Modelling the time-dependent frequency content of low-frequency volcanic earthquakes

Abstract

Low-frequency volcanic earthquakes and tremor have been observed on seismic networks at a number of volcanoes, including Soufrière Hills volcano on Montserrat. Single events have well known characteristics, including a long duration (several seconds) and harmonic spectral peaks (0.2–5 Hz). They are commonly observed in swarms, and can be highly repetitive both in waveforms and amplitude spectra. As the time delay between them decreases, they merge into tremor, often preceding critical volcanic events like dome collapses or explosions. Observed amplitude spectrograms of long-period volcanic earthquake swarms may display gliding lines which reflect a time dependence in the frequency content. Using a magma-filled dyke embedded in a solid homogeneous half-space as a simplified volcanic structure, we employ a 2D finite-difference method to compute the propagation of seismic waves in the conduit and its vicinity. We successfully replicate the seismic wave field of a single low-frequency event, as well as the occurrence of events in swarms, their highly repetitive characteristics, and the time dependence of their spectral content. We use our model to demonstrate that there are two modes of conduit resonance, leading to two types of interface waves which are recorded at the free surface as surface waves. We also demonstrate that reflections from the top and the bottom of a conduit act as secondary sources that are recorded at the surface as repetitive low-frequency events with similar waveforms. We further expand our modelling to account for gradients in physical properties across the magma–solid interface. We also expand it to account for time dependence of magma properties, which we implement by changing physical properties within the conduit during numerical computation of wave propagation. We use our expanded model to investigate the amplitude and time scales required for modelling gliding lines, and show that changes in magma properties, particularly changes in the bubble nucleation level, provide a plausible mechanism for the frequency variation in amplitude spectrograms.