Recovery of Material Parameters and Friction Laws Associated with Earthquakes, Interseismic Slip, and Tidal Deformation

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The study of earthquake physics remains highly challenging because of its complex dynamics and multifaceted nature. This research takes on the challenge of mitigating the impacts of earthquakes through mathematical understanding. It holds the promise of producing fundamentally new insights in fault physics and advancing the knowledge of friction laws, nucleation and rupture dynamics, localization of (micro)seismicity, crustal rheology, and monitoring stress and material properties. Determining the friction during an earthquake is required to understand when and where earthquakes occur. While this case cannot be reasonably studied in isolation, it is a central thrust of the research. A study of earthquake physics comprises nonlinear (segmented) fault dynamics, formulated as an inverse problem. Faults have nontrivial geometry, dependent on material properties of juxtaposed crustal blocks changing in time, stress, and general rheology of Earth’s crust and upper mantle and large-scale deformation. Tidal forcing will be exploited to enable the study of buoyancy structure deep in our planet's interior. Results will yield procedures for monitoring and obtaining invaluable information about rheology and microstructure in the subsurface, which could also be employed in geothermal exploration and carbon dioxide sequestration. The project offers, via collaborations, a unique interdisciplinary educational experience for the students giving them a much broader appreciation of the importance of novel techniques and real-life implications. The investigator will study inverse problems associated with earthquakes, interseismic slip, and tidal deformation. These inverse problems are defined through systems of partial differential equations describing elastic-gravitational deformation and waves, coupled to nonlinear rate- and state-dependent friction laws on faults, as well as extensions to viscoelastic and nonlocal elastic behaviors accounting for microstructure and complex rheologies. The key advances will pertain to determining friction during an earthquake, gleaning information about friction laws on faults also during interseismic deformation, in conjunction with recovering anisotropic elastic / viscoelastic / nonlocal-elastic material parameters in the crust and fault zones exploiting ruptures, dislocation, and microseismic clouds as sources as well as tidal forcing of the Moon. The rigorous study of possible rapid recovery of a moment tensor (earthquake magnitude and focal mechanism for early warning) from prompt elastogravity signals will be included in the analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.