1. GEO 5/6690 Geodynamics 05 Nov 2014 © A.R. Lowry 2014 Read for Fri 7 Nov: T&S 226-241 Last Time: Flexural Isostasy Tharsis example Is the Tharsis province a surface load (volcanic construction) or internal load response (single-plume buoyancy) or both? Approach 1: Solve for loads for the entire range of possible density, T e, load depth parameters This gives load scenarios ranging from 50% of topography due to plume, to 0%, to negative plume buoyancy (so puts bounds on possible loading!) Approach 2: Find the model parameters that minimize correlation of the surface and internal loads Results in ~4% of topography from plume buoyancy, reasonable T e ~ 110 km, unreasonable(?) surface density of 2600 kg/m 3, indeterminate crustal thickness & mantle density…

2. Next Journal Article(s) Reading: For Monday Nov 10: Willett et al. (1985) A thermo- mechanical model of continental lithosphere, Nature 314 520-523.

3. T e Estimation: T e that minimizes correlation of the load fields is permitted to vary spatially. Low T e is found in regions of high heat flow and active extension; higher T e in stable lithosphere. Seismicity and deformation tend to focus at transitions from high to low T e.

4. Audet & Bürgmann Nat. Geosci. 2011

5. So why do we keep comparing images like this?

6. And this?

7. Earth interseismic deformation is predominantly viscoelastic flow, but Flow rheology is poorly known MOTIVATION: Latychev et al, GRL, 2005 Data used to estimate viscosity include: Uplift from post-glacial rebound Pleistocene lakeshore rebound Postseismic relaxation GPS surface velocities Proxy from seismic velocities Sample the Earth Poorly Relationship Poorly Determined

8. Flexural isostatic model assumes a perfectly elastic plate or shell… Rocks in the real Earth fracture and flow. What does T e mean in that context? T e and Rheology

9. Identity relating Effective Elastic Thickness T e to flexural rigidity D RelationshipEquation Parameters “Leaf-Spring” approximation for multilayer bending D = D m + D c Young's Modulus E Poisson's Ratio Flexural rigidity and bending moment M Plate bending curvature K Definition of bending moment Truncation of bending fiber stress  f by Yield Strength Envelope Depth of plane of neutral bending z n defined by minimum moment Yield Strength Envelope  YSE Friction coefficient  Pore fluid pressure Strain Rate  Power law A, n, H * Temperature T.

10. Flow Rheology… (Here, represented as a yield strength envelope) depends on: Temperature T Lithology (pyroxene > olivine > feldspar > quartz) Water fugacity f H2O (and to a lesser extent) Strain rate  Grain size d Pressure P. Ideally, we’d use geophysics to determine 3D variation of each field independently…

11. First need independent constraint of the geotherm… T e and Rheology

12. Buehler & Shearer, JGR 2010Schutt et al., in preparation P n velocity variation Moho temperature from P n & mineral physics Moho temperature T Moho from P n phase: