Measurements of mean sound velocities in the first, largely unlithified layers in the seafloor were made using the sonobuoy technique in several areas in the northern Indian Ocean. Older measurements were added to new measurements, and regressions for mean and instantaneous velocity versus one-way travel time of sound are presentd for the central Bengal Fan, the central Andaman Sea Basin, the Nicobar Fan, and the Sunda Trench. New data and regression equations are presented for the Mergui-north Sumatra Basin and for four forearc basins between Sumatra and Java and the Sunda Trench. Minimum velocity gradients were found in those areas where sedimentation rates were high, and sediments have accumulated in thick sections which have not had time to fully consolidate (porosity in the top of the sediment section has not been fully reduced under overburden pressure). These minimum velocity gradients (just under the seafloor) were found in the four forearc basins where they ranged from 0.34 s-1 to 0.84 s1 with an average of 0.58 s1. The near-surface velocity gradient in the Sunda Trench was 1.33 s-1, but was higher in the adjacent, fossil Nicobar Fan (1.62 s-1). In the surface of the Bengal Fan the velocity gradient was low in the upper fan (0.86 s-1), high in the central fan (1.94 s-1), and again lower in the southern fan (1.18 s-1), which may support sedimentation models calling for bypassing of the central fan and higher rates of accumulation on the soutern fan.