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

Abstract

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.

Nearly Magnitude‐Invariant Stress Drops in Simulated Crack‐Like Earthquake Sequences on Rate‐and‐State Faults with Thermal Pressurization of Pore Fluids

“…The third method of averaging is consistent with energy partitioning (Noda & Lapusta, ; Noda et al, ). This stress drop is also part of the averaged shear stress versus slip evolution curve that conserves both the total strain energy released as well as the dissipated energy as discussed in section .…”

“…The average curve construction has been shown to preserve total strain energy released and dissipated energy (Noda & Lapusta, ). However, it does not necessarily preserve the breakdown energy as the minimum shear stress of the average curve does not have a simple relation to the minima of the curves of each ruptured point.…”

“…One can illustrate the energy balance by a representative average shear stress versus slip curve (Figure 4). We follow the averaging methodology of Noda and Lapusta (2012) to perform this calculation, which involves taking the stress versus slip evolution of every ruptured point and averaging them in slip rather than in time. Thus, this can only be done once the event is complete, and the stress versus slip evolution is known everywhere.…”

Rupture-dependent breakdown energy in fault models with thermo-hydro-mechanical processes

“…In the case of the initial stress equal to the peak stress, the diagram simplies to that in (B). Note that this diagram is an approximation even if the local behavior is governed by linear slip-weakening friction, since different points of the rupture would have different slip, including near-zero slip close to the rupture edges, and averaging over the dynamic rupture would produce a different curve from the local behavior (Noda and Lapusta, 2012).…”

“…The local slip and stress evolution are determined at every point along the fault within our simulations at all times, thus we can calculate the local dissipation and breakdown energy throughout each rupture as well as study these quantities evolve in different ruptures throughout the sequence. We can also compute the average energy quantities and construct the average stress vs. slip curves for the total rupture process in a manner that preserves the overall energy partitioning (Noda and Lapusta, 2012).…”