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Fig. 5 | Progress in Earth and Planetary Science

Fig. 5

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

Fig. 5

Comparison of the thick solution \(T^{{{\text{thick}}}}\) and the planar solution \(T^{{{\text{plane}}}}\). The ratio between \(\left( {T^{{{\text{thick}}}} \left( {x, t} \right) - T_{0} } \right)\) and \(\left( {T^{{{\text{plane}}}} \left( {x, t} \right) - T_{0} } \right)\) and its deviation from unity are plotted against the nondimensional parameter \(l/2\sqrt {\alpha \left( {t - t_{{\text{s}}} } \right)}\) when a, b \(x/2\sqrt {\alpha \left( {t - t_{{\text{s}}} } \right)} = 0\), and c, d \(x/2\sqrt {\alpha \left( {t - t_{{\text{s}}} } \right)} = 5\), respectively. The solutions were calculated using Eqs. (19), (20), and (23). The other nondimensional parameters were set to \(t_{{\text{s}}} /t = \left( {10^{ - 8} , 10^{ - 5} } \right)\), \(c_{3} t = \left( {10^{5} , 10^{11} } \right)\), and \(c_{5} /c_{4} = \left( {0, 10} \right)\)

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