Cross-correlation waveforms of seismic noise in the Seattle basin, Washington, were analyzed to determine the group velocities of surface waves and constrain the shear-wave velocity (VS) for depths less than about 2 kilometers (km). Twenty broadband seismometers were deployed for about 3 weeks in three dense arrays separated by about 5 km, with minimum intra-array station spacing of about 0.5 km. Cross correlations of only 9 days of noise recordings produced Green’s functions at periods of 2 to 6 seconds (s) for sites about 5 km apart. Usable noise correlations for shorter periods of 0.5 to 1.0 s were found for sites within the arrays separated by 1 to 2 km. We bandpass filtered the inter- and intra-array cross-correlation waveforms to determine Love-wave group velocities at periods of 0.5 to 6 s for paths within the Seattle basin and at 3 to 5 s for paths crossing the southern edge of the basin. We developed a non-linear inversion program to determine VS profiles that fit the observed group velocities for paths in the basin. We found that these group velocities are well fit by a variety of VS profiles, each with a distinct jump in VS at depths ranging from 0.9 to 1.3 km. This jump in VS is inferred to represent the top of bedrock. The observed group velocities are not matched by models with the top of bedrock at 0.7-km depth or shallower. The group velocities are also fit by a model with no large jumps in VS in depths less than 2.4 km. The VS profile for the middle of the basin from Stephenson and others (2017), with a depth to bedrock of 0.9 km, also adequately fits the group velocity observations, if a velocity gradient is added from 0.05- to 0.1-km depth. The results indicate that short (3-week) deployments of seismometers to record seismic noise may provide useful constraints on the VS of sedimentary basins.