SUMMARY

This study investigates the strain energy change caused by earthquake faulting. While conventional theories often assumed uniform stress change on the fault plane, this study supposed the slip fluctuation and non-uniform stress change on the fault. By using a stochastic modelling of the slip distribution, we represent the ensemble average of the strain energy change by using the power spectral density function of the slip fluctuation. This yields the following results. (1) When the initial stress is uniform and the earthquake contains a fluctuating slip distribution, the released strain energy is less than the one by an earthquake with the uniform stress change on the fault with the same seismic moment. (2) On the other hand, when the initial stress is fluctuating, the earthquake contains a fluctuating slip distribution, and the final stress is uniform, the released strain energy is more than the one by an earthquake with the uniform stress change on the fault. (3) The stress drop becomes large due to the fluctuating slip distribution from the viewpoint of the strain energy release. We derived the analytical solution of the stress change by using the power spectral density function of the random slip fluctuation. (4) The strain energy change is proportional to the seismic moment when ${\epsilon ^2}/a \propto {( {{M_0}} )^{ - 1/3}}$ (${\epsilon ^2}$ is the variance of the fractional slip fluctuation and $a$ is the correlation distance). (5) The energy balance gives the value of initial stress that is required for the earthquake generation. In order to generate an earthquake, the initial stress needs to be larger than the sum of half of the stress drop and the apparent stress. In other words, earthquakes having rich short-wavelength components in the slip distribution are not generated under a low initial stress level.

中文翻译：

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地震断层释放的应变能与随机滑动分量

概要

本研究调查了地震断层引起的应变能变化。传统理论通常假定断层平面上应力均匀变化，而本研究假定断层上的滑动波动和应力变化不均匀。通过使用滑动分布的随机模型，我们通过使用滑动波动的功率谱密度函数来表示应变能变化的总体平均值。这产生以下结果。（1）当初始应力是均匀的并且地震包含波动的滑移分布时，在相同的地震矩下，在相同的断层上应力均匀变化的地震中，释放的应变能小于地震的释放。（2）另一方面，当初始应力波动时，地震包含波动的滑移分布，最终应力是均匀的，在断裂上应力均匀变化的情况下，释放的应变能大于地震所释放的应变能。（3）从应变能释放的角度来看，由于滑移分布的变化，应力下降变大。我们利用随机滑动波动的功率谱密度函数导出了应力变化的解析解。（4）应变能变化与$ {\ epsilon ^ 2} / a \ propto {（{{{M_0}}）^ {-1/3}} $（$ {\ epsilon ^ 2} $是分数滑差的方差，而$ a $是相关距离。（5）能量平衡给出地震发生所需的初始应力值。为了引发地震，初始应力必须大于应力降和表观应力的一半之和。换句话说，在低初始应力水平下不会产生在滑动分布中具有短波分量丰富的地震。