This paper presents a detailed seismic reflection profile taken over the deep ocean. Clear sub-bottom reflections and refractions are obtained which are interpretable to show the variation of velocity with depth. From the travel-time difference between the bottom reflection and a prominent sub-bottom reflection as a function of range and frequency and from the variation of the amplitudes of the bottom and sub-bottom reflections with frequency and angle of incidence, the conclusion is reached that the sediment is dispersive, i.e, that the velocity of sound propagation through it is a function of frequency. Further it is concluded that at lower frequencies the velocity in the sediment near the bottom is less than that in the adjacent ocean. This rather unexpected geophysical phenomenon is explained theoretically in terms of propagation in a porous media.The low velocity sediment forms a wave guide between the higher velocity ocean above and the higher velocity sediment beneath. This resultant wave guide explains previously observed single-frequency arrivals.