We simulate 0- to 0.5-Hz 3D wave propagation through the Southern California Earthquake Center seismic velocity reference model, version 2, for the 1994 Northridge earthquake in order to examine the effects of anelastic attenuation and amplification within the near-surface sediments. We use a fourth-order finite-difference staggered-grid method with the coarse-grained frequency-independent anelastic scheme of Day and Bradley (2001) and a variable slip distribution from kinematic inversion for the Northridge earthquake. We find that the near-surface material with S-wave velocity (Vs) as low as 500 m/sec significantly affects the long-period peak ground velocities, compared with simulations in which the S-wave velocity is constrained to 1 km/sec and greater. Anelastic attenuation also has a strong effect on ground-motion amplitudes, reducing the predicted peak velocity by a factor of up to 2.5, relative to lossless simulations. Our preferred Q model is Qs/Vs = 0.02 (Vs in meters per second) for Vs less than 1–2 km/sec, and much larger Qs/Vs (0.1, Vs in meters per second) for layers with higher velocities. The simple model reduces the standard deviation of the residuals between synthetic and observed natural log of peak velocity from 1.13 to 0.26, relative to simulations for the lossless case. The anelastic losses have their largest effect on short-period surface waves propagating in the Los Angeles basin, which are principally sensitive to Qs in the low-velocity, near-surface sediments of the basin. The low-frequency ground motion simulated here is relatively insensitive to Qp, as well as to the values of Qs at depths greater than roughly that of the 2-km/sec S-wave velocity isosurface.