Rheology and the Dynamics of Subduction Bruce Buffett, UC Berkeley May 6, 2016 The Open University

(S. Rost) Mantle Convection Plate tectonics is the surface expression of mantle convection - source of buoyancy - source of dissipation - kinematic constraint Influence of plates Recycling the thermal boundary layer promotes cooling

Boundary-Layer Theory Predictions 1. Heat Flow 2. Velocity 3. Plate Size D Rayleigh Number D Oxburgh & Turcotte (1978)

Dynamics of Subduction i) old lithosphere supplies buoyancy for convection ii) bending resists subduction of old (thick) plates Interplay of Forces depends on R

Dynamics of Subduction i) old lithosphere supplies buoyancy for convection ii) bending resists subduction of old (thick) plates Interplay of Forces “radius of curvature adjusts to prevent bending resistance from becoming large” (Davies, 2009) depends on R

Experimental constraints on the strength of the lithospheric mantle Journal of Geophysical Research: Solid Earth Volume 115, Issue B8, B08204, 12 AUG 2010 DOI: /2009JB Volume 115, Issue B8, Mei et al. (2010) composite rheology: brittle, low-T plasticity and high-T plasticity Experimental constraints on the strength of the lithospheric mantle

Deformation of Lithosphere distance along plate: s curvature strain-rate

Deformation of Lithosphere distance along plate: s curvature strain-rate Benioff Zone Bevis (1986)

Bending Stress Find the stress that accommodates the strain rate Buffett & Becker (2012) H mech ~ 60% H therm stress insensitive to u 0 stress saturates (n ~ 14)

Outer Rise Earthquakes Craig et al. (2014)

Torque Balance Moment M A balance requires When stresses (or moment M) saturate a balance is not possible

Other Forces Low pressure in lubricating layer thickness ~ 1 km Nature of slab interface influences (or controls?) evolution of curvature overriding plate could climate influence dissipation at subduction zones? 1. Lubrication Theory

A Numerical Investigation Holt et al. (2015)

Curvature of Subducting Plate Holt et al. (2015) Overriding Plate ThicknessSubducting Plate Thickness

Curvature of Subducted Lithosphere Buffett & Heuret (2011)

Does this Happen on Earth? Holt et al. (2015) Bird et al. (2008)

Conclusions rheology of lithosphere has a strong influence on subduction best estimates suggest a highly nonlinear stress dependence (n~14) geometry (and dissipation) of slab controlled by overlying lithosphere? a rich and complex dynamics

Connection to Dissipation bending force D Rate of Work (Power) Thin-Plate Theory Dissipation

Does this Happen on Earth? Holt et al. (2015) Bird et al. (2008) a)

Plastic Plate In-Plate Force N(s) slab pull bending force D

Earthquake Focal Mechanisms Integrate force balance D tension compression (plastic)

A Global Compilation Heuret (2005) SimpleNot so simple

Relative Importance of Forces Rate of work done by slab pull W sp = u F sp W sp  H Buffett & Rowley (2006)

Dependence on Age Radius of CurvatureDissipation (Plastic) Buffett & Heuret (2011)

Laboratory-Based Rheology What can laboratory studies tell us? 1. Mohr-Coulomb model (Byerlee, 1978) 2. Low-temperature creep (high  n and low T) (Mei et al., 2010) 3. High-temperature creep (high  n and high T) (Hirth and Kohlstedt, 2003) Build a composite rheology for subducted lithosphere

Bending Moment Moment is nearly independent of plate velocity slab behaves like a perfectly plastic solid Moment M(s) age

Example Central Aleutian -use spline fit to compute K(s) and evaluate strain-rate -use composite rheology to evaluate stress and moment M(s) K(s)

Example Central Aleutian Bending force K(s) M(s) (comparable to ridge push force; 20% of slab pull force)

Connection to Climate?

Conclusions Forsyth & Uyeda (1975)

A Connection to Great Earthquakes? Curvature is driven by buoyancy and opposed by stress on fault (  = 10 MPa) Ratio of moments

Initiation of Subduction McKenzie (1977) F sp + F rp > F f + F b Typical values (in N/m) XX u > 1.3 cm/yr Subduction

Initiation of Subduction Gurnis et al. (2004) 2cm/yr 109 km XX

Variations in Curvature with Age Equivalent radius of curvature Viscous dissipation (  = 3x10 22 Pa s) Su u: subduction velocity H: plate thickness

The Art of Modeling.. cannot be learned by reading books and articles The reason Books and articles remove the “scaffolding”; they do not reflect the way the results were actually obtained. Scaling, G.I. Barenblatt (2003)