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

The strain energy released during an earthquake is consumed by processes related to seismic radiation or dissipation. Deep fault drilling and subsequent temperature measurements in a thick fault zone immediately after an event have provided important insights into this dissipation process. By employing an analytical solution to the heat conduction problem, which involves the sudden injection of an infinitesimally thin heat source into an infinite medium, previous drilling projects have estimated the strength of the heat source and the level of shear stress from observed temperature anomalies. However, it is unclear under what conditions this analytical source solution can be regarded as a good approximation for the thick fault problem, a situation which has led to uncertainty of the approximation error in these previous studies. In this study, I first derived an analytical solution for the thick fault problem that accounted for experimentally derived slip-weakening friction. I then validated the derived solution both analytically and numerically. Using the derived thick solution, I next demonstrated that the thick, planar, and source solutions can be considered equivalent under the typical conditions of the previous drilling projects. Therefore, the slip parameters estimated by using the source solution obtained by these studies are appropriate. These results suggest that coseismic information with spatio-temporal extent, such as shear stress and friction coefficient, are lost due to heat diffusion when the temperature observations are conducted; thus, they cannot be inferred directly from observed temperature anomalies. These results also suggest that for most drilling projects, including future ones, the observed temperature distribution can be well explained by using the source solution instead of the thick solution as long as coseismic slip is not markedly delocalized and the spatial extent of the temperature measurements is not significantly larger than the diffusion length.