The dispersion of sound in sediment

The attenuation of sound through a wide variety of sediments is proportional to the first power of frequency. In order that a plane wave remain causal after suffering such an attenuation, it must also be dispersed. The dispersion necessary to maintain causality in typical sediment is shown to have a logarithmic dependence on frequency and to be measurably large. A truncated parametric array is used to provide a wideband pulse whose travel through a typical medium sand is observed. The measured dispersion is in agreement with the theoretical prediction, exhibiting a variation in phase velocity of 0.5% across a frequency range of 50–350 kHz.