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## Using seismic data to directly invert for the dynamic stress evolution during earthquake rupture

Benchun Duan, Qingjun Meng, Dunyu Liu, & Yongen Cai

Submitted September 11, 2022, SCEC Contribution #12354, 2022 SCEC Annual Meeting Poster #049

The static stress drop value and dynamic stress evolution process during earthquake rupture provide essential information of fault frictional behavior that governs earthquake rupture dynamics. At present, most of earthquake stress drop and evolution studies are based on kinematic slip inversions, and these stress calculations are strongly dependent on the quality of kinematic slip inversion results. Several fully dynamic inversion methods in the literature require a lot of dynamic rupture forward modeling that makes them cumbersome with limited applicability. A recent study by Xie and Cai (2018, JGR) develops an earthquake static stress model in which static deformation in the medium is the direct result of static stress changes on the fault, instead of static fault slip. In this study, we extend this model to the dynamic process and 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 this fault stress model to directly invert for dynamic stress evolution on the fault plane, by fitting seismic waveforms recorded by local stations. In this inversion method, we calculate the numerical Greenâ€™s functions once only, using an explicit finite element method EQdnya with a unit stress change (1 MPa applied over 1 time step) along strike, dip and normal directions on each subfault patch. During inversion, a linear least-squares solver, with bounds or linear constraints, is used to invert for stress evolution history (source time function) on each subfault. 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. We tested the method on a synthetic model, a checkerboard model and applied it to the 2016 Mw 5.0 Cushing (Oklahoma) earthquake. The inverted stress evolution also determines the slip evolution on the fault plane, thus we can further obtain the stress and slip relationship and quantify variations of slip-weakening distance D0 on the ruptured fault plane.

Key Words
stress inversion, slip inversion, stress evolution, seismic data

Citation
Duan, B., Meng, Q., Liu, D., & Cai, Y. (2022, 09). Using seismic data to directly invert for the dynamic stress evolution during earthquake rupture. Poster Presentation at 2022 SCEC Annual Meeting.

Related Projects & Working Groups
Seismology