Sonobouy records with smoothly curved travel time data are found most commonly near rapidly outbuilding shelves and near the mouths of major rivers. It is judged that the smooth increase of velocity with depth is most likely where sediments are young and have accumulated rapidly. These sonobuoy records are amenable to analytical techniques for determining velocity gradients in shelf sediments. These methods are simpler and more accurate than those used in deep water (if the source and receiver are at the surface). Also, sea floor sound velocity can be determined by measureing the critical angle of reflection from sea floor multiples, which form an energetic and clearly defined wedge of closely spaced multiples slightly later than the simple sea floor reflection. Velocity inversion techniques applied the travel time data provide accurate velocity-depth information. These techniques show that shelves with sections of rapidly accumulating sediments are ideal for the measurement of detailed velocity characteristics. A method is proposed for measuring in situ attenuation on shelves where the velocity increases smoothly with depth. The method takes advantage of the apparent lack of prominent reflectors in rapdily accumulating sediment bodies and uses the decay in amplitude observed between first-arrival refractions and their simple multiples. In this proposed technique, the first-arrival refractions are considered to be the 'source.' Simple ray theory shows that maximum focusing occurs in the shallow curved path arrivals at a velocity cusp. The velocity cusps can form in shallow water (less than about 100 m) only when the velocity contrast at the sea floor is nonexistent or slightly positive.