Estimation of the critical slip-weakening distance: Theoretical background

It has been shown that a trade-off exists between estimates of the breakdown strength drop and the critical slip-weakening distance (e.g., Guatteri and Spudich, 2000). For this reason, only the fracture energy, proportional to these two parameters, may be estimated from waveform modeling. However, Mikumo et al. (2003) proposed a new technique to estimate the slip-weakening distance of earthquakes, separate from the fracture energy. For this method to be valid, the peak slip-velocity time must be close to the stress breakdown time. Here we explain the theoretical background of this assumption and clarify the limitations of this technique using numerical simulations based on the boundary integral equation method. The theoretical analysis using the boundary integral equation and some numerical tests indicates that a rather smooth rupture process and relatively sharp change in stress at the stress breakdown time in the slip-weakening curve ensure the validity of the method.