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

SUMMARYLong-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 1992 August and 1993 January and at Galeras volcano, Colombia, in 1993 January. 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 2006 December and 2007 January. 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 1993 January, 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 1993 January. 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.