Constraints on crustal stress from fault slip data and topography

地壳中的力会导致持续的变形，在大多数地方，地壳变形会导致破坏性地震。地壳力和形变分别由应力张量和应变张量表示。地表形变通常通过大地测量技术进行测量，并提供对地壳应变场的洞察。另一方面，直接测量压力是困难和昂贵的。因此，与应变相比，地壳应力场知之甚少。在地震中，最近尚未破裂的断层周围的应变表明了这些断层的加载速度，而地震期间的应变提供了有关断层如何在深处滑动的信息。然而，必须注意的是，地震本质上是一种应力现象，断层不断地加载，直到断层上累积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关于地震潜力的信息，但对孕震应力的洞察可以提高对地震危险性的估计。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，对引起这些地震的应力的大小的量化一直难以捉摸。在地形起伏较高的地方，地形本身会对断层产生显著的应力。尽管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的大小。除了对地震过程的了解外，这项研究还将有助于更广泛地了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中到大的大陆地震相一致的孕震应力的方向和强度。研究人员试图回答三个主要问题：1)地壳中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相比如何？3)地形应力与同震滑动相关吗？要回答这些问题，需要知道地形和构造应力张量场。地形应力是扰动地形区域中横向不变的岩石静应力的应力的不均匀分量。跨断层的地形应力可能相当不均匀，在断层上增加了10兆帕的剪应力和50兆帕的正应力。断层地应力的变化与跨断层的同震滑动之间的相关性表明，地应力场对破裂模式起着调制作用。在这项研究中，将发展一种径向基函数有限差分法(RBF-FD)来计算地形应力。RBF-FD方法考虑了不均匀的弹性性质和密度，适用于高地形梯度，并计算了整个地下表面的应力。这项研究将使用贝叶斯方法来估计张量构造应力，当加上地形应力时，这些应力与已知的断层滑动一致。为了进一步限制应力，震源机制和地震附近的地质观测将包括在内。研究人员将进一步分析估计的应力，包括调查地形应力与同震滑动之间的相关性，约束机械断层参数，以及比较不同构造体制下的推断应力。对孕震应力的约束有可能对地震力学和活动构造问题有实质性的洞察力。

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.