On Averaging Interface Response During Dynamic Rupture and Energy Partitioning Diagrams for Earthquakes

Earthquakes occur as dynamic shear cracks and convert part of the elastic strain energy into radiated and dissipated energy. Local evolution of shear strength that governs this process, which is variable in space and time, can be studied from laboratory experiments and rupture models. At the same time, increasingly accurate measurements of radiated energy and other quantities characterize earthquakes in a rupture-averaged way. Here, we present and study two approaches to averaging frictional dissipation during dynamic rupture. The first one is based on the actual progression of dissipation, but the associated averaged shear stress does not reflect the local friction behavior. The second one is constructed to preserve prevailing features of local stress-slip response and performs well in the examples studied. The developed approach should be useful for visualizing energy partitioning in dynamic models and linking them to observations using diagrams that reflect dominant features of local stress evolution.