It is necessary to understand ground-motion amplification by sediment, defined as the ratio of ground motions at sediment sites to those at rock sites, to predict seismic loadings for earthquake engineering. At sediment sites, observed weak-motion amplifications from magnitude 3 to 4 aftershocks of the 1994 Northridge earthquake were twice as large as magnitude 6.7 mainshock amplifications. Amplitude-dependent (nonlinear) amplification by sediment is one explanation. However, earthquake simulations with empirical impulse responses and elastic finite-difference calculations with weakly heterogeneous, random three-dimensional (3D) crustal velocity variations show that linear wave propagation can explain observed (apparently nonlinear) sediment responses. Random 3D velocity variations also reproduce the observed log-normal dispersion of peak ground motions. Deterministic wave propagation models are not adequate to quantify the scaling and dispersion of near-source ground motions.