Theory for attenuation and dispersion of acoustic propagation through a muddy medium

Mud as a medium typically consists of clay particles, small silt particles (primarily quartz), and water. The clay particles lock together in what is called a card-house configuration, and the silt particles are held in suspension by the card house. The low frequency velocity of sound waves appears to be well-predicted by the Mallock-Wood theory that gives weighted averages of bulk compressibility and material density. At low frequencies, the attenuation is caused by the viscous dag of the water on the suspended silt particles, and the attenuation varies as the frequency squared. The deviation of the phase velocity from the low frequency limit at low frequencies is less well-understood but appears to vary as the frequency to the three-halfs. At higher frequencies, the dominant mechanism appears to be a relaxation mechanism associated with the card house. Each clay particle carries a net electrical charge and the resulting repulsion forces the clay particles to be spatially separated. However, the particles tend to stick together edge to face, and the van der Waals attraction between the clay particles tends to dominate over the electrostatic repulsion. However, the passage of a sound wave temporarily breaks some van der Waals bonds and they subsequently recombine as the acoustic pressure ebbs. The present paper seeks to quantify the effects of the relaxation processes. It is demonstrated that the latter leads to an attenuation that, at higher frequencies, varies nearly linearly with frequency. [Work supported by ONR.]