Numerical investigation of shear zone formation: implications for bimaterial instability and surface heat flux

Abstract

I have performed numerical modeling dealing with shear/frictional heating within the lithosphere using high resolution finite element method. I have focused on three different subjects I-III: I) shear heating at the bi-material interface, II) the efficient numerical scheme for calculation of shear heating and III) frictional heating at the fault plane. Those three subjects are strongly related in terms of mathematical similarity and numerical techniques. In subject I, thermal–mechanical numerical simulations were computed to understand the effects of shear modulus contrast on asymmetric instabilities. Strain-rate and stress-dependent rheology are used with a wide range of activation energy 0–850 kJ mol–1 for all models. Numerical results with enough shear modulus contrast show asymmetric shear instability, which is generated around the interface and then propagates across the interface. Two parts of the lithosphere with different shear moduli (stiff for higher and soft for lower shear modulus lithospheres), which are simply connected to each other without a pre-defined weak zone, were compressed at a constant rate of 2 cm yr–1. The shear modulus contrast has to be close to two for triggering asymmetric shear instability and is found to be by far a more important controlling factor in causing shear instability than activation energy of the creep law. My finding stresses that naturally occurring shear modulus contrast has also important impact on many geological problems related to bimaterial instability. In subject II, I tested an adaptive time-stepping scheme, in particular, the adaptive time-stepping scheme (ATS) where the implicit is adopted for stages of quasi-static deformation and the explicit for stages involving short timescale nonlinear feedback. To investigate the efficiency of this adaptive scheme, I compared it with implicit and explicit schemes for two different cases involving: (1) shear localization around the predefined notched zone and (2) asymmetric shear instability from a sharp elastic heterogeneity. The ATS resulted in a stronger localization of shear zone than the other two schemes. This is because either implicit or explicit schemes alone cannot properly simulate the shear heating due to a large discrepancy between rates of overall deformation and instability propagation around the shear zone. My comparative study shows that, while the overall patterns of the ATS are similar to those of a single time-stepping method, a finer temperature profile with greater magnitude can be obtained with the ATS. The ability to model an accurate temperature distribution around the shear zone may have important implications for more precise timing of shear rupturing, which is important in geodynamics. In subject III, I have studied with high-resolution finite element simulations the potential thermo-mechanical effects ensuing from positive feedback between temperature-dependent thermal conductivity k(T)∝(1/T)^b and frictional heating in a crust-lithosphere system with both brittle and viscoelastic rheology. The variable conductivity together with frictional heating causes drastic reduction in thermal conductivity and these changes can influence the heat-flux near major faults. When b = 1, the temperature is 400 K higher under the fault than that in uniform conductivity case. This is caused by the reduction in thermal conductivity under the surface fault with the temperature rise. Consequently, frictional heating dominates over vertical heat diffusion. In spite of the high temperature around the fault in variable conductivity cases, the surface heat-flux is 60 (for b = 0.5) to 80% (for b = 1) lower than that in the uniform conductivity case. The fault is thermally insulated by the vertical conductivity contrast between the warm frictional zone and the adjacent cold region underneath. I may be able to explain partly the lack of heat-flow anomalies near major faults and also concur with previous hypotheses on the nature of the shear strength associated with these faults.