GEO 5/6690 Geodynamics 05 Nov 2014 © A.R. Lowry 2014 Read for Fri 7 Nov: T&S 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…

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

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.

Audet & Bürgmann Nat. Geosci. 2011

So why do we keep comparing images like this?

And this?

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

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

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.

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…

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

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: