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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