Impact of Friction and Scale-Dependent Initial Stress on Radiated Energy-Moment Scaling

The radiated energy coming from an event depends on a number of factors, including the friction and, crucially, the initial stress. Thus we cannot deduce any scaling laws without considering initial stress. However, by simulating long sequences of events, where the system evolves to a statistically steady-state, we can obtain the appropriate distribution of initial stresses consistent with the dynamics and a given friction. We examine a variety of frictions, including power-law slip dependence, and explore a variety of scaling relations, with the aim of elucidating their radiated energy-moment scaling. We find, contrary to expectations, that apparent stress is not seen to increase with earthquake size for power-law weakening. For small and for large events, little change in apparent stress is seen with increasing rupture size, while intermediate sized events interpolate in between. We find the origin of this unexpected lack of size dependence in systematic changes of initial stress, with bigger events tending to sample regions of lower initial stress. To understand radiated energy-moment scaling, scale-dependent initial stress needs to be considered