Many recent studies have tried to determine the influence of geometry of faults in earthquake mechanics. In this paper, we suggest a new interpretation of the effect of geometry on the stress on a fault. Starting from the representation theorem, which links the displacement in a medium to the slip distribution on its boundary, and assuming homogeneous infinite medium, a regularized boundary-element equation can be obtained. Using this equation, it is possible to separate the influence of geometry, as expressed by the curvatures and torsions of the field line of a dislocation on the fault surface, which multiply the slip, from the effect of the gradient of slip. This allows us to shed new light on the mechanical effects of geometrical complexities on the fault surface, with the key parameters being the curvatures and torsions of the slip field on the fault surface. We have used this new approach to explain further the false paradox between smooth-and-abrupt-bends (see Sato et al. (2019)) as well as to re-interpret the effect of roughness on a fault.

中文翻译：

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曲率，断层几何复杂性之间的机械联系：应用于弯曲、扭结和粗糙断层

许多最近的研究试图确定断层几何形状对地震力学的影响。在本文中，我们建议对几何形状对断层应力的影响进行新的解释。从表示定理开始，将介质中的位移与其边界上的滑移分布联系起来，假设均匀的无限介质，可以得到一个正则化的边界元方程。使用这个方程，可以将几何学的影响与滑动梯度的影响分开，如断层表面上位错场线的曲率和扭力所表示的，它们乘以滑动。这使我们能够对断层表面上几何复杂性的机械效应有了新的认识，关键参数是断层表面滑移场的曲率和扭转。我们已经使用这种新方法来进一步解释平滑和突然弯曲之间的错误悖论（参见 Sato 等人（2019））以及重新解释粗糙度对断层的影响。