Simulation of Earthquake Ground Motions Using Auto- regressive Moving Average (ARMA) Model
Shin-Wen Chen
Abstract
Human being use instruments to observe the phenomena of the natural world. Recorded data are available in the form of sequences of observations at uniformly spaced points in time. Such a sequence of n observations is called a discrete time series. For a stochastic process, every realization may possess the same probabilistic structure. Therefore, for a given specified process about specific-earthquake or a specific-site, we can recover the real data reasonably accuracy using the given process.
In this study, we want to construct a stochastic model from the past seismic data, and then to derive relevant measurement such as response spectra from the simulated ground motions generated from the fitted model. But two questions arise in using the stochastic approach. The first is how to construct an appropriate model to describe the dynamic behavior of observed earthquake ground motions. So in this paper, Autoregressive Moving Average (ARMA) models has been applied to the analysis of earthquake acceleration time series. We can derive a discrete stationary linear transfer function, is also called ARMA filter. But the series which we want to analyze should be a stationary series, so some transformations must be first applied. The method of transformation is to derive a ˇ§variance envelopeˇ¨ from original data. To generate a simulated time series, a sequence of white noise is generated, passed through the estimated ARMA filter, and retransformed using the obtained variance function. The method is to parametric time series model building for earthquake acceleration series. Therefore the second question is what relationship between estimated model parameters and variables, for example earthquake intensity, distance to the epicenterˇK.and so on.
This simulation procedure is demonstrated on the three components of the San Fernando earthquake(6.3) recorded at 8244 Orion Boulevard.
Reference
Polhemus N W, Cakmak A S. Simulation on earthquake ground motions using autoregressive moving average (ARMA) models, Earthquake Engineering and Structural Dynamics, 9, 343-354.
(Abstract) (Full text)
Chang M K, Kwiatkowski J W, Nau R F, Oliver R M and Pister K S. ARMA Models for Earthquake Ground Motions, Earthquake Engineering and Structural Dynamics, 10, 651-662.
(Abstract) (Full text)