Spatial variability of strong ground motion: novel system-based technique applying parametric time series modelling

Abstract

Spatial variability of strong ground motion within the dimensions of a horizontally extended structure is often described in terms of spectral parameters, such as autospectral densities and cross-spectral densities of motion, recorded at an array of closely spaced sensors. Traditionally, windowed and tapered periodogram techniques have been used in processing strong-motion array data, whereby spectral quantities are estimated. This approach involves large variances in the computed estimates, which can be reduced by decreasing the bandwidth of smoothing windows. A major problem in such applications is the selection of an optimal window, for which, as far as we know, no formal mathematical criteria exist. In this paper we propose a novel technique, based on parametric time series modelling, to replace the periodogram technique for estimating spectral quantities relevant to the description of spatial variability of ground motion. By using actual earthquake data recorded by a strong-motion array, we demonstrate that autoregressive (AR) time series modelling can be used in spectral analysis of strong-motion array data. Such models can easily be calibrated using a variant of least squares techniques, and well-defined statistical criteria are used to identify an optimal model to describe the recorded data. The application of AR modelling eliminates the subjective judgement involved in periodogram techniques and provides stabler estimates of lagged coherencies.