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研究震源力学模型的一个新方向是用动态扩展的剪切裂纹模拟地震破裂过程。本文利用裂端有塑性区薄层且断层面上有摩擦力的平面剪切裂纹错动模式来表示地震破裂过程,对运动方程和边界条件进行拉氏变换和傅氏变换,利用维纳-霍普(Wiener-Hopf)方法和卡格尼阿(Cagniard)方法得到了断层面上的位移和应力表达式。根据裂端附近的能量平衡条件,计算了地震破裂的平均速度和塑性区尺度,还讨论了断层面上的位错分布函数,并对某些前震地震波高频成分增多的现象提出了解释。在本文假定的参数条件下,地震破裂的平均速度c=0.72β,β是介质的剪切波速。塑性区尺度约为地震新断层总长度(包括塑性区)的12％。按本文的结果,由于破裂速度的增加,前震的震波初动半周期减小的异常幅度不会超过39％。
A new direction of studying the source mechanical model is to simulate the earthquake rupture process with dynamically expanding shear cracks. In this paper, the rupture process of the earthquake is represented by the plane shear crack dislocation mode with the thin plastic layer at the crack tip and the friction surface on the fault plane. The Laplace transform and Fourier transform of the motion equation and boundary conditions are carried out. The Wiener-Hopf method and the Cagniard method are used to obtain the displacement and stress expressions on the fault plane. According to the energy balance condition near the crack tip, the average velocity of rupture and the scale of plastic zone are calculated, and the distribution function of dislocation on the fault plane is also discussed. Some phenomena of the increase of high frequency components of some seismic waves are also explained. Under the parameters assumed in this paper, the average velocity of earthquake rupture is c = 0.72β, β is the shear wave velocity of the medium. The size of the plastic zone is about 12% of the total length of the new earthquake fault (including the plastic zone). According to the results of this paper, due to the increase of fracture velocity, the anomalous amplitude of the first half-period of shock wave of foreshock decrease will not exceed 39%.