A physical model for volcanic eruption tremor

Seismic waves are commonly used to monitor unrest before, during, and after volcanic eruptions. The source of seismic tremor during a sustained explosive volcanic eruption is not well understood. Recent observations of the 2016 eruption of Pavlof Volcano, Alaska, revealed a change in the relationship (hysteresis) between ash plume height and seismic amplitude over time. Based on similarities in physical processes and observed seismic tremor in rivers, we explore two key sources of seismic energy in the volcanic conduit: (1) forces exerted by particle impacts and (2) dynamic pressure changes by the turbulent flow. We develop a physical model calculating the seismic power spectral density (PSD), where forces on the conduit wall are convolved with the Green's function for Rayleigh waves. Using reasonable eruption parameters, the model is able to reproduce the frequency spectrum from the Pavlof eruption, although the modeled amplitudes are generally lower. We test the relative importance of different eruption parameters, including grain size, velocity, and conduit dimensions. We find that turbulence generally dominates over particle impacts. However, to reach the PSD amplitude during the Pavlof eruption, large grain sizes are required, as they have the greatest relative influence on the modeled amplitude. The hysteresis between plume height and seismic amplitude can then potentially be explained by grain size changes. The PSD shape is mostly determined by the Rayleigh-wave quality factor Q, and substantial variations in seismic amplitude can be modeled assuming a constant mass eruption rate.