The relationship between frequency and velocity of elastic waves through water saturated carbonate sedimentary rocks can be studied indirectly by comparing data measured at one ultrasonic frequency on samples with a wide range of characteristic frequencies as defined by Biot (1956a, b). The characteristic frequency can be calculated from porosity and permeability. Data measured under dry conditions may be Gassmann substituted and then indirectly correspond to low frequency data (Gassmann 1951). Samples measured below their characteristic frequency display an apparent negative dispersion where velocity in the water saturated case is lower than would be expected according to Biot theory. This effect could rather be due to frame-softening than to dispersion. Samples measured above their characteristic frequency display positive dispersion. In most cases the dispersion matches the one expected from Biot's model; but in a significant number of cases a squirt flow mechanism may be invoked, where the squirt probably is a consequence of a heterogeneous depositional texture giving rise to a heterogeneous pore structure.