Beginning of Earthquakes Determined from Seismic Initiation Phase

首先，提出了一种确定初始破裂过程震源参数的反演方法。初始断裂过程用Sato和Kanamori(1999)的模型进行模拟，在该模型中，断裂从预先存在的裂纹的末端开始。该模型中的源参数是预先存在的裂纹的半径、动应力降以及控制随后的破裂扩展的触发因子。在实际衰减介质中，品质因数Qp是一个额外的未知参数。数值实验表明，由于这三个参数之间的权衡，预先存在的裂纹半径、触发因子和QP不能很好地反演。因此，我们的目标是以一种稳健的方式估计这些参数，如下所示。假设触发因子只取两个值；对应于自发模型的10^-3；和对应于触发模型的单位。对于以40为增量从40到280的每个QP值，我们确定了…通过最小化从起始到第一个峰值的P波速度波形的残差平方和来增大预先存在的裂缝的半径、应力降和最终裂缝的半径。最后，我们选择了一组参数，给出了从第一个周期开始到结束的波形的残差平方和的最小值。用多个合成数据对该算法进行了测试，发现该算法能够恢复预期的参数。然后将其应用于1984年长野西部地震震源区7次微震(M0.1~2.6)的初始P波。结果，五个事件被发现更符合自发模型，另外两个事件符合触发模型。对于属于自发模型的事件，预存裂纹半径的估计范围为3-9m，同时发现，在第一个峰值之后的时间内，理论波形与观测波形不能很好地吻合。这可能是因为我们的震源模型中关于破裂停止的假设过于简单，即破裂在最后阶段瞬间停止。较少

First, we developed an inversion method for determining the source parameters of initial rupture process. The initial rupture process is simulated with the Sato and Kanamori's model (1999) in which a rupture starts from the ends of a pre-existing crack. The source parameters in this model are the radius of pre-existing crack, dynamic stress drop, and the trigger factor that controls the ensuing rupture propagation. In the real attenuating medium, the quality factor Qp stands as an additional unknown parameter. Numerical experiments showed that the radius of pre-existing crack, the trigger factor and Qp are not well retrieved because of the trade-off among the three parameters. Therefore we aimed at estimating those parameters in a robust manner as follows. The trigger factor was assumed to take only two values ; 10^<-3> corresponding to the Spontaneous model and unity corresponding to the Trigger model. For each of Qp values varied from 40 to 280 in an increment of 40, we determined th … More e radius of pre-existing crack, stress drop and the radius of the eventual crack by minimizing the sum of squared residuals for the P-wave velocity waveform from onset to the first peak. Finally, we chose a set of parameters that gives the minimum of sum of squared residuals for the waveform from onset to the end of the first cycle. This algorithm was tested with several synthetic data and found able to recover the expected parameters. Then we applied it to initial P-waves of seven microearthquakes (M0.1〜2.6) which occurred in the source region of the 1984 Western Nagano earthquake. As a result, five events were found better fit to the Spontaneous model and two others fit to the Trigger model. For the events categorized as the Spontaneous model, the estimated radii of pre-existent cracks range in 3-9 m. At the same time, we found that the theoretical waveform cannot be well fitted to the observed one for the time after the first peak. This probably results from too simple an assumption on the stopping of rupture in our source model, i.e., the rupture stops instantaneously at the final stage. Less