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

地震物理学的研究由于其复杂的动力学和多方面的性质仍然具有很大的挑战性。这项研究承担了通过数学理解减轻地震影响的挑战。它有望在断层物理学中产生全新的见解，并推进摩擦定律，成核和破裂动力学，（微）地震活动的定位，地壳流变学以及监测应力和材料特性的知识。确定地震期间的摩擦力是了解地震发生的时间和地点所必需的。虽然这个案例不能孤立地进行合理的研究，但它是研究的核心。地震物理学的研究包括非线性（分段）断层动力学，作为一个反问题。断层具有非平凡的几何形状，取决于随时间变化的并置地壳块体的材料性质、应力、地壳和上地幔的一般流变学以及大规模变形。潮汐力将被用来研究我们星球内部深处的浮力结构。结果将产生程序，用于监测和获得有关地下流变学和微观结构的宝贵信息，这些信息也可用于地热勘探和二氧化碳封存。该项目通过合作为学生提供了独特的跨学科教育体验，使他们对新技术和现实生活影响的重要性有了更广泛的认识。研究人员将研究与地震、震间滑动和潮汐变形有关的反问题。这些反问题定义通过系统的偏微分方程描述的弹性重力变形和波，耦合到非线性率和状态相关的摩擦法故障，以及扩展到粘弹性和非局部弹性行为占微观结构和复杂的流变学。关键的进展将涉及确定地震期间的摩擦，收集有关断层摩擦规律的信息，也在地震间变形期间，结合恢复地壳和断层带中的各向异性弹性/粘弹性/非局部弹性材料参数，利用破裂，位错和微震云作为来源以及月球的潮汐力。分析中将包括对可能从瞬时弹性重力信号中快速恢复力矩张量（地震震级和震源机制）的严格研究。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.