Dependence of slip weakening distance (D(c)) on final slip during dynamic rupture of earthquakes

In this study, we aim to understand the dependence of the critical slip weakening distance (Dc) on the final slip (Dtot) during the propagation of a dynamic rupture and the consistency of their inferred correlation. To achieve this goal we have performed a series of numerical tests suitably designed to validate the adopted numerical procedure and to verify the actual capability in measuring Dc. We have retrieved two kinematic rupture histories from spontaneous dynamic rupture models governed by a slip weakening law in which a constant Dc distribution on the fault plane as well as a constant Dc/Dtot ratio are assumed, respectively. The slip velocity and the shear traction time histories represent the synthetic ‘real’ target data which we aim to reproduce. We use a 3-D traction-at-split nodes numerical procedure to image the dynamic traction evolution by assuming our modelled slip velocity as a boundary condition on the fault plane. We assume a regularized Yoffe function as source time function in our modelling attempts and we measure the critical slip weakening distance from the inferred traction versus slip curves at each point on the fault. We compare the inferred values with those of the target dynamic models. Our numerical tests show that fitting the slip velocity functions of the target models at each point on the fault plane is not enough to retrieve good traction evolution curves and to obtain reliable measures of Dc. We find that the estimation of Dc is very sensitive to any small variation of the slip velocity function. An artificial correlation between Dc/Dtot is obtained when a fixed shape of slip velocity is assumed on the fault (i.e. constant rise time and constant time for positive acceleration) which differs from that of the target model. We point out that the estimation of fracture energy (breakdown work) on the fault is not affected by biases in measuring Dc.