We installed a dense array of 41 digital seismographs in San Jose, California, to evaluate in detail the effects of a deep sedimentary basin and shallow sedimentary deposits on earthquake ground motions. This urban array is located near the eastern edge of the Santa Clara Valley and spans the Evergreen sedimentary basin identified by gravity data. Average station spacing is 1 km, with three stations initially spaced 110 m apart. Despite the high-noise urban environment, the stations of the array successfully triggered on and recorded small local earthquakes (M 2.5-2.8 at 10-25 km distance) and larger regional events such as the M 5.0 Bolinas earthquake (90 km distance), M 4.6-5.6 earthquakes near Mammoth Lakes (270 km distance), M 4.9-5.6 events in western Nevada (420 km distance) and the M 7.1 Hector Mine earthquake (590 km distance). Maps of spectral ratios across the array show that the highest amplitudes in all frequency bands studied (0.125-8 Hz) are generally observed at stations farther from the eastern edge of the Santa Clara Valley. Larger spectral amplitudes are often observed above the western edge of the Evergreen Basin. Snapshots of the recorded wavefield crossing the array for regional events to the east reveal that large, low-frequency (0.125-0.5 Hz) arrivals after the S-wave travel from south to north across the array. A moving-window, cross-correlation analysis finds that these later arrivals are surface waves traveling from the south. The timing and propagation direction of these arrivals indicates that they were likely produced by scattering of incident S waves at the border of the Santa Clara Valley to the south of the array. It is remarkable that the largest low-frequency phases at many of the valley sites for regional events to the east are basin surface waves coming from a direction about 70 degrees different from that of the epicenters. Basin surface waves emanating from the eastern edge of the valley are also identified by the cross-correlation analysis.