Rupture velocity is a fundamental feature of earthquake behavior. How rupture velocity is defined can therefore affect our understanding of earthquake physics. Based on dynamic rupture simulations, we compare the tangent and average rupture velocities calculated via one- and two-dimensional gradients. Two strike-slip scenarios with free-surface-induced supershear ruptures are presented within a homogeneous and a depth-dependent stress regime, respectively. Although both scenarios produce a daughter crack that propagate over the seismogenic depth, in the depth-dependent case the 1D and 2D rupture velocities capture different features: A 1D horizontal gradient measurement implies a supershear rupture, while a 2D gradient measurement reveals sub-Rayleigh rupture propagation everywhere except very close to the free surface. A large area on the fault with the 1D horizontal tangent rupture velocity does not necessarily produce an observable Mach front, which arises the importance of rupture velocity definitions in supershear analysis.

中文翻译：

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超剪切断裂，子裂纹和断裂速度的定义

破裂速度是地震行为的基本特征。因此，如何定义破裂速度会影响我们对地震物理学的理解。基于动态破裂模拟，我们比较了通过一维和二维梯度计算的切线速度和平均破裂速度。在均匀应力和深度依赖的应力状态下，分别出现了两种带有自由表面引起的超剪切断裂的走滑情形。尽管这两种情况均会产生一个沿地震发生深度扩展的子裂纹，但在与深度有关的情况下，一维和二维破裂速度具有不同的特征：一维水平梯度测量表明存在超剪切破裂，而二维梯度测量表明存在次瑞利破裂。在非常靠近自由表面的地方传播。