The 1994 Northridge mainshock and its aftershocks show a complex pattern of peak accelerations at stations located in the Los Angeles Basin. The waveforms contain multiples of body-wave phases and extensive surface waves at frequencies mostly below 1 Hz. In particular, for stations at distances greater than 18 km, secondary arrivals show larger accelerations than the direct S-wave arrivals. The mainshock waveforms are further complicated by irregularities of the source rupture. We use 2D finite difference to evaluate the effect of lateral variations in seismic velocity on the amplitude of shear-wave energy and to distinguish the effects of source and propagation path. We model waveforms from one aftershock recorded at nine stations deployed along a 60-km-long profile extending into the Los Angeles Basin. We use a two-dimensional slice through the 3D tomography model of the Los Angeles Basin in the 2D finite-difference calculations. These synthetic waveforms fit the aftershock waveforms significantly better than corresponding waveforms determined from simple 1D velocity models. With the addition of a thin low-velocity surface layer above the tomography model, the finite-difference synthetics reproduce most of the important features of the recorded data, in particular, the large-amplitude arrivals 7 to 10 sec following the direct S arrival. These arrivals correspond to the SS arrival, which is sharply refracted at the basin edge, and the S-wave with multiple legs trapped by the dipping near surface gradient. For large earthquakes located either inside or outside the basin, these phases can be the cause of the largest and hence potentially most hazardous shaking in the Los Angeles Basin.