Earth Systems Science Computational Centre, School of Earth Sciences, University of Queensland, St Lucia, QLD 4072, Australia.
Philos Trans A Math Phys Eng Sci. 2010 Jan 13;368(1910):119-30. doi: 10.1098/rsta.2009.0190.
No complete physically consistent model of earthquake rupture exists that can fully describe the rich hierarchy of scale dependencies and nonlinearities associated with earthquakes. We study mesh sensitivity in numerical models of earthquake rupture and demonstrate that this mesh sensitivity may provide hidden clues to the underlying physics generating the rich dynamics associated with earthquake rupture. We focus on unstable slip events that occur in earthquakes when rupture is associated with frictional weakening of the fault. Attempts to simulate these phenomena directly by introducing the relevant constitutive behaviour leads to mesh-dependent results, where the deformation localizes in one element, irrespective of size. Interestingly, earthquake models with oversized mesh elements that are ill-posed in the continuum limit display more complex and realistic physics. Until now, the mesh-dependency problem has been regarded as a red herring-but have we overlooked an important clue arising from the mesh sensitivity? We analyse spatial discretization errors introduced into models with oversized meshes to show how the governing equations may change because of these error terms and give rise to more interesting physics.
目前并不存在一个完全符合物理规律的地震破裂模型，能够全面描述与地震相关的丰富的多层次尺度依赖性和非线性。我们研究了地震破裂数值模型中的网格敏感性，并证明这种网格敏感性可能为生成与地震破裂相关的丰富动力学的潜在物理机制提供隐藏线索。我们专注于不稳定的滑动事件，这些事件发生在地震中，当破裂与断层的摩擦弱化有关时。通过引入相关的本构行为来直接模拟这些现象会导致网格依赖性的结果，其中变形集中在一个单元中，而与大小无关。有趣的是，在连续体极限下具有过大网格元素的地震模型表现出更复杂和现实的物理现象。到目前为止，网格依赖性问题一直被视为一个误导，但我们是否忽略了一个重要的线索，这个线索源于网格敏感性？我们分析了过大网格模型中引入的空间离散化误差，以展示由于这些误差项，控制方程可能会发生怎样的变化，并产生更有趣的物理现象。
