Plate tectonics generated by nonlinear rheology in mantle convection models & application to thermo-chemical evolution Paul J. Tackley, UCLA (some parts from Shunxing Xie, Stephane Labrosse) Plan Review ‘plate problem’ and rheology 3D simulations of mantle convection show how pseudo-plastic yielding leads to plate- like behavior Other important effects Strain weakening Viscosity stratification (asthenosphere) Application to planetary evolution From Published Papers EPSL 157, 9-22, 1998 Geochem., Geophys. Geosystems 2000 (2 papers) AGU Plate Motions Monograph 121, 2000 Proc. R. Soc. Lond. A., in press 2002 Viscosity (T) : how much? exp(E/kT) where E~400 kJ/mol T from 1600 -> 300 K =>4x1056 variation => RIGID LID! Expect rigid lid: Earth unusual ? Mars: rigid lid Had plate tectonics early? Venus: rigid lid Plate tectonics->rigid lid? Episodic overturn? Plates and mantle ‘Traditional’ approach 2 separate systems plates ‘drive’ mantle (plate tectonicists) mantle ‘drives’ plates (geodynamicists) Self-consistent approach one system same rheology applies everywhere: h(T,p,e,C,d,history) Rheology Typical mantle convection models: temperature-dependent è or è3 Realistic: as above plus: highly nonlinear @ high stress (yielding) history-dependent (e.g., strain weakening) dependent on grain-size, composition, volatile content... elasticity and brittle failure Too complicated: what is most important? Yield strength of rocks Increases with confining pressure (depth) then saturates Strength profile of oceanic lithosphere Lithospheric deformation Brittle faults: upper part (10-20km?), velocity weakening (rate&state-dependent friction) Ductile shear zones: semi-brittle or plastic flow, strain weakening Distributed viscous creep (mantle) *The strongest part of the lithosphere is in a ductile creep regime* Model 100% internally-heated, RaH=106. 8x8x1 periodic domain Boussinesq Newtonian temperature-dependent viscosity (≤factor 105) visco-plastic yield stress: either constant with depth (‘ductile’) proportional to depth (‘brittle’/’Bylerlee') composite (both of the above) (later) strain-weakening or strain-rate weakening (no elasticity) Equations Boussinesq, infinite Prandtl number h i , j v j,i P Ra.Tz v ˆ yield h heff min (T), 2e Ý T v 0 T v .T 2 t 34 MPa 70 MPa 86 MPa 120 MPa 168 MPa 200 MPa 340 MPa Surface Strain Rate and V RaH=2e7; YS=50 MPa (2e4) QuickTime™ and a Anima tion d ecompressor are neede d to see this picture. RaH=2e7; YS=150 MPa (6e4) QuickTime™ and a Anima tion d ecompressor are neede d to see this picture. By S. Labrosse Mixed internal+basal heating Shows episodic merging of QuickTime™ an d a decompressor downwellings are need ed to see this picture. Core heat flow driven by upper boundary layer Characterizing plate tectonics 'Plateness': Most deformation focused in narrow zones ~15% of surface area (Stein) Significant toroidal motion Spreading centers: passive, symmetric Subduction: single-sided Strike-slip boundaries Earth’s Tor/Pol ratio ~0.3-0.5 (excluding net rotation) Time-Dependence Yield stress increases top to bottom Scaling of plate diagnostics with Yield Stress Does low viscosity beneath the lithosphere help? ‘Asthenosphere’ Decouples piecewise continuous plate motion from distributed mantle deformation ? Want to add in such a way that viscosity is unchanged elsewhere Define ‘solidus’ T=T0+A*depth, decrease h by factor 10 when T reaches solidus (in reality getting close to solidus is sufficient) Varying yield strength Time evolution Greatly improves plate quality So far…instantaneous rheology Isn’t history dependence important? i.e., Strain weakening, and healing Strain weakening? Observed in laboratory Expected in theory Evidenced in the field Mechanisms: Dynamic recrystallization => small grains Volatile infiltration + reactions Viscous dissipation Provides positive feedback leading to strain localization and narrow shear zones Mantle shear zone in Greenland X-section thru shear zone Simplified 'Damage' evolution dD A : e R(T)D Ý dt h h undam aged(1 D) e.g., R(T) 1/ h (T) h hT,z, e,history Ý If A and R very large => strain-rate weakening Comparison of various rheologies Forms lithospheric shear zones …works with more realistic viscosity profile Instantaneous flow with strain rate weakening. Simple 2-lyr model Same with bigger box Simple yielding doesn’t produce plate-like motion Add SW to time-dep models …but doesn’t have a large effect on diagnostics Divergence: Poloidal field Vorticity: Toroidal field Surface Strain rate Divergence Vorticity Pol- & Toroidal with depth Continents aid 1-sided subduction, but add time-depn Summary Successes and failures Robust successes: Linear 'subduction' Linear passive spreading centers+rifts Less Robust successes: Toroidal:Poloidal ratio realistic (sometimes) 1-sided subduction (sometimes) Failures: No focused pure strike-slip margins Things that 'help' Buoyant continents (toroidal flow, 1-sided subduction) 'melting' (focuses MOR) Mantle viscosity stratification (?) Future directions Greater realism Actual rheologies instead of idealized (but not well known) Higher convective vigor Spherical geometry Use to study planetary thermal and chemical evolution Direct simulation and Calibrate/determine scaling for parameterized models Mantle convection models and geochemistry Paul J. Tackley and Shunxing Xie ESS and IGPP, UCLA Integrating Geodynamic and Geochemical Models of Mantle Evolution and Plate Tectonics Motivation Gechemistry and dynamics inextricably linked: Composition affects density, rheology, heating rate Dynamics affects melting, differentiation, mixing Test hypothesized chemical models and processes in a self-consistent manner What works? What model(s) produce results that satisfy both chemical and physical observational constraints? Approach Add tracking of trace & major element chemistry to a numerical convection-plate tectonics code TEST cartoon models: which ones “work” both geophysically and geochemically? Chemical model Major elements: 2-components: ‘crust’ (basalt/eclogite)<-> ‘residue’ (harzburgite). Melts when T reaches solidus (Herzberg et al 2000; Zerr et al 1998) melt instantly removed to form surface crust. Chemical density variation constant with depth except for basalt->eclogite (2.5% in presented models) Trace elements: 207Pb, 206Pb, 204Pb, 143Nd, 144Nd, 147Sm, 235U, 238U, 3He, 4He 36Ar, 40Ar, 40K, 232Th Initial concentrations represent mantle after extraction of CC 3.6 Ga ago. Radioactive decay Partitioning between crust + residue on melting. Coefficients from (Hiyagon+Ozima 86) and (Hofmann 88). Noble gases outgas on melting (99% in presented models) Physical model Compressible anelastic Cylindrical geometry (2-D) Viscosity dependent on: Temperature (factor 106) Depth (factor 10, exponential) Stress (yielding gives different lid behaviors including “plate-like”) Mixed basal and internal heating Geochemical evolution: Focus on 2 cases Differing initial conditions: Chemically homogeneous Chemically layered 50% of isotopes concentrated into lower 20% of mantle 3He concentration calculated to give 8 or 35 times atmospheric today Not yet Earth-like but display some of proposed processes so useful to analyze Convective vigor too low (V~0.3 cm/yr, flux~30mW/m2) Viscosity too high, rheology less T-dependent that Earth (mantle gets too hot, too much melting+differentiation) Homogeneous start: after 1 and 2 Gyr 1 Gyr 2 Gyr C T QuickTime™ and a Anima tion d ecompressor are neede d to see this picture. QuickTime™ and a Anima tion d ecompressor are neede d to see this picture. Homogeneous start (after 3.6 Gyr) Layered start: after 200 Myr and 2.5 Gyr QuickTime™ and a Anima tion d ecompressor are neede d to see this picture. QuickTime™ and a Anima tion d ecompressor are neede d to see this picture. Layered start: present day (3.6 Gyr) Noble gas outgassing: too much(?) Ratios in melted material (last 150 Myr) 3He/4He Pb ratios in melted material Thermal evolution strongly affected by magmatism: simple example Calculation takes into account decay of radiogenic elements and cooling of the core Boussinesq, constant viscosity, but: Viscosity is strongly dependent on mean temperature, realistic activation energy Isochemical case QuickTime™ and a Anima tion de compressor are neede d to se e this picture. Core cooling reduces it to nearly internally-heated convection with differentiation QuickTime™ and a Anima tion de compressor are neede d to se e this picture. Hot layer forms at base Core cooling much reduced QuickTime™ and a Anima tion de compressor are neede d to se e this picture. Heat flow is almost constant Temperature varies much less THE END Yielding generates “plate tectonics” a low- viscosity zone (asthenosp here) helps greatly YS~100 MPa is needed Goals ‘Complete’ understanding of mantle:plate tectonic system Apply to specific events on Earth Understand evolution of Earth, Venus, Mars, e.g., Early plate tectonics on Mars? Episodic plate tectonics on Venus? Pre-plate-tectonics regime on Earth? Rheological Model Strongly temperature-dependent viscosity (many orders of magnitude) +depth-dependent yield stress (brittle) +constant yield stress (ductile) +strain weakening & healing ('damage') No elasticity!
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