Modeling of non-stationary phase spectrum of earthquake motions 5

在这个研究项目的第一部分，我们开发了一个实用的模型来模拟地震、地面运动的相谱。我们使用了群延迟时间的概念，它是由相位谱相对于循环频率的导数定义的。我们发现它受近震源区破裂方向性的强烈影响，并推导出群延迟时间的平均值和标准差的回归方程。用模拟的样品相位谱进行了模拟。地震。假设在观测站给出傅里叶幅度谱的运动。将它们的时程与观测的时程进行了比较。来证明它的效率。在第二部分中，我们提出了一种定义群延时空间相关性的方法，并将其应用于利用阵列观测数据模拟未观测点处的地震运动。其中卡尔曼填充了…应用更多的测量技术来模拟每个未观测点处的样本组延迟时间。使用模拟的样本相位谱来模拟每个未观测点处的地震运动。模拟的观测点运动与观测记录吻合较好。这种分析方法对于条件模拟未观测位置的地震运动是非常有前途的。众所周知，任意的振幅和相谱不能用来模拟有因果关系的地震运动。因此，在本研究的第三部分，我们开发了一种新的方法来模拟地震运动，该方法可以考虑到因果关系特征。我们还指出，不仅需要定义群延迟时间的平均值和标准差，还需要定义频率之间的群延迟时间的相关性。通过将群延时的自相关函数定义为指数型，证明了由位相信息可以合理地合成非平稳地震运动。较少

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