High-resolution computer simulations of earthquake sequences in three or even two dimensions pose great demands on time and energy, making lower-cost simplifications a competitive alternative. We systematically study the advantages and limitations of simplifications that eliminate spatial dimensions in quasi-dynamic earthquake sequence models, from 3D models with a 2D fault plane down to 0D or 1D models with a 0D fault point. We demonstrate that, when 2D or 3D models produce quasi-periodic characteristic earthquakes, their behavior is qualitatively similar to lower-dimension models. Certain coseismic characteristics like stress drop and fracture energy are largely controlled by frictional parameters and are thus largely comparable. However, other observations are quantitatively clearly affected by dimension reduction. We find corresponding increases in recurrence interval, coseismic slip, peak slip velocity, and rupture speed. These changes are to a large extent explained by the elimination of velocity-strengthening patches that transmit tectonic loading onto the velocity-weakening fault patch, thereby reducing the interseismic stress rate and enhancing the slip deficit. This explanation is supported by a concise theoretical framework, which explains some of these findings quantitatively and effectively estimates recurrence interval and slip. Through accounting for an equivalent stressing rate at the nucleation size h* into 2D and 3D models, 0D or 1D models can also effectively simulate these earthquake cycle parameters. Given the computational efficiency of lower-dimensional models that run more than a million times faster, this paper aims to provide qualitative and quantitative guidance on economical model design and interpretation of modeling studies.

中文翻译：

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地震周期的特征：0D 与 3D 数值模型的跨维度比较


对三维甚至二维地震序列进行高分辨率计算机模拟对时间和精力提出了很高的要求，这使得成本较低的简化成为一种具有竞争力的替代方案。我们系统地研究了准动态地震序列模型中消除空间维度的简化的优点和局限性，从具有 2D 断层面的 3D 模型到具有 0D 断层点的 0D 或 1D 模型。我们证明，当 2D 或 3D 模型产生准周期特征地震时，它们的行为在质量上与低维模型相似。某些同震特性（例如应力降和断裂能）很大程度上由摩擦参数控制，因此在很大程度上具有可比性。然而，其他观察结果在数量上明显受到降维的影响。我们发现复发间隔、同震滑移、峰值滑移速度和破裂速度相应增加。这些变化在很大程度上可以通过消除速度强化断层来解释，这些断层将构造载荷传递到速度弱化断层上，从而降低震间应力率并增加滑动赤字。这一解释得到了简洁的理论框架的支持，该框架定量地解释了其中一些发现，并有效地估计了复发间隔和滑移。通过将形核尺寸h * 处的等效应力率考虑到 2D 和 3D 模型中，0D 或 1D 模型也可以有效地模拟这些地震周期参数。鉴于低维模型的计算效率比运行速度快一百万倍以上，本文旨在为经济模型设计和建模研究的解释提供定性和定量指导。