A simple approach to quantify crack geometry and fluid properties at the long-period seismic source

The fluid-filled crack model has been considered as a model of the resonator at the source of long-period (LP) seismic events. Crack geometry and fluid acoustic properties were estimated by comparing observed peak frequencies of LP events with resonance frequencies of the crack model. However, this comparison required extensive numerical computations. Recently, Maeda and Kumagai (GRL, 2013; 2016 AGU Meeting) proposed an analytical formula for resonance frequencies of the crack model, which enables us to conduct the comparison in a simple and systematic way. In this study, we developed a method to estimate the crack model parameters from observed peak frequencies of LP events using the analytical formula, and applied it to LP events observed at Kusatsu-Shirane volcano, Japan, and at Galeras volcano, Colombia. First, we took the ratios of observed peak frequencies of LP events to the lowest one. Next, we took the ratios of resonance frequencies of various modes using the analytical formula. We systematically varied the assumed resonance mode in the denominator of the ratios from the lowest mode to higher modes, and estimated W/L (the ratio of crack width to length) and C (crack stiffness) that best explained several successive observed peak frequencies in each event. The estimated crack parameters were reasonably explained by assuming misty gas at Kusatsu-Shirane volcano and dusty gas at Galeras volcano, and provided realistic estimates of L (18-250 m). We found that our estimates of C, W/L, and L/d, where d is the crack aperture, took similar values: C = 1.1-7.2, W/L = 0.54-0.90, and L/d = (2-6)×103. This implies the existence of similar crack geometrical conditions to generate crack resonances or LP events. This study indicates that our method based on the analytical formula is useful to estimate the crack model parameters and is widely applicable to LP events at different volcanoes.