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旋律，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，即在观测和已知随机过程场的部分样本实现的条件下模拟随机过程场的方法，尽管在工程应用中具有重要的实用价值，但它的发展是相对较新的。本研究的目的是开发一个地震波传播的实时监测系统，为地震减灾计划的发展提供帮助。本研究的主要发现总结如下。提出了一种时空高斯场条件模拟的时间域内插方法。在该方法中，采用了一种简单的自回归模型，该模型表达了空间和时间偏差现象的本质属性。提出了一种估计条件非高斯平移随机场的理论公式。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，又基于非高斯变量到高斯变量的变换，考虑了非高斯变量之间的相关性。提出了条件随机有限元的概念。本文提出的方法可应用于一般随机场的更新，如用有限元模型描述系统的物理行为。提出了随机场的采样方法、非平稳现象的快速小波变换等重要课题，并展望了今后的研究方向。

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.