Scaling of slip weakening distance with final slip during dynamic earthquake rupture

We discuss physical models for the characteristic slip weakening distance D_c of earthquake rupture with particular focus on scaling relations between D_c and other earthquake source parameters. We use inversions of seismic data to investigate the breakdown process, dynamic weakening, and measurement of D_c. We discuss limitations of such measurements. For studies of breakdown processes and slip weakening, it is important to analyze time intervals shorter than the slip duration and those for which slip velocity is well resolved. We analyze the relationship between D_c and the parameters D_c′ and D_a, which are defined as the slip at the peak slip velocity and the peak traction, respectively. We discuss approximations and limitations associated with inferring the critical slip weakening distance from D_c′. Current methods and available seismic data introduce potential biases in estimates of D_c and its scaling with seismic slip due to the limited frequency bandwidth considered during typical kinematic inversions. Many published studies infer erroneous scaling between D_c and final slip due to inherent limitations, implicit assumptions, and poor resolution of the seismic inversions. We suggest that physical interpretations of D_c based on its measurement for dynamic earthquake rupture should be done with caution and the aid of accurate numerical simulations. Seismic data alone cannot, in general, be used to infer physical processes associated with D_c, although the estimation of breakdown work is reliable. We emphasize that the parameters T_acc and peak slip velocity contain the same dynamic information as D_c and breakdown stress drop. This further demonstrates that inadequate resolution and limited frequency bandwidth impede to constrain dynamic rupture parameters.