and Nebel, O., 2018, Geological archive of the onset of plate tectonics: Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, v. 376, no. 2132.&lt;/p&gt;

Earth's supecontinental climate control

&lt;p&gt;Supercontinent assembly and breakup can influence the rate and global extent to which insulated and relatively warm subcontinental mantle is mixed globally, potentially introducing lateral oceanic-continental mantle temperature variations that regulate volcanic and weathering controls on Earth's long-term carbon cycle for a few hundred million years. In this talk we explore some remarkable consequences of this class of mantle climate control consistent with varied observational constraints. Whereas the relatively unchanging and ice sheet-free climate of the Nuna supercontinental epoch (1.8&amp;#8211;1.3 Ga) is an expected consequence of thorough mantle thermal mixing, the extreme cooling-warming climate variability of the Neoproterozoic Rodinia episode (1&amp;#8211;0.63 Ga), marked by discontinuous periods of global glaciation (snowball Earth), is a predicted effect of protracted subcontinental mantle thermal isolation.&lt;/p&gt;