Beginning of Earthquakes Determined from Seismic Initiation Phase

首先，我们开发了一种确定初始破裂过程源参数的反演方法。最初的破裂过程是用佐藤和金森的模型（1999）模拟的，在这个模型中，破裂是从预先存在的裂缝的末端开始的。该模型中的源参数为预先存在裂纹的半径、动应力降和控制随后破裂扩展的触发因子。在实际衰减介质中，质量因子Qp作为一个附加的未知参数。数值实验表明，由于裂纹半径、触发因子和Qp三者之间的权衡关系，不能很好地恢复裂纹半径、触发因子和Qp。因此，我们的目标是以如下的稳健方式估计这些参数。假设触发因子只取两个值；10^<-3>对应于自发模型和统一对应于触发模型。对于每个Qp值在40 ~ 280之间以40为增量，我们通过最小化p波速度波形从开始到第一个峰值的残差平方和来确定预先存在裂纹的半径、应力降和最终裂纹的半径。最后，我们选择了一组参数，这些参数给出了波形从开始到第一个周期结束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，结果表明该算法能够恢复预期参数。然后将其应用于1984年长野西部地震震源区发生的7次0.1 ~ 2.6级微地震的初始p波。结果发现，五个事件更适合自发模型，另外两个事件更适合触发模型。对于自发模式事件，预估裂缝半径在3 ~ 9 m之间。同时，我们发现理论波形在第一个峰值之后的一段时间内不能很好地拟合观测波形。这可能是由于我们的源模型中对破裂停止的假设过于简单，即破裂在最后阶段立即停止。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