Approximate analytical HVSR curve using multiple band-pass filters and potential applications

Abstract

The Nakamura method, which utilizes the Horizontal to Vertical Spectral Ratio (HVSR) analysis, is widely used for seismic microzonation studies. The HVSR is an easy tool for estimation of site response resonances based on recorded ambient noise; however, it gives amplifications at resonant frequencies that are poorly correlated to the actual amplifications during strong ground motion.Generally, the site response, including any resonant effects, depends on the amplitude, frequency and duration of ground motion. An approach was proposed previously by McGuire [1], in which the transfer function of the soil response was approximated as a Single Degree of Freedom (SDOF) oscillator with one resonant frequency, obtained from the maximum in HVSR. A new approach is developed here, in which the entire HVSR curve is approximated by a manageable set of parallel band-pass resonators. Each individual oscillator is defined by three parameters: center frequency, gain, and steepness (Q factor). This approximation allows for the development and use of an analytical model of the HVSR curve.The application of the new approach is demonstrated on data recorded by the stations of the Southern Ontario Seismic Network (SOSN/Polaris), which have well studied characteristics and site response [2,3]. Data collected at each site consists of noise recordings to obtain the HVSR, as well as earthquake records. The analytical HVSR curves for each station are used to remove the site effect component from the recorded seismograms.