Seismic Tremors and Three-Dimensional Magma Wagging

Abstract:

Seismic tremor is a feature shared by many silicic volcanoes and is a precursor of volcanic eruption. Many of the characteristics of tremors, including their frequency band from 0.5 Hz to 7 Hz, are common for volcanoes with very different geophysical and geochemical properties. The ubiquitous characteristics of tremor imply that it results from some generation mechanism that is common to all volcanoes, instead of being unique to each volcano.

Here we present new analysis on the magma-wagging mechanism that has been proposed to generate tremor. The model is based on the suggestion given by previous work (Jellinek & Bercovici 2011; Bercovici et.al. 2013) that the magma column is surrounded by a compressible, bubble-rich foam annulus while rising inside the volcanic conduit, and that the lateral oscillation of the magma inside the annulus causes observable tremor. Unlike the previous two-dimensional wagging model where the displacement of the magma column is restricted to one vertical plane, the three-dimensional model we employ allows the magma column to bend in different directions and has angular motion as well.

Our preliminary results show that, without damping from viscous deformation of the magma column, the system retains angular momentum and develops elliptical motion (i.e., the horizontal displacement traces an ellipse). In this ‘‘inviscid’’ limit, the magma column can also develop instabilities with higher frequencies than what is found in the original two-dimensional model. Lateral motion can also be out of phase for various depths in the magma column leading to a coiled wagging motion. For the viscous-magma model, we predict a similar damping rate for the uncoiled magma column as in the two-dimensional model, and faster damping for the coiled magma column. The higher damping thus requires the existence of a forcing mechanism to sustain the oscillation, for example the gas-driven Bernoulli effect proposed by Bercovici et al (2013). Finally, using our new 3-D model, the spectrum of displacement and unsynchronized cross-correlation between displacements measured from different locations can be calculated, and this can be compared to more detailed seismic measurements on well monitored volcanoes.