Theory of acoustic propagation in a multi-phase stratified liquid flowing within an elastic-walled conduit of varying cross-sectional area

A theoretical solution is derived for the sound field in an arbitrarily layered viscous fluid moving with the non-negligible Mach number within a duct with elastic walls and varying cross-sectional area. The solution is applied to the interpretation of infrasonic and seismic signals preceding and accompanying volcanic eruptions, and can be used to study the acoustic response of various types of volcanic fluids, including magma–gas mixtures, ash–gas mixtures, and bubble-rich liquids. The acoustic field in a magma conduit can be propagated into the atmosphere through an open vent, and coupled into the ground through the displacement of the magma conduit walls. The theoretical solutions predict that fluids moving with the non-negligible Mach number will exhibit significant attenuation in the upstream direction, thereby reducing the quality factor of the conduit resonance. Thus, acoustic energy generated during an eruption may be preferentially radiated downstream, exacerbating the acoustic decoupling between the upper and lower parts of a stratified magma column. A source model for a repeated cavitation process is introduced as a possible excitation mechanism for tremor signals.