On the Characterisation of the Phase Spectrum for Strong Motion Synthesis

Abstract

A new approach has been presented to characterise phase spectra for simulating realistic nonstationary characteristics in synthetic accelerograms. The phase characteristics of the recorded earthquake accelerograms have been studied for this purpose and it has been found that the phase curve/unwrapped phases exhibit a monotonic downward trend which allows the problem of phase characterisation to be cast as a constrained nonlinear programming problem. The phase spectrum is first characterised by matching mean and variance of the generated distribution of relative phases with those obtained from recorded motions. As a practical application, it is shown how phase spectra can be characterised for an ensemble of synthetic accelerograms so as to maximise the severity of sample realisations.

Synthesis of Vibration Waves Based on Wavelet Technology

“…Unlike fluctuating wind, the seismic is a classical non-stationary process; consequently, an envelope function f (t) should be multiplied in Eq. (19).…”

“…For seismic wave synthesis, recorded accelerograms show clear non-stationary of strong ground motion which can influence structural responses significantly. To meet the non-stationary frequency and amplitude characteristics, stationary random accelerograms were multiplied by a non-stationary envelope function with the frequency contents and phases of the trigonometric time series changed to a time-dependent function [3,5,7,11,12,16,19,21]. Thus the ensemble averages of the modified accelerograms would not keep constant in time-domain and might be considered as "non-stationary".…”

Phase Derivatives and Simulation of Strong Ground Motions

“…(The equation for the distribution in Nigam [1982] differs from that in Nigam [1984]; the later equation predicts a bimodal distribution, but my simulations show that it is incorrect and that the earlier equation is correct.) Other authors have studied phase differences as a means of characterizing and simulating ground motions (e.g., Ohsaki et al, 1984;Sawada, 1984;Thráinsson et al, 2000;Shrikhande and Gupta, 2001;Montaldo et al, 2003;Thráinsson and Kiremidjian, 2002). Liao and Jin (1995) explicitly used the derivative of the phase, rather than phase difference.…”

“…The use of group velocity to determine the relative arrivals of motion at different frequencies for multiple modes has been used by Trifunac and colleagues (e.g., Trifunac, 1971;Wong and Trifunac, 1979) to simulate strong ground motion. In the engineering literature, a number of papers have appeared in which "phase differences" play a central role in simulating earthquake ground motions (e.g., Ohsaki, 1979;Ohsaki et al, 1984;Sawada, 1984;Thráinsson et al, 2000;Shrikhande and Gupta, 2001;Montaldo et al, 2003;Thráinsson and Kiremidjian, 2002), but aside from a scalar factor involving the frequency increment, these phase differences are nothing more than a finite-difference approximation of the derivative of the phase with respect to frequency and thus are an approximation of the group delays, well known in studies of dispersed waves (e.g., Udias, 1999). This article has several purposes: to acquaint engineers with work of seismologists involving group delays and vice versa and to introduce an extension of the widely used stochastic method for simulating strong ground motions (Boore, 2003b) that will produce simulated motions with nonstationary frequency content, such as produced by basin waves (e.g., Boore, 1999;Joyner, 2000).…”

A phase model of earthquake motions based on stochastic differential equation

“…Kimura (1986) presented a method to simulate earthquake motion by controlling the group delay time. Shrikhande et al (2001) cast the problem of characterizing phase spectra in the form of a constrained nonlinear programming problem and modeled the phase curve of a earthquake ground motion by a piecewise-linear generic curve superimposed with zero-mean Gaussian residual phases to capture the characteristics of the time-domain envelope of the earthquake ground motion. Boore (2003) listed several advantages to using group delay rather than phase differences.…”