In a study of the dependence of the velocity of compressional waves in marine sediments upon the thickness of overburden, the velocity-depth relationship in shelf sediments is shown to be distinctly different from that in deep basin sediments. The difference between the two cases may be illustrated by comparing the straight lines that best represent the data. These areEquationwhere V is in km/sec and Z is in kilometers. Shallow and deep water are defined arbitrarily to be under 100 fathoms and over 1,500 fathoms respectively.The observed variation of average compressional velocity in the shallow and deep water sediments, taken together with the known limited range of variation of velocity for a given porosity, yields limits in turn upon the porosity-depth dependence in the two environments. It is shown that at the same depth of overburden porosity is much greater in deep water sediments than in shallow.A physical argument is presented to show that there is implicit in the observed narrow range of variation of velocity with porosity a simple relation between porosity and rigidity. Thus quantitative estimates of shear velocity may be made from compressional velocity alone. In this way the original data are used to place rather narrow limits on the depth variation of shear velocity, porosity, and density. A number of comparisons with observation are employed to test the conclusions at each stage of the discussion.