A study of localization limiters and mesh dependency in earthquake rupture

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.