Magma wagging and whirling in volcanic conduits

Seismic tremor characterized by 0.5-7 Hz ground oscillations commonly occur before and during eruptions at silicic volcanoes with widely ranging vent geometries and edifice structures. The ubiquitous characteristics of this tremor imply that its causes are potentially common to silicic volcanoes. Here we revisit and extend to three dimensions the magma-wagging model for tremor Jellinek and Bercovici, 2011, Bercovici et al., 2013, wherein a stiff magma column rising in a vertical conduit oscillates against a surrounding foamy annulus of bubbly magma, giving rise to tremor. While prior studies were restricted to two-dimensional lateral oscillations, here we explore three-dimensional motion and additional modes of oscillations. In the absence of viscous damping, the magma column undergoes 'whirling' motion: the center of each horizontal section of the column traces an elliptical trajectory. In the presence of viscous effect we identify new 'coiling' and 'uncoiling' column bending shapes with relatively higher and comparable rates of dissipation to the original two-dimensional magma wagging model. We also calculate the seismic P-wave response of the crustal material around the volcanic conduit to the new whirling motions and propose seismic diagnostics for different wagging patterns using the time-lag between seismic stations. We test our model by analyzing pre-eruptive seismic data from the 2009 eruption of Redoubt Volcano. In addition to suggesting that the occurrence of elliptical whirling motion more than 1 week before the eruption, our analysis of seismic time-lags also implies that the 2009 eruption was accompanied by qualitative changes in the magma wagging behavior including fluctuations in eccentricity and a reversal in the direction of elliptical whirling motion when the eruption was immediately impending.