Low frequency volcanic earthquakes, characterised by slowly decaying harmonic codas of 0.5-5Hz, have been observed on many volcanoes and are considered key tools in monitoring and eruption forecasting. The common element in a variety of models proposed for the origin of these earthquakes is resonance of a fluid body within a volcanic edifice. The source of the resonance is believed to consist of dispersive interface waves, trapped at the fluid-solid boundaries. The amplitude decay or attenuation of these earthquake signals can be decomposed into radiative and intrinsic components, and in this way yield information about both the geometry and fluid properties of the resonating source body. This thesis presents a study of the attenuation of low-frequency volcanic earthquakes, with particular emphasis on quantitatively linking seismic signals to magmatic processes and properties. The effect of the intrinsic attenuation of the fluid on the amplitude decay of low-frequency volcanic earthquakes is examined using a viscoelastic finite-difference model of seismic wave propagation. It is shown that the viscosity of the fluid contributes 23.6±2.26% less than previously thought to the apparent attenuation, and that its effect may have been substantially overestimated in previous studies. A physical explanation for this lies in understanding the fundamental differences between acoustic and interface waves. An analytical approach demonstrates that, for a set of realistic volcanic parameters, interface waves can be attenuated less than acoustic waves in a pure melt, if the longitudinal viscosity is at least 107 Pas. These results widen the set of possible resonators and imply that resonating volcanic conduits filled with high viscosity magma are viable sources for low-frequency seismicity. An automated method to measure the apparent attenuation of seismic signals is developed, tested, and applied to a dataset of low-frequency earthquakes from Soufri`ere Hills Volcano, Montserrat. Temporal trends in attenuation are observed and quantitatively interpreted as changes in magma viscosity. An estimate of the magma shear viscosity of 2.3 ± 2 × 105 Pas is obtained, demonstrating the ability of seismological data to place constraints on the magma properties.