I II n ! y ! c field x Multi-Scale Dynamics and Rheology of Mantle Convection with Plates Laura Alisic ([email protected]), Michael Gurnis (Seismological Laboratory, Caltech), Georg Stadler, Omar Ghattas (ICES, University of Texas at Austin), Carsten Burstedde (Rheinische Friedrich-Wilhelms-Universität Bonn) Key Points Global Plate Motions and Plateness Regional Plate Motions Model Constraints Microplates and Trench Rollback 15 cm/yr 15 cm/yr 15 cm/yr 0.00 0.25 0.50 0.75 ω deg/Ma 0.7 0.8 0.9 1.0 plateness 0.00 0.25 0.50 0.75 ω deg/Ma 0.7 0.8 0.9 1.0 plateness 0.00 0.25 0.50 0.75 ω deg/Ma 0.00 0.25 0.50 0.75 1.00 plateness 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ -18 -17 -16 -15 -14 e II [1/s] 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ -18 -17 -16 -15 -14 e II [1/s] 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 160˚ 160˚ 170˚ 170˚ 180˚ 180˚ 190˚ 190˚ -40˚ -40˚ -30˚ -30˚ -20˚ -20˚ -10˚ -10˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ 310˚ 310˚ 320˚ 320˚ 330˚ 330˚ 340˚ 340˚ 350˚ 350˚ -70˚ -70˚ -60˚ -60˚ -50˚ -50˚ -18 -17 -16 -15 -14 e II [1/s] 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 130˚ 130˚ 140˚ 140˚ 150˚ 150˚ 160˚ 160˚ 10˚ 10˚ 20˚ 20˚ 30˚ 30˚ 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 1 0.0 0.5 1.0 1.5 2.0 normvel 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 0.13 0.13 0.0 0.1 0.2 degMy 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 1 0.80 0.84 0.88 0.92 0.96 1.00 P2 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 1 0.0 0.5 1.0 1.5 2.0 normvel 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) -15 -16.0 -15.5 -15.0 -14.5 -14.0 e II [1/s] 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 8.7 0 5 10 15 cm/yr 0 10 20 Rollback (cm/yr) 0 5 10 15 20 25 Subducting plate velocity (cm/yr) 2.0 2.5 3.0 3.5 n 0 10 20 Rollback (cm/yr) 0 5 10 15 20 25 Subducting plate velocity (cm/yr) 0 200 400 600 800 1000 1200 σ y (MPa) 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 13.5 0 10 20 30 cm/yr 0 10 20 30 40 50 60 Rollback (cm/yr) 0 5 10 15 Subducting plate velocity (cm/yr) 2.0 2.5 3.0 3.5 n 0 10 20 30 40 50 60 Rollback (cm/yr) 0 5 10 15 Subducting plate velocity (cm/yr) 0 200 400 600 800 1000 1200 σ y (MPa) 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 11.1 0 5 10 15 20 cm/yr 0 10 20 30 40 50 60 Rollback (cm/yr) 0 5 10 15 20 25 Subducting plate velocity (cm/yr) 2.0 2.5 3.0 3.5 n 0 10 20 30 40 50 60 Rollback (cm/yr) 0 5 10 15 20 25 Subducting plate velocity (cm/yr) 0 200 400 600 800 1000 1200 σ y (MPa) 2.0 2.5 3.0 3.5 Stress exponent 0 200 400 600 800 1000 1200 Yield stress (MPa) 0.80 0.84 0.88 0.92 0.96 1.00 P2 Model 104 yield stress = 100 MPa stress exponent = 3.0 Model 109 yield stress = 1200 MPa stress exponent = 3.75 Model 107 yield stress = 800 MPa stress exponent = 3.0 Convective Stresses • Global dynamic models of mantle convection with plates, using Rhea with adaptive mesh refinement allowing for local resolution of 1 km • Composite viscosity with diffusion creep (linear), dislocation creep (nonlinear), and yield stress • Models have narrow plate boundaries, sharply defined slabs in the upper mantle, and tomography structure in the lower mantle • Yield stress and stress exponent are varied: Strength and nonlinearity • Models are tested with suite of constraints: Plate motions, plateness, minimum shallow slab strain rate from seismic moment release, state of stress from CMT stress axes • We study regional dynamics: Microplate motions and trench rollback as function of yield stress and strain rate • Stress exponent strongly affects model results • Emerging pattern: Yield stress important when low (< 200MPa). When yield stress is high, convective stress becomes more important and yield stress has no impact anymore New Hebrides Sandwich Marianas Figure 1. Typical global viscosity field. (a) Cut through the Pacific (PAC), Marianas (MAR) and Philippine (PS) plates. (b) Zoom-in on the Marianas slab, with nonlinear effects visible in the mantle wedge and slab hinge. (c) Further zoom-in on the mesh around the weak zone at the Marianas trench, as indicated by the white box in (b), with a highest resolution of ~1 km. Black: Rhea surface velocity. Green: NNR-NUVEL1A velocity. Plate motions fit observations reasonably well. PAC plateness is lowest at boundaries and in southwest corner. Plate motions are significantly slower, plateness worse. PAC plate is more stuck due to higher yield stress. Section ro- tation poles are more spread out, indicating more internal deformation. All plates speed up signifi- cantly, plateness improves. The effect of increase in nonlinear- ity (and therefore strain local- ization) is larger than the effect of increase in yield stress. Copper color scale: plateness, measure of rigidity of Pacific plate. Dots: section rotation poles for PAC. New Hebrides rolls back sufficiently. Tonga and Marianas do not roll back fast enough, and Scotia even shows trench advance. Increase in yield stress slows plates down, es- pecially the major plates. Increase in stress expo- nent causes higher strain rates and larger plate velocities. All mi- croplates now roll back rapidly. Black: Rhea velocities. White: NNR- NUVEL1A and velocities from Bird(2003). Background: surface strain rate. Figure 3: Model quantities as function of stress ex- ponent and yield stress, with contours denoting constraints. (a) PAC normalized velocity; (b) Global average normalized plate velocity; (c) PAC plateness; (d) Global average plateness; (e) Net surface rota- tion; (f) Global average shallow strain rate. Figure 2: Left: Global plate motions and plate- ness. Right: Regional plate motions and sur- face strain rate. Figure 4: Left: Trench rollback as function of stress exponent and yield stress, contour denotes constraint. Center: Trench rollback as function of subducting plate velocity, color coded by yield stress; dotted lines denote plate velocity constraints, shallow slab strain rate constraint shown as solid contour. Right: Trench rollback as function of subducting plate velocity, color coded by stress exponent. Tonga-Fiji Scotia Marianas Rollback, subducting plate ve- locity and strain rate con- straints lie close. Models with moderate to high stress expo- nents and yield stress match the constraints. Strain rate constraint is never reached. Only models with high stress exponent come close to matching rollback and subducting plate velocity constraints. The three constraints coincide well, and models with moder- ate stress exponent fit the constraints. The Marianas mi- croplate shows unusually sus- tained effect of yield stress, even for high yield stresses. Figure 5: Schematic of the behaviour of a resulting quantity, e.g. plate velocity, as function of stress exponent (n) and yield stress (σ y ). Dotted lines show contours, which are closer together for higher stress exponent. The transition stress between domains I and II is de- noted as the convective stress, σ c . Domain I: Yield stress and stress ex- ponent both have strong influence on the quantity. σ max = σ y < σ c Yield stress limits strength of material. Domain II: Yield stress has no bearing on the result, only the stress expo- nent has effect. σ max = σ c < σ y Convective stress determines bulk ambient stresses, yield stress affects only localized areas with high ambient stress. (a) (b) (c) (d) (e) (f) PAC PS MAR (a) (b) (c)