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An efficient boundary integral equation method applicable to the analysis of non-planar fault dynamics

机译：一种适用于非平面故障动力学分析的有效边界积分方程法

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摘要

We develop a novel and efficient boundary integral equation method based on the spatio-temporal formulation for the two-dimensional dynamic and quasistatic analyses of an earthquake fault in a single scheme. A major advantage of this method is its applicability to the analysis of non-planar faults with the same degree of accuracy as to that of planar faults. Calculation time and memory requirement are reduced through the employment of asymptotic representations of the integration kernels appearing in the convolution integral. Asymptotic kernels are factorized into terms dependent on space or time alone, resulting in efficient numerical computations. In addition, the dependence on time is found to vanish in the asymptotic kernels far behind the S -wave front, which also contributes to the time-saving efficiency of the calculations. We show that, in a dynamic analysis, if a 3% error is allowed for the slip rate, computation time and memory requirement are reduced by 25% and 45%, respectively, in an in-plane fault case, and by 60% and 75%, respectively, in an anti-plane fault case. This method can be employed as a powerful numerical tool in simulating an entire earthquake cycle consisting of both quasi-static and dynamic processes with a more realistic non-planar geometry of faults.
机译：我们基于时空公式开发了一种新颖有效的边界积分方程方法，可在单个方案中对地震断层进行二维动态和准静态分析。这种方法的主要优点是它适用于非平面故障的分析，其准确度与平面故障的准确度相同。通过使用卷积积分中出现的积分核的渐近表示，可以减少计算时间和内存需求。渐近核被分解为仅依赖于空间或时间的项，从而实现了高效的数值计算。另外，发现时间的依赖性在远于S波前沿的渐近核中消失，这也有助于节省计算时间。我们显示，在动态分析中，如果允许滑移率误差为3％，则在平面内故障情况下，计算时间和内存需求分别减少25％和45％，而在平面故障情况下分别减少60％和在发生反平面故障的情况下分别达到75％。该方法可以用作强大的数值工具，用于模拟由准静态过程和动态过程组成的整个地震循环，并具有更逼真的非平面断层几何形状。

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