Constraints on crustal stress from fault slip data and topography

地壳的力量导致持续的变形，在大多数地方，地壳变形导致破坏性地震。地壳力和变形分别用应力张量和应变张量在数学上表示。地表变形通常通过大地测量技术测量，并提供对地壳应变场的深入了解。另一方面，直接测量压力既困难又昂贵。因此，与应变相比，我们对地壳应力场知之甚少。在地震的情况下，最近没有破裂的断层周围的张力表明了这些断层的加载速度，而地震时的张力则提供了断层如何在深度滑动的信息。然而，必须指出的是，地震本质上是一种应力现象，断层不断受到载荷，直到断层上积累的应力超过了它们的强度。因此，虽然监测地表应变提供了一些地震潜在信息，但对发震应力的了解可以提前估计地震危险性。在过去的几十年里，在量化导致重大地震的应力方向方面取得了进展；然而，造成这些地震的压力的大小一直难以量化。在地势起伏较大的地方，地形本身对断层造成了很大的应力。虽然，地形断层应力只是总应力预算的一部分，但量化它可以限制导致重大地震的应力大小。除了对地震过程的理解之外，这项研究将有助于更广泛地理解活动构造和地壳变形。在这个项目中，研究人员将限制与最近的中大型大陆地震相一致的发震应力的方向和震级。研究人员试图回答三个主要问题：1)地壳构造应力的大小和方向是什么？2)孕震应力与同震应力变化如何比较？3)地形应力是否与同震滑动相关？回答这些问题依赖于了解地形和构造应力张量场。地形应力是干扰地形区域横向不变的静岩应力的应力的非均匀组成部分。断层上的地形应力可能相当不均匀，断层上的剪应力为10兆帕，正应力为50兆帕。地形断层应力变化与断层同震滑动之间的相关性表明，地形应力场调节破裂模式。在本研究中，将发展径向基函数有限差分（RBF-FD）方法来计算地形应力。RBF-FD方法考虑了非均匀的弹性特性和密度，适用于高地形梯度，并计算了整个地下的应力。该研究将使用贝叶斯方法来估计张拉构造应力，当加上地形应力时，该应力与已知的断层滑动一致。为了进一步约束应力，将包括震源机制和地震附近的地质观测。研究人员将进一步分析估计应力，包括研究地形应力与同震滑动之间的相关性，约束机械断层参数，并比较不同构造制度下的推断应力。对发震应力的限制有可能对地震力学和活动构造问题产生实质性的见解。

Forces in the Earth's crust lead to ongoing deformation, and in most places, crustal deformation results in destructive earthquakes. Crustal forces and deformation are mathematically represented by stress and strain tensors, respectively. Surface deformation is routinely measured through geodetic techniques and gives insight into the crustal strain field. On the other hand, measuring stress directly is difficult and costly. Hence, the crustal stress field is poorly known compared to strain. In the case of earthquakes, strain around faults that have not recently ruptured indicates the rates that those faults are being loaded, while strain during earthquakes yields information on how the faults slipped at depth. It is crucial to note, however, that earthquakes are inherently stress phenomena, with faults continually loaded until the built-up stress on the faults overcomes their strength. Therefore, while monitoring surface strain provides some information on earthquake potential, insight into seismogenic stresses can advance estimations of earthquake hazard. Over the past several decades, progress has been made in quantifying the orientations of the stresses that led to significant earthquakes; however, quantification of the magnitudes of the stresses that caused those earthquakes has been elusive. In places of high topographic relief, topography itself results in significant stresses on faults. Although, topographic fault stress is only one part of the total stress budget, quantifying it allows the magnitudes of stresses that led to significant earthquakes to be constrained. In addition to an understanding of earthquake processes, this research will contribute to a broader understanding of active tectonics and crustal deformation. In this project, the researcher will constrain the orientations and magnitudes of seismogenic stresses that are consistent with recent moderate to large, continental earthquakes. The researcher seeks to answer three primary questions: 1) What are the magnitudes and orientations of tectonic stress in the crust? 2) How do seismogenic stresses compare to coseismic stress changes? 3) Are topographic stresses correlated to coseismic slip? Answering these questions relies on knowing both the topographic and tectonic stress tensor fields. Topographic stresses are the heterogeneous component of stress that perturb a laterally invariant lithostatic stress in regions of topography. Topographic stresses can be quite heterogeneous across faults, adding shear stresses 10 MPa and normal stresses 50 MPa onto a fault. Correlations between variation of topographic fault stresses and coseismic slip across faults, suggest that the topographic stress field modulates rupture patterns. In this study, a radial basis function, finite difference (RBF-FD) method will be developed to calculate topographic stresses. The RBF-FD method allows for heterogeneous elastic properties and densities, holds for high topographic gradient, and computes stresses throughout the subsurface. The study will use Bayesian methods to estimate the tensorial tectonic stresses that when added to the topographic stresses are consistent with known fault slip. To further constrain stress, focal mechanisms and geologic observations nearby to the earthquakes will be included. The researcher will further analyze the estimated stresses, including investigating correlations between topographic stress and coseismic slip, constraining mechanical fault parameters, and comparing inferred stress in different tectonic regimes. Constraints on seismogenic stresses have the potential to yield substantial insight into issues of earthquake mechanics and active tectonics.