Consistency of ground-motion estimates made using system identification

This article isolates the systematic effects of the soil profile on earthquake ground motions recorded at vertical seismic arrays. An empirical Green's function is calculated for a soil interval between two sensors in a vertical array. The estimation technique used here falls into the category of site-response estimates but differs from the standard spectral ratio methods in that an extended Weiner filter (ARMA model) becomes the impulse-response function from one point to another in the soil profile. This method allows quantification of the accuracy of predicted ground motions at a given site with normalized mean square prediction errors generally under 10%, indicating effective and consistent estimates. The models are shown to reproduce site ground motions for inputs that differ over a wide range of peak ground acceleration (PGA), hypocentral locations, and over numerous occurrences. We demonstrate consistency of site ground-motion estimates at four sites that have undergone multiple strong shakings: Chiba, Japan; Garner Valley, California; Lotung, Taiwan; and Port Island, Japan. Consistency of site response over a wide range of shaking levels indicates an "effective" range of linear soil behavior for PGA up to 0.33 g at Chiba, 0.1 g at GVDA, and 0.21 g at Lotung. At Port Island, consistency was evident below 16 m at a surficial PGA of 0.54 g, but the surface layer liquefied. Results are presented as predicted time series and in the frequency domain with calculated variance. Results from Garner Valley and Chiba indicate that the location and magnitude of significant impedance contrasts within the soil profile control response. This article concentrates on levels of shaking that do not excite the soils into phase transitions. Our results indicate that strong nonlinear behavior (liquefaction) controls site response, but more minor and localized softening of the soil may not alter the site response enough to deter prediction within 10%.