This study addresses the topic of the spatial variation of seismic ground motions as evaluated from data recorded at dense instrument arrays. It concentrates on the stochastic description of the spatial variation, and focuses on spatial coherency. The estimation of coherency from recorded data and its interpretation are presented. Some empirical and semi-empirical coherency models are described, and their validity and limitations in terms of physical causes discussed. An alternative approach that views the spatial variation of seismic motions as deviations in amplitudes and phases of the recorded data around a coherent approximation of the seismic motions is described. Simulation techniques for the generation of artificial spatially variable seismic ground motions are also presented and compared. The effect of coherency on the seismic response of extended structures is highlighted. This review article includes 133 references. @DOI: 10.1115/1.1458013#

http://www.pages.drexel.edu/~zervaa/Zerva&Zervas.pdf

Spatial variation of seismic ground motions: An overview

A study of soil-structure interaction for seismically excited simple structures is made considering both kinematic and inertial interaction effects The information and concepts presented elucidate the nature and relative importance of the two effects and make it possible to assess readily the influences of the more important parameters The response quantities examined are the ensemble means of the peak values of the lateral and torsional components of the foundation input motion and of the associated structural deformations The results are evaluated over wide ranges of the parameters involved and are compared with those obtained for no soil-structure interaction and for kinematic interaction only Simple, physically motivated interpretations are given for the observed differences For the important special case of vertically incident incoherent waves, simple closed-form approximate expressions are presented for the transfer functions of circular massless foundations

Seismic Interaction of Structures and Soils: Stochastic Approach

An autoregressive model for univariate, one‐dimensional, nonstationary, Gaussian random processes with evolutionary power spectra is introduced. At the same time, an efficient technique for numerically generating sample functions of such nonstationary processes is developed. The technique uses a recursive equation which: (1) Reflects the nature of the nonstationarity of the process whose sample functions are to be generated; and (2) involves a normalized univariate, one‐dimensional white noise sequence. The coefficients of the recursive equation are determined using the autocorrelation function of the process, which in turn is calculated from the evolutionary power spectrum at every time instant. Using the recursive equation with those coefficients, sample functions over a specified domain can be generated with substantial computational ease. Univariate, one‐dimensional, nonstationary processes with three different forms of the evolutionary power spectrum are modeled, and their sample functions are genera...

Auto‐Regressive Model for Nonstationary Stochastic Processes

The fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description. A stochastic decomposition technique facilitates utilization of the FFT algorithm. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time‐dependent weights that are simulated by the FFT algorithm. The desired evolutionary spectral characteristics of the multivariate unidimensional process may be prescribed in a closed form or a set of numerical values at discrete frequencies. The effectiveness of the proposed technique is demonstrated by means of three examples with different evolutionary spectral characteristics derived from past earthquake events. The closeness between the target and the corresponding estimated correlation structure suggests that the simulated time series reflect the prescribed probabilistic characteristics extremely well. The simulation approach is computationally efficient, p...

Simulation of Multivariate Nonstationary Random Processes by FFT

The main motivation of this work is to analyze whether or not the presence of buildings is able to modify the seismic field significantly. We first present a numerical method able to account for a three-dimensional building distribution resting on a layered elastic-half-space. The proposed method is based on a variational coupling between Boundary Elements and modal representation for the buildings. Provided with the hypothesis of a stochastic homogeneous distribution of these buildings or a deterministic periodic one, a realistic model of an entire city may be accounted for. This method is applied to practical situations and it is shown that modifications of the incident field occur mainly for soft layered soils. However from an engineering point of view, it appears that the amplification levels are not significantly modified even in these extreme cases. Nevertheless, a strong scattering of the response inside the city depends on the nearby buildings can be observed.

Modifications of the ground motion in dense urban areas

Evaluation of kinematic interaction of soil-foundation systems by a stochastic model

This paper describes an effective method of obtaining covariance responses in recursive form for a multi‐degree‐of‐freedom linear structural system subjected to nonstationary random excitations. The earthquake excitations are expressed as a multiply‐correlated nonstationary autoregressive process model. By utilizing white noise characteristics of the AR model, this covariance response matrix equation is derived from state space matrix equation with mixed excitations and response components. Then, a torsional vibration model, subjected to two horizontal components of earthquake excitation, is analyzed. A BWR type nuclear power plant building is used as an example to show how recursive covariances are applied to evaluate statistical values of nonstationary maximum responses.

Kiyoshi Ishii

Papers

Evaluation of kinematic interaction of soil-foundation systems by a stochastic model

Recursive Covariance of Structural Responses

Deconvolution method between kinematic interaction and dynamic interaction of soil-foundation systems based on observed data