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Scaling of viscous shear zones with depth dependent viscosity and power law stress strain-rate dependence James Moore and Barry Parsons

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Introduction What are the dominant physical mechanisms that govern localisation of shear at depth in a strike-slip regime? Depth dependent viscosity Major control Shear zones of 3-7km for reasonable crustal parameters Non-linear stress strain-rate relationship Also significant, but secondary Thermomechanical coupling Further localisation consequence of a pre-existing narrow shear zone Scaling relation for continental lithologies Viscosity structures that explain post-seismic deformation at NAF Conclusions – 3-7km for crustal conditions etc. Results – scaling, DDV is major control (2-3 bullet points on here) What have I done, don’t worry about other people. Add solution figure in IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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2D approximation for infinitely long strike-slip fault. Stokes flow for anti-plane conditions: Far field driving velocities Rigid lid moves as block motion Model construction IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Contours at 10% intervals, dashed for 50% Width of domain: At the base of the layer, shear is widely distributed: Constant viscosity layer 90% of far field motion at 1.66d50% of far field motion at 0.56d IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Depth dependent viscosity IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Scaling of shear zone width with DDV Force balance: Simple scaling relation, valid for small z 0. IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Non-linear, uniform properties IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Scaling of shear zone width with n Horizontal derivative of the velocities is, in general, much greater than the vertical. Simple scaling relation, valid for large n: IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Scaling of shear zone width with n IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Arrhenius law Viscosity structure: 0 th order Taylor expansion: IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Arrhenius viscosity structure IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Arrhenius velocity field Arrhenius Depth Dependent IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Comparison of mechanisms Contours at 10% of driving velocity Material Parameters from Hirth & Kohlstedt (2003), Hirth et al. (2001) IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Combined scaling law Depth dependent Effective z 0 for Arrhenius Non-linear scaling IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Shear zone width for crustal lithologies Reasonable parameter values for continental crust outlined in yellow For 30km thick crust, expect shear zones of 3-7km IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Combined scaling law IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Recent observations Yamasaki et al require a region of low viscosity beneath the North Anatolian Fault to explain post-seismic transient deformation following the 1999 Izmit and Duzce earthquakes Could this be the fingerprint of a zone of localised shear? What are the viscosity structures from our model? IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Viscosity structures IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Depth dependence of viscosity produces narrow shear zones Power law rheology also provides a strong control Shear heating and further localisation of shear is a consequence of having a pre-existing narrow shear zone Viscosity structures generated by shear heating and/or power law rheology are important for the dynamics of post-seismic deformation Scaling law: IntroductionModelDepth dependentNon-linearArrheniusCombinedViscosity StructuresConclusions

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Fin Thank you for listening Moore and Parsons (submitted), Scaling of viscous shear zones with depth dependent viscosity and power law stress-strain rate dependence, Geophysical Journal International. This work was supported by the Natural Environment Research Council through a studentship to James Moore, the Looking into the Continents from Space project (NE/K011006/1), and the Centre for the Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET). We thank Philip England for helpful discussions during the course of this work.

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Scaling of shear zone width with DDV

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Shear Heating 0.1

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Linear ductile shear zones Exponentially Depth Dependent Viscosity Viscosity structure: Governing equation: Solution: Rheological Parameters z 0 : e-folding length η 0 : viscosity coefficient Variables u: velocity Rheological Parameters z 0 : e-folding length η 0 : viscosity coefficient Variables u: velocity Constants w: width of domain Rheological Parameters z 0 : e-folding length η 0 : constant viscosity Variables u: velocity Constants w: width of domain Rheological Parameters z 0 : e-folding length η 0 : constant viscosity Variables u: velocity

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Linear ductile shear zones Arrhenius law Viscosity structure: Thermal structure: Governing equation: Approximate solution may be obtained by Taylor expansion of RHS about z=1/2. Constants R: gas constant te: elastic lid thickness / d Rheological Parameters B: material constant Q: creep activation energy beta: Geotherm Variables T: temperature η: viscosity Constants R: gas constant te: elastic lid thickness / d Rheological Parameters B: material constant Q: creep activation energy beta: Geotherm Variables T: temperature η: viscosity

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Linear ductile shear zones Arrhenius law To a first order approximation this is equivalent to an exponentially depth dependent viscosity with Velocity profile at z=1 is accurately captured with this approximation Extremely high viscosity gradients in the shallow crust cause further shear localisation for z <1/2. Higher order approximation is in agreement with numerical results

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Non-linear ductile shear zones Uniform properties: Viscosity structure: Governing equation: Approximate solution assuming : Constants J 2 : Second invariant of strain tensor w: width of domain Rheological Parameters n: power law Variables u: velocity η: viscosity Constants J 2 : Second invariant of strain tensor w: width of domain Rheological Parameters n: power law Variables u: velocity η: viscosity

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Non-linear ductile shear zones Exponentially depth dependent viscosity: Viscosity structure: Governing equation: Approximate solution assuming : Constants J 2 : Second invariant of strain tensor w: width of domain Rheological Parameters n: power law Variables u: velocity η: viscosity Constants J 2 : Second invariant of strain tensor w: width of domain Rheological Parameters n: power law Variables u: velocity η: viscosity

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Additional Equations 1 st order approximate Arrhenius solution

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Previous work Yuen et. al. [1978] analysed the 1-D problem to investigate the relationship between thermal, mechanical and rheological parameters that govern shear zone behavior Once a shear zone forms it will remain localised due to shear-stress heating Thatcher and England [1998] investigated the role of thermomechnical coupling, or shear heating in the more complex 2-D problem Broad range of behaviors but for reasonable parameter values shear zones are narrow. Shear localisation driven by dissipative heating near the axis of the shear zone causing reduction in temperature dependent viscosity Takeuchi and Fialko [2012] used a time dependent earthquake cycle model Thermomechanical coupling with a temperature dependent power-law rheology will localise shear Do we need themomechanical coupling, or a power law rheology, to generate shear zone localisation?

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