Numerical Study on Earthquake Energy Partitioning: Relationships Among Radiated Energy, Seismic Moment, and Stress Drop

This paper aims at mechanistically studying some aspects of earthquake energy partitioning with a focus on the radiated energy ( E s ) and seismic moment ( M o ) relationships for investigating differences between estimates of average dynamic stress drop (∆ σ ¯ d ) and static stress drop (∆ σ ¯ s ). We evaluate to what extent a relatively simple but analytically verified faulting simulation can explain such differences. We adopt a numerical methodology developed in the 2‐D Universal Distinct Element Code to simulate fault slip with slip‐weakening responses. A method is introduced for recording the ground reaction to slip and from which we discuss the energy partitioning in ideal cases of rupture. We examine a shallow strike‐slip fault model where a locally peaked stress is gradually developed on the fault by applying tectonic stresses away from the fault surface until a rupture is initiated locally and propagated outward. The rupture is terminated when the available energy is exhausted by the fracture energy and friction work especially as the rupture is followed by a creep. With investigating roles of the available energy for rupture and the fracture energy, we display limited cases where M o does not, at least proportionately, scale with E s . Results show this is because M o , compared to E s , does not fully represent the energy available for initiating a rupture and the fracture energy consumed during its propagation. That is why 2 μE s / M o and 2 μE s / η R M o estimates, with the radiation ratio η R and rigidity μ , may significantly differ from∆ σ ¯ d and∆ σ ¯ s .