Empirical formula for the quality factors of crack resonances and its application to the estimation of source properties of long-period seismic events at active volcanoes

Abstract

Summary Long-period (LP) seismic events at active volcanoes are thought to be generated by oscillations of fluid-filled resonators. The resonator geometry and fluid properties of LP sources have been estimated by comparing observed frequencies and quality factors (Q) with those calculated by numerical simulations with a crack model. A method to estimate all the parameters of crack geometry and fluid properties using an analytical formula for crack resonance frequencies has recently been proposed, but this method requires long computational times to compare observed and simulated Q values, especially for LP events with large Q. To resolve this problem, we used numerical simulations to systematically investigate the empirical relation between Q and crack model parameters. We found that Q can be calculated with an empirical formula expressed by the crack width-to-length ratio and the ratio of P-wave velocity in the solid medium to sound speed in the fluid. We applied this formula to LP events at Kusatsu-Shirane volcano, Japan, between August 1992 and January 1993 and at Galeras volcano, Colombia, in January 1993. Assuming misty gas as the fluid in the crack at Kusatsu-Shirane and dusty gas as the fluid at Galeras, the empirical formula provided more detailed estimates of the parameters than those obtained previously using the Q values estimated in numerical simulations. We then applied the empirical formula to LP events with large Q values observed at Galeras between December 2006 and January 2007. When we assumed dusty gas as the fluid in the crack, we found decreasing trends in both crack volume and the gas-weight fraction of water vapour in the crack. We also found that the dust volume was proportionally related to the product of crack aperture and crack length or width. These trends and relations were similar to those in January 1993, suggesting that the LP events at Galeras between 2006 and 2007 were triggered by the explosive fragmentation of intruded magma and the production of a dusty gas, as was previously inferred for the LP events in January 1993. Welding of ash in the dusty gas and dense magma remaining in the conduit after fragmentation led to a decrease in the source crack size prior to the next LP event. These results demonstrate that our empirical formula for Q can be used to estimate the source properties of LP events with large Q values without requiring long computational times. Use of the formula may thus contribute to improved monitoring of fluid states and understanding of LP triggering processes beneath many volcanoes.

Pressure-Driven Opening and Filling of a Volcanic Hydrofracture Recorded by Tuffisite at Húsafell, Iceland: A Potential Seismic Source

“…A similar model has been proposed at Galeras volcano, with LP events suggested to represent the propagation and increase in volume of a vertical crack injected by a gas-ash mixture (Taguchi et al, 2018). Both the crack volume and mass fraction of gas within the crack were inferred to have decreased as ash was deposited and welded before the next LP event (Taguchi et al, 2021). We propose that the Húsafell tuffisite represents the fossil record of exactly this type of LP seismic swarm.…”

“…To produce long-lasting oscillations with Q significantly greater than 100, there needs to be a large density difference between the fluid and the surrounding rock (Chouet, 1996). Computed synthetic waveforms for fluid-filled cracks indicate that very high Q-values (e.g., Q = 400 at Tungurahua Volcano, Molina et al, 2004) are best explained if the fluid is a dusty or misty gas with low sound speed (Kumagai and Chouet, 2000;Taguchi et al, 2021). In this volcanic scenario, the dust is inferred to be fine-grained particles of volcanic ash.…”

Resonances of Fluid‐Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

“…However, it is possible that the first two spectral peaks in the seismic data do not correspond to the fundamental mode and first higher mode if any of them are not properly excited. For instance, previous studies of VLP and LP events (Kumagai, 2006;Taguchi et al, 2018Taguchi et al, , 2021 indicated that the observed lowest frequencies were not the fundamental mode. To examine this hypothesis, we compute the frequency ratios between the first 5 resonant modes and the ratios between the first 4 longitudinal modes of a rectangular crack with varying C L and aspect ratios α (see Tables S7-S10 in the Supporting Information S1).…”

Laboratory Measurements of the Impact of Fracture and Fluid Properties on the Propagation of Krauklis Waves

“…While brittle failure earthquakes occur in these areas, pressure changes in fluid‐filled cavities can produce other types of signals. At volcanoes, LP events, as a low‐frequency signal with the resonant property, have been interpreted to be the far‐field seismic response of oscillations of fluid‐filled cavities during fluid transport, and therefore, it serves as an important eruption precursor (Chouet, 1986; Chouet & Matoza, 2013; Liang et al., 2020; Taguchi et al., 2021; Waite et al., 2013). Due to this low resonant frequency, researchers relate LP events to a slow wave trapped in fluid‐filled fractures called the Krauklis wave that contains the same resonance information about the fracture and fluid properties (Gräff et al., 2019; Lipovsky & Dunham, 2015; Tary et al., 2014).…”