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Table 1 Parameters used to calculate the example solutions

From: Frictional heating in a thick fault zone with empirical slip-weakening friction: implications for slip parameter estimation from temperature observations in deep fault drilling

Parameter Symbol Value Unit References
Thermal diffusivity \(\alpha\) \(5.0\times {10}^{-7}\) \({\mathrm{m}}^{2} \; {\mathrm{s}}^{-1}\) Hirono and Hamada (2010)
Thermal conductivity \(K\) \(1.43\) \(\mathrm{W} \; {\mathrm{m}}^{-1} \; {\mathrm{K}}^{-1}\)  
Specific heat capacity \(c\) \(1300\) \(\mathrm{J} \; {\mathrm{kg}}^{-1} \; {\mathrm{K}}^{-1}\) Hirono and Hamada (2010)
Bulk rock density \(\rho\) \(2200\) \(\mathrm{kg} \; {\mathrm{m}}^{-3}\) Hirono et al. (2006)
Fluid density \({\rho }_{\mathrm{f}}\) \(1000\) \(\mathrm{kg} \; {\mathrm{m}}^{-3}\)  
Deformation depth   \(1111\) \(\mathrm{m}\) Kano et al. (2006)
Initial temperature \({T}_{0}\) \(46.5\) \(^\circ \mathrm{C}\) Kano et al. (2006)
Peak friction coefficient \({f}_{\mathrm{p}}\) \(1.0\)   Tanikawa and Shimamoto (2009)
Steady-state friction coefficient \({f}_{\mathrm{ss}}\) \(0.2\)   Tanikawa and Shimamoto (2009)
Characteristic length \({d}_{\mathrm{c}}\) \(2.5\) \(\mathrm{m}\) Tanikawa and Shimamoto (2009)
Slip displacement   \(8.3\) \(\mathrm{m}\) Ma et al. (2006)
Slip duration \({t}_{\mathrm{s}}\) \(6\) \(\mathrm{s}\) Ma et al. (2006)
Half width of the fault zone \(l\) \(1 \times 10^{ - 2}\) \(\mathrm{m}\) Ma et al. (2006)
Gravitational acceleration \(g\) \(9.8\) \(\mathrm{m} \; {\mathrm{s}}^{-2}\)  
Total width of the systema   \(1.8 \times 10^{ - 1}\) \(\mathrm{m}\)  
Element sizea \({\Delta }x\) \(6.06 \times 10^{ - 4}\) \(\mathrm{m}\)  
  1. aFor numerical solutions