`Long-period' seismic events are the most important seismic signals related to the internal systems of volcanoes, e.g. Soufriere Hills Volcano, Montserrat (Chouet et al., 1994, Neuberg et al., 1998}. These signals are thought to be produced by a resonating system of a fluid trapped within a solid, e.g. a magma-filled conduit within elastic volcanic rock. Such a model was used in Neuberg (2002), but assumed no seismic attenuation, though the large gas volume fraction in the conduit, might have a highly dissipative effect on the waves. This attenuation needs to be added to the magma model to give a more thorough understanding of how the magma properties change and how these properties effect seismic waves.

Attenuation of a seismic wave is quantified by using the `Quality Factor', Q:

where W_ave is the average stored energy during one oscillation, and DeltaW is the amount of energy dissipated in this oscillation (O'Connell and Budiansky, 1978).

As the amount of gas dissolved increases as you go up the magma conduit, we would expect the attenuation to increase as well, i.e., Q decreases.
 
 

Figure 1 (left) shows that as you go up the conduit, then indeed the attenuation increases (Q decreases). The level of attenuation within the conduit is extremely high compared to the surrounding elastic rock. This is mainly due to the high levels of gas within the conduit. Another effect is that as you increase the frequency of the seismic wave, the attenuation along a seismic path also increases, because the wave oscillates more often and dissipates more energy. This means that signals of higher frequencies are likely to be damped completely before they reach the surface, and are therefore undetected by the seismic stations. This attenuation effect could be one of the reasons why `Long-Period' signals have such characteristic low frequencies.

The bulk viscosity of the bubble-melt mixture is another important factor when considering the propagation of seismic waves. Due to the supersaturated nature of the bubble-melt mixture, a seismic wave travelling through the conduit will experience an energy boost during the decompression phase, allowing an increase in amplitude of the wave (Lensky et al., 2002, in press). This ability of the bubble-melt mixture to release energy is indicated by a negative bulk viscosity.
 

The definition of the bulk viscosity (Malvern, 1969) is, where delta sigma is the applied stress of the system, due to the pressure, and epsilon is the strain rate. After a decompression the magma will be supersaturated, as the pressure increases with depth in the conduit, the level of supersaturation also increases. This can be seen in Figure 2 (left), as the depth in the conduit increases, the bulk viscosity, zeta, decreases becoming more negative, indicating the increasing level of supersaturation.

The effects of the bubble-melt mixture on the propagation of seismic signals, e.g. attenuation due to gas content and possible bulk viscosity amplification, are investigated and modelled. In turn, the effect of the seismic waves on the properties of the bubble-melt mixture is the other main topic in this project. Models of the two-phase magma conduits assume the seismic waves have no effect on the properties of the bubble-melt mixture. This is unrealistic as it has been shown that pressure waves can increase the rate of bubble growth, by a process called `rectified diffusion', (Brodsky et al., 1998). The bubble growth could be accelerated to the point where fragmentation of the melt occurs sooner than if there was no pressure wave travelling through the conduit, triggering a volcanic eruption.
 

References:

Brodsky E., Sturtevant S. and Kanamori H., 1998. Earthquakes, volcanoes and rectified diffusion, J. Geophys. Res. 103, B10, 23827-23838.

Chouet B., Pate R., Stephens C., Lahr J. and Power J., Precursory swarms of long-period events at Redoubt Volcano (1989-1990), Alaska: Their origin and use as a forecasting tool, J. Volcanol. Geotherm. Res., 62, 95-135.

Lensky N. and Lyakhvsky V. and Navon O., 2002. Expansion dynamics and volatile-supersaturated liquids and bulk viscosity of bubbly magmas, J. Fluid Mech., in press.

Malvern L.E., 1969. Introduction to the mechanics of a continuous medium, in "Series in engineering of the physical science", Ed. Prentice-Hall.

Neuberg J., Baptie B. and Luckett R. and Stewart R., 1998. Results from the broadband seismic network on Montserrat, GRL, 19, 3661-3664.

Neuberg J. and O'Gorman C., 2002. A model of the seismic wavefield in gas-charged magma: application to Soufriere Hills volcano, Montserrat, in "The eruption of Soufriere Hills Volcano, Montserrat, from 1995 to 1999, Ed. Druitt T.H. and Kokelaar B.P., Geological Society of London Memoir, 21, 603-609.

O'Connell R. and Budiansky B., 1978. Measures of dissipation in viscoelastic media, GRL, 5, 1:5-8.