Statistics – Computation
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008epsc.conf..217a&link_type=abstract
European Planetary Science Congress 2008, Proceedings of the conference held 21-25 September, 2008 in Münster, Germany. Online a
Statistics
Computation
Scientific paper
Background Several first-order aspects of the dynamics of Venus' mantle remain poorly understood. These include (i) how Venus' mantle loses its radiogenic heat, which is expected to be about the same as Earth's, despite the presence of stagnant lid convection. Hypotheses that have been advanced (summarised in [1]) are conduction through a thin lithosphere, episodic overturn of the lithosphere, magmatic heat transport, and concentration of almost all heat-producing elements into the crust, but there are problems with all of these taken individually. A thick lithosphere may not be consistent with admittance ratios, magmatic heat transport would require a too-large resurfacing rate, and a large concentration of heat-producing elements in the crust would cause weakness and possibly melting in the deep crust. (ii) The relatively long-wavelength distribution of surface features, which is surprising because numerical models and analogue laboratory experiments of stagnant-lid convection produce relatively short-wavelength convective cells. (iii) The inferred (from crater distributions [2]) relatively uniform surface age of 500-700 Ma. (iv) Whether the highlands are above mantle downwellings as on Earth or above mantle upwellings [3]. (v) How the mantle can have outgassing only 25% of 40Ar [4] but supposedly most of its water [5]. (vi) The cause of coronae and relationship to mantle processes [6]. Model To study some of these questions, we take advantage of advances in computational capabilities to perform integrated thermo-chemical convection models of Venus' evolution over 4.5 billion years, in 3-D spherical geometry as well as 2-D spherical annulus geometry [7]. These models include realistic ("laboratory") rheological parameters for diffusion creep and dislocation creep based on [8][9], which are also composition-dependent, and plastic yielding based on Byerlee's law, which might cause changes in tectonic regime (e.g., episodic plate tectonics). Crustal formation and the resulting differentiation of the crust and mantle are modelled using a self-consistent melting criterion, which also allows outgassing and trace element partitioning to be tracked [10][11], as well as the mean age of the crust. Phase transitions in both the olivine system and pyroxene-garnet system are included. The concentration of heat-producing elements is assumed to be the same as in bulk silicate Earth and decreases with time, and cooling of the core is tracked using a parameterised core heat balance. Geoid and surface topography are calculated using a self-gravitating formulation. Thus, the model constitutes an attempt to incorporate as much realism as is presently feasible in global-scale 3-D spherical simulations. Simulations are performed using StagYY, which uses a finite volume multigrid solver on the Yin-Yang spherical grid [12], and is developed from the earlier cartesian Stag3D [13]. Analysis We are performing a systematic suite of simulations varying uncertain properties and parameters, related to rheology, melting+eruption, and initial condition, and compare model results to observations of: • Surface topography. This includes the general (qualitative) distribution of highlands and lowlands, the hypsometric distribution, and the lateral spectrum. • Geoid. The spectrum and amplitude of the geoid, the extent to which is is correlated with topography, and admittance ratios. These have previously been used to argue for a thick lithosphere and lack of asthenosphere, but are non-unique, so it may well be possible to produce the observed signatures in other ways, in a selfconsistent convection calculation. • The mean surface age, meaning the time since the basalt was erupted, and the statistical distribution of surface ages. This will be compared to constraints from crater statistics and from geomorphological interpretations. • Crustal deformation rates in the last part of the evolution (e.g., [14]). • The mean crustal thickness, although this is not well constrained from an observational perspective. • Outgassing of radiogenic argon (40Ar) and of nonradiogenic volatiles (e.g., water). If much magmatism occurs early on, then it should be possible to obtain the loss of most of the water while retaining the majority of radiogenic 40Ar, because 40Ar had not yet been produced early on. In the future, we plan to include the dependence of rheology on water concentration. • The general distribution of crustal features and similarities to features on Venus such as coronae. • The time evolution of heat flux through the CMB, to constrain when a dynamo might have occurred, and to understand why there is no geodynamo today. Of particular interest is whether a smooth evolution can satisfy the various constraints, or whether episodic or catastrophic behaviour is needed, as has been hypothesised by some authors. Figure 1 shows preliminary results for a case in which the crustal rheology is the same as that of the upper mantle. Over time, the crust becomes at least as thick as the mechanical lithosphere, and delamination occurs from its base. A thick crust is a quite robust feature of these calculations. A few strong plumes rise from the CMB. About 50% of radiogenic Argon is outgassed in this case. References [1] Turcotte, D. L. (1995) JGR, 100, 16931-16940. [2] Hauck, S. A. et al. (1998) JGR, 103, 13635-13642. [3] Bindschadler, D. L. et al. (1992) JGR, 97, 13495- 13532. [4] Kaula, W. M. (1999) Icarus, 139, 32-39. [5] Kaula, W. M. (1994) Phil. Trans. R. Soc. Lond. A, 349, 345-355. [6] Johnson, C. L. and Richards, M. A. (2003) JGR 108, doi:10.1029/2002JE001962. [7] Hernlund, J. W. and P. J. Tackley (2008) PEPI, submitted. [8] Karato, S. and P. Wu (1993) Science, 260, 771-778. [9] Yamazaki, D. and S. Karato (2001) Amer. Mineral., 86, 385-391. [10] Nakagawa, T. and P. J. Tackley (2005) Gcubed, 6, doi:10.1029/2005JB003751. [11] Xie, S. and P. J. Tackley (2004) PEPI, 146, 417- 439. [12] Tackley, P. J. (2008) PEPI, submitted. [13] Tackley, P. J. (1993) GRL, 20, 2187-2190. [14] Grimm, R. E. (1994) JGR, 99, 23163-23171.
Armann Marina
Tackley Paul J.
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