The proximity of several recent earthquakes to the Los Angeles sedimentary basin provides an opportunity to isolate the effects of the basin on wave propagation. The 4 October 1987 aftershock (ML = 5.3) of the Whittier Narrows sequence and the 28 June 1991 Sierra Madre mainshock (ML = 5.8) are on a similar azimuth to stations overlying the deepest part of the basin. A distinctive feature of records from basin stations recording the 4 October after-shock is the large amplitude of multiple S, SS, etc. The multiples have up to twice the amplitude of the direct S phase on the tangential component. At such a short range, less than 25 km, a horizontal seismic velocity gradient is needed to turn rays rapidly enough for large-amplitude multiples to form. A forward modeling approach is employed, using finite-difference numerical techniques that produce double-couple point-source solutions. A model based on a recent geologic cross section constructed for the east edge of the Los Angeles Basin generates more phases than are seen in the seismic records. Simpler models, based on dipping layers with low shear velocities in the top few layers, fit the data better. The seismic velocity, depth, and dip of the layers are varied to fit the timing between the direct P, the direct S, and the first S multiple. The timing and amplitude of the direct and first multiple S pulses are well modeled, though the phase of the first multiple does not match the data. Including a steeply dipping west edge in the basin model has little effect on the synthetic waveforms, except at distances near that basin edge. The amplitude of SS is greatest in the deepest part of the basin, where it is two times larger than direct S. The coda duration increases from 8 sec to more than 20 sec from the NE to the SW. The Sierra Madre mainshock occurred about 25 km to the NE of the Whittier Narrows sequence. The model for Whittier Narrows was extended to this distance, with a shallow basin between Whittier and the Sierra Madre hypocenter to simulate the San Gabriel sedimentary basin. Phases generated by the edge of the deep basin continue to dominate the synthetic waveforms, but this model generates a lengthy coda. This study shows that specific phases with frequencies up to 1 Hz that have traveled through deep sedimentary basins can be explained by two-dimensional seismic velocity models.