**Journal of Geophysical Research: Solid Earth**

# Acoustic properties of a crack containing magmatic or hydrothermal fluids

## Abstract

We estimate the acoustic properties of a crack containing magmatic or hydrothermal fluids to quantify the source properties of long-period (LP) events observed in volcanic areas assuming that a crack-like structure is the source of LP events. The tails of synthetic waveforms obtained from a model of a fluid-driven crack are analyzed by the Sompi method to determine the complex frequencies of one of the modes of crack resonance over a wide range of the model parameters α/*a* and ρ_{f}/ρ_{s}, where αis the *P* wave velocity of the rock matrix, *a* is the sound speed of the fluid, and ρ_{f} and *p _{s}* are the densities of the fluid and rock matrix, respectively. The quality factor due to radiation loss (

*Q*) for the selected mode almost monotonically increases with increasing α/

_{r}*a*, while the dimensionless frequency (

*v*) of the mode decreases with increasing α/

*a*and ρ

_{f}/ρ

_{s}. These results are used to estimate

*Q*and

*v*for a crack containing various types of fluids (gas-gas mixtures, liquid-gas mixtures, and dusty and misty gases) for values of

*a*, ρ

_{f}, and quality factor due to intrinsic losses (

*Q*) appropriate for these types of fluids, in which

_{i}*Q*is given by

*Q*

^{−l}=

*Q*

_{r}

^{−l}+

*Q*

_{i}

^{−1}. For a crack containing such fluids, we obtain

*Q*ranging from almost unity to several hundred, which consistently explains the wide variety of quality factors measured in LP events observed at various volcanoes. We underscore the importance of dusty and misty gases containing small-size particles with radii around 1 μm to explain long-lasting oscillations with

*Q*significantly larger than 100. Our results may provide a basis for the interpretation of spatial and temporal variations in the observed complex frequencies of LP events in terms of fluid compositions beneath volcanoes.