Modeling of non-stationary phase spectrum of earthquake motions 5

在本研究计画的第一部份中，我们发展了一个实用的模型来模拟地震动的相位谱。我们使用了群延迟时间的概念，它是由相位谱相对于圆频率的导数定义的。我们发现它强烈地受到近源区破裂方向性的影响，并推导出群延迟时间的平均值和标准差的回归方程。利用模拟样品的相位谱进行了模拟。地震假设观测站给出了傅立叶振幅谱，并将它们的时间历程与观测值进行了比较。为了证明效率。第二部分提出了一种定义群延迟时间空间相关性的方法，并将其应用于利用阵列观测数据模拟未观测点的地震动。其中，卡尔曼文件 关于我们 采用一种随机技术模拟了每个未观测点处的样本群延迟时间。用模拟样本相位谱模拟各观测点的地震运动。观测点的模拟运动与观测记录吻合较好。这种分析方法对于未知地点地震运动的条件模拟是很有前途的。众所周知，任意的振幅谱和相位谱不能用来模拟具有因果关系的地震运动。因此，在本研究的第三部分，我们发展了一种新的方法来模拟地震运动，可以考虑因果关系的特点。同时指出，不仅需要定义群延迟时间的平均值和标准差，还需要定义群延迟时间在频率之间的相关性。通过定义群延迟时间的自相关函数为指数函数型，证明了利用震相信息可以合理地合成非平稳地震动。少

In the first part of this research project we developed a practical model to simulate a phase spectrum of.earthquake.ground motions. We used the concept of group delay time which is defined by the derivative of a phase spectrum with respect to circular frequency. We found that it was strongly affected by the rupture directivity in the near source regions and derive regression equations for mean and standard deviation of group delay time. Simulated sample phase spectra were used to simulate. earthquake. motions assuming that Fourier amplitude spectra were given at observation stations. Their time histories were compared with the observed ones. To demonstrate the efficiency. of propose, model of the group delay time we simulated response spectrum compatible design earthquake motions.In the second part we proposed a method to define spatial correlation of group delay time and apply it to simulate earthquake motions at unobserved points using array observation data. In which the Kalman fil … More tering technique was applied to simulate a sample group delay time at each unobserved point. A simulated sample phase spectra was used to simulate earthquake motions at each unobserved point. The simulated motions at observation points coincided well with observed records. This analytical method is very promising for conditional simulationn of earthquake motion at unobserved locations.It is well known that arbitrary amplitude and phase spectra cannot be assigned to simulate an earthquake motion with causality. In the third part of this research, we therefore developed a new method to simulate earthquake motion which could take into account the causality characteristics. We also pointed out that, we needed to define not only the average and standard deviation of group delay time but also the correlation of group delay time between frequencies. : We demonstrated that a non-stationary earthquake motion could be synthesized from phase information reasonably by defining the auto correlation function of group delay time as exponential function type. Less