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 (d), and introduce demands for lifeline systems and foundations. Spatially variable ground motions (SVGM) are quantified by: (1) 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. We examine empirical relations for the three SVGM sources through analysis of data from the Borrego Valley Differential Array (BVDA) in California and re-analysis of data from the LSST array in Taiwan, both having a number of stations at d < 120 m. We show that Vapp from the two arrays have medians of 2.1 and 2.6 km/s and natural log standard deviations of about 0.5. We show that previous models for lagged coherency and standard deviation from amplitude variability have bias, and propose revisions. We 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.

A model for horizontal peak ground strain (PGS) is developed in consideration of three fundamental contributions to spatially variable ground motion (SVGM): (1) spatial incoherence effects, which contribute to phase variability in a stochastic sense; (2) wave passage effects, which contribute to phase variability in a deterministic sense; and (3) amplitude variability. Previous models for each of these effects are reviewed and compared to array data from Borrego Valley, California. Published empirical models for coherency and amplitude variability are found to represent reasonably well the Borrego data. We extend previous work by considering correlations of amplitude and phase variability (generally found to be small) and characterizing the coherency-dependent probabilistic distribution of phase variability. Using the aforementioned amplitude and phase variability models, a procedure is developed to generate simulated acceleration records from a seed record. The procedure is applied to a suite of Northridge earthquake recordings to predict ground strains, which are found to be strongly dependent on the peak ground velocity (PGV) of the seed motion and the separation distance between the seed and simulated motions. The dependence of PGS on PGV saturates for large PGV (> 50 cm/sec).