Probabilistic Characterization of Spatially Correlated Response Spectra for Earthquakes in Japan by Katsuichiro Goda and Gail M. Atkinson Abstract Seismic hazard and risk assessments of spatially distributed infrastructur- al systems require seismic demand models that capture random but correlated simul- taneous seismic effects at multiple sites. This study characterizes spatially correlated ground-motion parameters probabilistically using comprehensive databases of the K-NET and KiK-net strong-motion networks in Japan by developing a ground-motion prediction equation and then investigating the correlation structure of regression resid- uals from the prediction equation. Analysis results indicate that (1) interevent residuals of ground-motion parameters at different vibration periods are more strongly correlated than intraevent and total residuals with zero separation distance; and (2) intraevent spatial correlation coefficients can be described as a simple exponential decay function that is independent of the way the event-based intraevent standard deviation is calcu- lated, of the earthquake type, and of the vibration period. The developed overall cor- relation model of spatially correlated ground-motion parameters may be used for seismic hazard and risk assessments in a subduction environment. Introduction Peak ground motions and response spectra are often characterized using ground-motion prediction equations (GMPEs), which give the ground-motion parameters as func- tions of magnitude, distance, and other variables, and are the essential elements of probabilistic seismic hazard and risk analysis (McGuire, 2004). A conventional seismic hazard and risk assessment is often focused on a single site. How- ever, if assessments for multiple sites are of interest, the correlation structure of peak ground motions and response spectra at different locations for the same seismic event must be established and considered (Goda and Hong, 2008a,b). This consideration is needed to capture random but corre- lated simultaneous seismic effects at multiple sites, inducing interevent correlation and intraevent correlation. Empirical assessments of the intraevent spatial correla- tion of ground-motion parameters, such as the peak ground acceleration (PGA), the peak ground velocity (PGV), and the pseudospectral acceleration (PSA) of single-degree-of- freedom oscillators, have been recently investigated in the literature (e.g., Boore et al., 2003; Kawakami and Mogi, 2003; Wang and Takada, 2005; Goda and Hong, 2008a). These studies carry out statistical analysis of residuals associated with GMPEs in isolation from regression analysis. On the other hand, the direct incorporation of a parametric spatial correlation model into regression analysis in de- veloping GMPEs was investigated by Hong et al. (2009); that study validated the empirical assessment of the spatial correlation model by Goda and Hong (2008a) for a set of California data. The application of the developed spatial cor- relation model to seismic risk assessment of multiple build- ings was demonstrated by Goda and Hong (2008b), which clearly showed a significant impact of spatial correlation on the probability distribution of aggregate seismic losses of spatially distributed buildings. Consequently, accurate seismic loss estimation, successful seismic risk management, and decision making require the proper treatment of spatial correlation. There are several issues regarding spatial correlation that require further research. They include different decay rates of spatial correlation as a function of separation distance be- tween two sites, as reported in different studies (Boore et al., 2003; Wang and Takada, 2005; Goda and Hong, 2008a); this might indicate that the decay rate depends on region and earthquake type. This is important if several earthquake types are considered in seismic hazard and risk analysis. For in- stance, in western Canada, significant contributions come from three distinct types of seismic events: shallow crustal earthquakes, inslab subduction earthquakes, and interplate Cascadia subduction earthquakes (Hong and Goda, 2006); however, it is unknown whether the spatial correlation model for one region/type is applicable to others. Furthermore, the use of different approaches in evaluating spatial correlation appears to result in different models (Goda and Hong, 2008a; Hong et al., 2009). It is thus important to examine whether the adopted analysis method gives robust estimates of the spatial correlation of ground-motion parameters. To investigate these issues, a detailed assessment of the spatial correlation of ground-motion parameters is carried out 3003 Bulletin of the Seismological Society of America, Vol. 99, No. 5, pp. 3003–3020, October 2009, doi: 10.1785/0120090007