Real time interpolation of earthquake wave propagation

纵观随机过程和现场模拟的历史，无条件模拟一直是主要的主题，在结构、地震及相关工程中得到了广泛的应用。然而，随机过程和场的条件模拟方法的发展，即随机过程场的一些样本实现被观察和已知的条件下的模拟，是相对较新的起源，尽管它在工程应用中非常有用。本研究的目的是建立一个地震波传播的实时监测系统，为地震减灾规划的制定提供帮助。本研究的主要发现总结如下：1。提出了一种时空高斯场条件仿真的时域插值方法。该方法采用了一种简单的自回归模型，表达了时空偏差现象的特性。提出了一种估计条件非高斯平移随机场的理论公式。本文提出的非高斯条件随机场估计理论既基于条件高斯随机场的估计理论，又考虑了非高斯变量之间的相关性，将非高斯变量转化为高斯变量。提出了条件随机有限元法的概念。本文提出的方法可以应用于更新一般的随机场，如用有限元模型描述系统的物理行为。最后提出了本研究的几个重要课题，随机场的采样方法，非平稳现象的快速小波变换以及今后的研究方向。

Throughout the history of stochastic process and field simulation, unconditional simulation has been the main theme, it has been widely applied in structural, earthquake and related engineering. However, development of the method of conditional simulation for stochastic process and fields, i.e. simulation of stochastic process fields under the condition that some of their sample realizations are observed and known is of relatively recent origin, in spite of its significant usefulness in engineering applications.The objective of this research is to develop a real time monitoring system of earthquake wave propagation, which may be contribute to the development of the earthquake disaster mitigation program. The major findings of this research are summarized as follows.1. A time domain interpolation method of conditional simulation on a temporal and spatial gaussian field was developed. In this method a simple auto-regressive modeling which expresses the very property of spatially and temporally deviating phenomena was employed.2. A theoritical formulation is presented to estimate conditional non-gaussian translation stochastic fields. Proposed estimation theory of non-gaussian conditional stochastic fields is based both on the estimation theory of conditional gaussian stochastic fields and on the transformation of non-gaussian variables to gaussian variables taking account of the correlation between non-gaussian variables.3. The concept of conditional stochastic finite element method is proposed. The method developed here may be applied to updating a general stochastic field such as the physical behavior of the system was described by the finite element modeling.4. Some important topics, sampling method for stochastic fields, fast wavelet transformation for nonstationary phenomena and future perspectives of this research are also suggested.