An analytical formula for the longitudinal resonance frequencies of a fluid-filled crack

Abstract

The fluid-filled crack model has been widely used to interpret the peak frequencies of long-period (LP) seismic events at volcanoes. Up to now, numerical methods have been used to compute resonant frequencies in the model. We propose a simple analytical formula for the longitudinal resonance frequencies of a fluid-filled crack. We evaluated the formula by comparing its results with the resonant frequencies computed by finite difference method code. The comparison revealed that the formula well describes the resonant frequencies of both 2-D and 3-D cracks. The formula enables simple and rapid estimates of the fluid properties and geometries of LP source cracks. Key Points We propose a formula for the resonant frequenciesof a fluid-filled crack The formula well describes the frequenciescomputed by both 2D and 3D FDM The formula helps in the interpretation ofthe peak frequencies of LP events ©2013. American Geophysical Union. All Rights Reserved.