Engineering characterization of spatially variable earthquake ground motions

Earthquake ground motions exhibit spatial variability manifest as random variations of Fourier amplitude and phase. These variations increase with frequency and distance between observations points (xi) and can introduce significant demand for lifeline systems (e.g., pipelines) and foundations. Spatially variable ground motions (SVGM) are quantified by: (I) apparent horizontal wave velocity (Vapp), which controls wave passage effects that shift Fourier phase; (2) lagged coherency, representing random phase variations; and (3) standard deviation terms representing Fourier amplitude variability.;I examine empirical relations for the three SVGM sources through re-analysis of a data from the LSST array in Taiwan and analysis of new data from the Borrego Valley Differential Array (BVDA) in California, both having xi < ∼ 120 m. I show that Vapp at BVDA has a median of 2.9 km/s, coefficient of variation of about 0.5, and no systematic variation with relative ray path/array azimuths. I show that previous models for lagged coherency and standard deviation from amplitude variability have bias, and propose revisions. I show that amplitude and coherency residuals from the baseline model are uncorrelated, although frequency-to-frequency residuals for both quantities are weakly correlated for small frequency offsets.;I then develop simulation procedures that modify a seed motion in a manner compatible with the three sources of SVGM. Simple modifications of Fourier amplitude and phase with a random number generator introduce non-physical stationary noise characteristics. This is addressed by developing a Frequency-Dependent Windowing routine that modifies time windows of the motion within frequency bands. High frequencies are modified in short windows and low frequencies in long windows. This preserves non-stationary ground motion characteristics in motion suites with the desired SVGM characteristics, and is useful for engineering applications requiring spatially variable waveforms for response history analyses.;The final topic addressed is extensional ground strains from SVGM. Suites of SVGMs are generated and strain histories computed. Peak ground strains (PGS) are found to increase with peak velocity ( PGV), similar to previous work, but also decrease with xi and saturate for PGV>∼80 cm/s, which has not been previously observed. The dependence of PGS on xi is confirmed from array recordings.