The importance of Grain-Size Evolution for the tectonic regime divergence of Venus and Earth
Authors: Manjón-Cabeza Córdoba Antonio , Rolf Tobias 
Published: September 2022

&lt;p&gt;&lt;strong&gt;Introduction&amp;#160;&amp;#160; &amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; &lt;/strong&gt;The surfaces of Venus and Earth display striking differences in geology, tectonism, and volcanic activity, which is particularly intriguing given the similar radius and bulk composition of the two planets. The most evident difference is the lack of well-developed plate tectonics on Venus &lt;em&gt;[e.g., 1]&lt;/em&gt;. However, Venus&amp;#8217; tectonic mode also differs from that of the classical stagnant-lid bodies &amp;#8211; Mars, Mercury and the Moon &lt;em&gt;[2]&lt;/em&gt;. A profound description and definition of Venus&amp;#8217; tectonic regime remains to be made &lt;em&gt;[3]&lt;/em&gt;, but it has to explain Venus&amp;#8217; relatively young and uniformly-aged surface under the condition of rather limited large-scale horizontal surface motion.&lt;/p&gt;
&lt;p&gt;One promising hypothesis to explain the lack of mobile lid tectonics on Venus is that rheological healing is enhanced on Venus&amp;#8217; surface, because the high surface temperature causes faster growth of grains. Faster healing causes more rapid recovery from previous deformation that caused grain shrinking and weakening of crustal rocks &lt;em&gt;[e.g., 4]&lt;/em&gt;. In principle, this should the planet to form a global network of coherent plates. Although this possibility has been demonstrated with theoretical scalings and thin-sheet modelling &lt;em&gt;[4]&lt;/em&gt;, no systematic study exists to investigate this process in fully dynamic models of mantle convection that self-consistently generate a range of tectonic modes relevant for Venus and Earth&lt;em&gt; [e.g., 5,6]&lt;/em&gt;. Using such models coupled to grain size evolution (GSE), we test the hypothesis that enhanced grain growth &amp;#8211; due to higher, Venusian surface temperature &amp;#8211; is capable of shutting down mobile lid tectonics.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Methods &lt;/strong&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; To test our hypothesis, we compute 2D models of mantle flow coupled to GSE in spherical annulus geometry using StagYY &lt;em&gt;[7]&lt;/em&gt; in the extended Boussinesq approximation. We employ a rheology that accounts for diffusion and dislocation creep in a composite Arrhenius formulation, depending on stress and grain size. In addition, the models feature a yield stress, the maximum stress rocks can sustain before deforming plastically. Upon reaching it, the model rheology is dominated by pseudoplastic yielding, leading to locally reduced viscosity as described in previous works &lt;em&gt;[see e.g., 5,6].&lt;/em&gt; Grain size &lt;em&gt;(D)&lt;/em&gt; is tracked using Lagrangian tracers following the equation &lt;em&gt;[8]&lt;/em&gt;:&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;305&quot; height=&quot;104&quot; /&gt;&lt;/p&gt;
&lt;p&gt;where&lt;em&gt;&amp;#160;k&lt;/em&gt;&lt;em&gt;&amp;#160;&lt;/em&gt;and &lt;em&gt;c&lt;/em&gt; are (semi-)empirical factors for grain growth and reduction, respectively. &lt;em&gt;E&lt;/em&gt;&amp;#160;is the activation energy controlling the thermal sensitivity of the grain growth, &lt;em&gt;p&lt;/em&gt;&amp;#160;is the grain growth exponent, &lt;em&gt;f&lt;/em&gt;&amp;#160;is the temperature-dependent fraction of the dissipation &lt;em&gt;&amp;#968;&lt;/em&gt; that is used to reduce grain size. In our systematic investigation, we vary the GSE parameters as well as the surface temperature of the planetary body to predict interior dynamics and surface tectonic modes as a function of the lithospheric yield stress. We then evaluate how applicable the models are to Earth and Venus.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Results&lt;/strong&gt; &amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; An example model assuming Earth-like surface temperature &amp;#8211; representative of the Earth-like mobile lid regime &amp;#8211; is shown in Figure 1. This model almost continuously features at least one site of major subduction, which cools the mantle to comparably moderate internal temperature. Low grain size is obtained mainly in subduction zones, while high grain size is characteristic of (hot) plumes. As a result, viscosity variations are smoothened with respect to models without grain size. An exception to that correlation is the low viscosity area below plates, where high temperatures correlate with low grain sizes, resulting in a weaker asthenosphere.&lt;/p&gt;
&lt;p&gt;&lt;img src=&quot;&quot; alt=&quot;&quot; width=&quot;798&quot; height=&quot;468&quot; /&gt;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;&lt;em&gt;Figure 1&lt;/em&gt;&lt;/strong&gt;&lt;em&gt;: Snapshot of the (left) viscosity and (right) grain size field for a simulation with low surface temperature, representative of the mobile-lid regime. Values are dimensionless and are with respect to reference values of 6.21 Pa s for viscosity and 2.89x10&lt;sup&gt;6 &lt;/sup&gt;m for grain size.&lt;/em&gt;&lt;/p&gt;
&lt;p&gt;Upon increasing the yield stress, the simulations promote a more episodic and, eventually, a stagnant-lid behavior with a continuously immobile lithosphere, as it has been described before. However, the GSE parameters affect the transition from the mobile to stagnant via the episodic regime. In particular, episodic subduction occurs preferentially when grain growth is boosted with respect to grain reduction (increased ). However, neither enhanced grain reduction (increased ) nor enhanced grain growth seem to strongly change the critical yield stress for entering the stagnant lid regime&lt;/p&gt;
&lt;p&gt;Cases with substantially higher surface temperature (as relevant for Venus) are to be performed for this abstract. According to the GSE equation, higher &amp;#160;should boost grain growth and therefore enhance episodicity. However, effects of increasing &amp;#160;are expected to differ from that of increasing &amp;#160;as above, because the former may have less impact on the deeper mantle than the latter, with possible implications for the mantle-lithosphere coupling. These differences will be presented.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;Link to future Venus missions&lt;/strong&gt; &amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; Our study aims to shed light on the characteristics of Venus&amp;#8217; tectonic regime and its thermomechanical origin, thereby pointing to potential differences in lithospheric strength and structure as well as in plate-mantle coupling on Venus and Earth. The array of missions during the upcoming decay of Venus will deliver new observables linked to lithospheric structure, which will help to constrain such generic numerical models. In particular, VERITAS aims to map &amp;#8211; structurally and compositionally &amp;#8211; the surface of Venus, which will help to infer the stress state of the lithosphere and the interior of the planet &lt;em&gt;[9,10]&lt;/em&gt;. Regardless, many other lithospheric and upper mantle characteristics will remain difficult to pinpoint with the next missions. Therefore, modelling studies such as ours provide important complementary insight, in particular with respect to Venus&amp;#8217; evolution to its current state.&lt;/p&gt;
&lt;p&gt;&amp;#160;&lt;/p&gt;
&lt;p&gt;&lt;strong&gt;References&lt;/strong&gt;&lt;/p&gt;
&lt;p&gt;&lt;em&gt;[1] Phillips &amp; Hansen, 1994, Annu. Rev. EPS 22, 597-654; [2] Tosi &amp; Padovan, 2020, AGU Geophysical Monograph, 263, 455-489; [3] Byrne, 2021, PNAS 118; [4] Bercovici &amp; Ricard, 2014, Nature, 508, 513-516; [5] Armann &amp; Tackley, 2012, JGR Planets, 117(2); [6] Rolf et al., 2018, Icarus, 313, 107-123, [7] Tackley, 2008, PEPI, 171, 7-18; [9] Freeman et al., 2016, IEEE; [10] Cascioli et al., 2021, The Planetary Science Journal, 2(6)&lt;/em&gt;&lt;/p&gt;