Fragmentation plays a critical role in eruption explosivity by influencing the eruptive jet and plume dynamics that may initiate hazards such as pyroclastic flows. The mechanics and progression of fragmentation during an eruption are challenging to constrain observationally, limiting our understanding of this important process. In this work, we explore seismic radiation associated with unsteady fragmentation. Seismic force and moment tensor fluctuations from unsteady fragmentation arise from fluctuations in fragmentation depth and wall shear stress (e.g., from viscosity variations). We use unsteady conduit flow models to simulate perturbations to a steady-state eruption from injections of heterogeneous magma (specifically, variable magma viscosity due to crystal volume fraction variations). Changes in wall shear stress and pressure determine the seismic force and moment histories, which are used to calculate synthetic seismograms. We consider three heterogeneity profiles: Gaussian pulse, sinusoidal, and stochastic. Fragmentation of a high-crystallinity Gaussian pulse produces a distinct very-long-period (VLP) seismic signature and associated reduction in mass eruption rate, suggesting joint use of seismic, infrasound, and plume monitoring data to identify this process. Simulations of sinusoidal injections quantify the relation between the frequency or length scale of heterogeneities passing through fragmentation and spectral peaks in seismograms, with velocity seismogram amplitudes increasing with frequency. Stochastic composition variations produce stochastic seismic signals similar to observed eruption tremor, though computational limitations restrict our study to frequencies less than 0.25 Hz. We suggest that stochastic fragmentation fluctuations could be a plausible eruption tremor source.

Explosive volcanic eruptions radiate seismic waves as a consequence of pressure and shear traction changes within the conduit/chamber system. Kinematic source inversions utilize these waves to determine equivalent seismic force and moment tensor sources, but relation to eruptive processes is often ambiguous and nonunique. In this work, we provide an alternative, forward modeling approach to calculate moment tensor and force equivalents of a model of eruptive conduit flow and chamber depressurization. We explain the equivalence of two seismic force descriptions, the first in terms of traction changes on the conduit/chamber walls, and the second in terms of changes in magma momentum, weight, and momentum transfer to the atmosphere. Eruption onset is marked by a downward seismic force, associated with loss of restraining shear tractions from fragmentation. This is followed by a much larger upward seismic force from upward drag of ascending magma and reduction of magma weight remaining in the conduit/chamber system. The static force is upward, arising from weight reduction. We calculate synthetic seismograms to examine the expression of eruptive processes at different receiver distances. Filtering these synthetics to the frequency band typically resolved by broadband seismometers produces waveforms similar to very long period (VLP) seismic events observed in strombolian and vulcanian eruptions. However, filtering heavily distorts waveforms, accentuating processes in early, unsteady parts of eruptions and eliminating information about longer time scale depressurization and weight changes that dominate unfiltered seismograms. The workflow we have introduced can be utilized to directly and quantitatively connect eruption models with seismic observations.

Inflationary deformation and very long period (VLP) earthquakes frequently accompany basaltic caldera collapses, yet current interpretations do not reflect physically consistent mechanisms. We present a lumped parameter model accounting for caldera block/magma momentum change, magma chamber pressurization, and ring fault shear stress drop. The effect of pressurizing a spheroidal chamber is represented as a tri-axial expansion source, and the combined caldera block/magma momentum change as a vertical single force. The model is applied to Kīlauea 2018 caldera collapse events, accurately predicting near field static/dynamic ground motions. In addition to the tri-axial expansion source, the single force contributes significantly to the VLP waveforms. For an average collapse event with fully developed ring fault, Bayesian inversion constrains ring fault stress drop to ~0.4 MPa and the pressure increase to ~1.7 MPa. That the predictions fit both geodetic and seismic observations confirms that the model captures the dominant caldera collapse mechanisms.