Propagation of acoustic waves in a viscoelastic two-phase system: influence of gas bubble concentration

Volcanic explosions generate pressure perturbations in the atmosphere and a seismic wavefield in the ground. The source is therefore well coupled with the atmosphere and the ground. The acoustic and elastic wavefields reflect dynamical processes at the source and the viscoelastic properties of the magma-gas medium. At low pressure (<10 MPa), magma cannot be considered as a homogeneous medium, and must be treated as a mixture of fluid magma and gas bubbles. Acoustic waves are strongly affected by the transmission properties of the magma-gas medium. We analyze the propagation of the acoustic wavefield in a two-phase medium in which the viscosity and compressibility are spatially inhomogeneous. Gas bubble nucleation starts when the magma pressure drops below the supersaturation level (at a depth of a few hundred m for H2O in basaltic magmas) and the gas-volume fraction increases toward the surface, reaching its maximum value at the magma-air interface. The variation of gas-volume fraction is non-linear with depth and is particularly strong at shallow depths (<50 m). Density and sound velocity of the mixture drop drastically and the shear viscosity of the mixture increases with decreasing depth. Under these conditions, we tested if the propagation of an acoustic wavefield generated by a source embedded in the magma column can generate an infrasonic wavefield in the atmosphere. The acoustic wavefield in the magma is here modeled as function of the void fraction in the magma and resonance is considered to be induced only by body-wave. Large gas bubble concentrations (>70%) strongly affect the propagation properties of the acoustic wavefield. We found that the amplitude of the infrasonic wavefield in the atmosphere typically recorded in case of strombolian explosions (2×105 Pa) can be explained by a deep (>50 m) source embedded in the magma conduit only if a very large unrealistic pressure drop (1013 Pa) is assumed. The strong damping, linked to the poor elastic properties of the shallow magma-gas mixture, prevents the efficient propagation of the acoustic waves in the magma-gas mixture, and resonance of body waves cannot occur. Infrasonic waves can be transmitted from the magma to the atmosphere only when the source is very shallow (<10 m). In conclusion, we neglect the possibility that resonance of body waves can induce infrasonic waves in the atmosphere. Moreover, we introduce new evidence of a strong attenuation induced by the shear viscosity on the propagation of elastic waves in a gas-rich magma. We believe that this latter result could have also a large impact on all the theories based on the resonance of elastic waves in a conduit as model to explain tremor and/or LP events on volcanoes.