Olivine deforms by dislocation creep with the flow law

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Plates, creep and convection: the mantle in motion

Problem

Olivine deforms by dislocation creep with the flow law ε˙=Aσnexp⁡(−Ea/RT)\dot\varepsilon = A\sigma^n\exp(-E_a/RT), where σ\sigma is in MPa\mathrm{MPa}, A=1.1×105 MPa−n s−1A = 1.1\times10^{5}\,\mathrm{MPa^{-n}\,s^{-1}}, n=3.5n = 3.5, Ea=530 kJ mol−1E_a = 530\,\mathrm{kJ\,mol^{-1}}, and R=8.314 J mol−1 K−1R = 8.314\,\mathrm{J\,mol^{-1}\,K^{-1}}. At a depth in the asthenosphere where T=1573 KT = 1573\,\mathrm{K} and the differential stress is σ=0.30 MPa\sigma = 0.30\,\mathrm{MPa}, and neglecting the pressure term pVapV_a of the full flow law, find: ((a)) the strain rate ε˙\dot\varepsilon; ((b)) the effective viscosity ηeff=σ/(2ε˙)\eta_{\rm eff} = \sigma/(2\dot\varepsilon).

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