Dynamic stress evolution during earthquake rupture contains information of fault frictional behavior that governs dynamic rupture propagation. Most of earthquake stress drop and evolution studies are based on kinematic slip inversions. Several dynamic inversion methods in the literature require dynamic rupture modeling that makes them cumbersome with limited applicability. In this study, we develop a fault-stress model of earthquake sources in the framework of the representation theorem. We then propose a dynamic stress inversion method based on the fault-stress model to directly invert for dynamic stress evolution process on the fault plane by fitting seismic data. In this inversion method, we calculate numerical Green’s function once only, using an explicit finite element method EQdyna with a unit change of shear or normal stress on each subfault patch. A linear least-squares procedure is used to invert for stress evolution history on the fault. To stabilize the inversion process, we apply several constraints including zero normal slip (no separation or penetration of the fault), non-negative shear slip, and moment constraint. The method performs well and reliably on a synthetic model, a checkerboard model and the 2016 Mw 5.0 Cushing (Oklahoma) earthquake. The proposed fault-stress model of earthquake sources with inversion techniques such as one presented in this study provides a new paradigm for earthquake source studies using seismic data, with a potential of deciphering more physics from seismic recordings of earthquakes.

Dynamic modeling of sequences of earthquakes and aseismic slip (SEAS) provides a self-consistent, physics-based framework to connect, interpret, and predict diverse geophysical observations across spatial and temporal scales. Amid growing applications of SEAS models, numerical code verification is essential to ensure reliable simulation results but is often infeasible due to the lack of analytical solutions. Here, we develop two benchmarks for three-dimensional (3D) SEAS problems to compare and verify numerical codes based on boundary-element, finite-element, and finite-difference methods, in a community initiative. Our benchmarks consider a planar vertical strike-slip fault obeying a rate- and state-dependent friction law, in a 3D homogeneous, linear elastic whole-space or half-space, where spontaneous earthquakes and slow slip arise due to tectonic-like loading. We use a suite of quasi-dynamic simulations from 10 modeling groups to assess the agreement during all phases of multiple seismic cycles. We find excellent quantitative agreement among simulated outputs for sufficiently large model domains and small grid spacings. However, discrepancies in rupture fronts of the initial event are influenced by the free surface and various computational factors. The recurrence intervals and nucleation phase of later earthquakes are particularly sensitive to numerical resolution and domain-size-dependent loading. Despite such variability, key properties of individual earthquakes, including rupture style, duration, total slip, peak slip rate, and stress drop, are comparable among even marginally resolved simulations. Our benchmark efforts offer a community-based example to improve numerical simulations and reveal sensitivities of model observables, which are important for advancing SEAS models to better understand earthquake system dynamics.