Empirical Relation for the Quality Factors of Crack Resonances and Its Application to Estimate Source Properties of Volcanic Long-period Seismic Events

Long-period (LP) seismic events are thought to arise from the oscillations of a fluid-filled resonator. The resonator geometry and fluid properties of LP sources have been estimated by comparing observed frequencies and quality (Q) factors to those calculated from a crack model. Recently, a method to estimate all the parameters of crack geometry and fluid properties was proposed. In this method, observed frequencies were compared to those calculated by an analytical formula for the crack resonance frequencies. However, observed Q factors were compared to those calculated by numerical simulations of the crack model, which took extensive computational time especially for LP events with large Q factors. To resolve this problem, we systematically investigated the relation between Q factors and the crack model parameters by numerical simulations. Then we found an empirical relation, indicating that Q factors of the crack resonances are expressed as functions of α/a and W/L, where α is the P wave velocity of the solid, a is the sound speed of the fluid in the crack, and L and W are crack length and width, respectively. To test the applicability of this empirical relation, we used it to analyze LP events at Galeras volcano, Colombia, in January 1993, which have been thought to be generated by the resonances of a crack filled with dusty gas produced by fragmentations of intruded magma. Our estimates of the crack model parameters were almost same as those using the Q values estimated from the numerical simulations. We further applied the empirical relation to analyze LP events with large observed Q values in May 1993 and December 2006, assuming dusty gas as the fluid in the crack. The empirical relation enables us to estimate all the crack model parameters for these LP events without long computational time, and we found decreasing trends in both crack volume and gas-weight fraction of water vapor in the crack. These trends were similar to those in January 1993, and LP events in May 1993 and December 2006 may also have occurred in association with magma intrusions. These results demonstrate that the empirical relation for Q factors obtained in this study is useful to estimate the source properties of LP events and may contribute to improve monitoring of fluid states beneath volcanoes.