Sound speeds and densities are calculated for three different types of fluids: gas-gas mixture; ash-gas mixture; and bubbly liquid. These fluid properties are used to calculate the impedance contrast (Z) and crack stiffness (C) in the fluid-driven crack model (Chouet: J. Geophys. Res., 91 (1986) 13,967; 101 (1988) 4375; A seismic model for the source of long-period events and harmonic tremor. In: Gasparini, P., Scarpa, R., Aki, K. (Eds.), Volcanic Seismology, IAVCEI Proceedings in Volcanology, Springer, Berlin, 3133). The fluid-driven crack model describes the far-field spectra of long-period (LP) events as modes of resonance of the crack. Results from our calculations demonstrate that ash-laden gas mixtures have fluid to solid density ratios comparable to, and fluid to solid velocity ratios lower than bubbly liquids (gas-volume fractions <10%). This difference results in synthetic far-field spectra with higher impedance contrasts and narrower spectral bandwidths for ash-laden gas mixture than spectra for bubbly liquids. Spectral characteristics are described in terms of the quality factor Q-1. Q-1 is measured by the ratio of the frequency of the dominant spectral peak to the bandwidth of the peak measured at one half of its amplitude. This factor expresses the losses of energy due to elastic radiation Q-1r and other dissipative mechanisms Q-1i at the source, Q-1 = Q-1r + Q-1i. Spectra for LP events recorded at active volcanoes such as Galeras in Colombia and Kilauea in Hawaii, have Q-1 factors in the range of 0.1-0.002. The Q-1r factors due to radiation loss calculated for a sphere filled with a H2O-CO2 or H2O-SO2 gas mixture, vary between 0.0015 and 0.0040 with a change in wt% H2O at 800-1600 K and 10-50 MPa. For gas-rich mixtures, Q-1r has a strong dependence on resonator geometry (spherical versus rectangular). The spectra from a resonating sphere filled with gas-rich mixture yields values of Q-1r an order of magnitude smaller than those from a rectangular crack. For a resonating crack filled with an ash-gas mixture (or pseudogas), Q-1r varies parabolically from ???0.006 for an ash-rich mixture, to 0.0015 or 0.0023 for a H2O-rich or CO2-rich mixture at 800 K and 25 MPa. For low (<20%) gas-volume fraction fluids (foams, bubbly fluids and ash-rich pseudogases), the magnitudes for Q-1r are independent of crack geometry. Spectra associated with a foam (gas-volume fractions 10-90%) or bubbly basalt (gas-volume fractions <10%) may have a dominant spectral peak with values of Q-1r on the order of 0.01 and 0.1, respectively. The spectra from a resonating sphere filled with a foam containing >20% gas-volume fraction yields values of Q-1r similar to those for a rectangular crack. As with gas-gas and ash-gas mixtures, an increase in mass fraction narrows the bandwidth of the dominant mode and shifts the spectra to lower frequencies. Including energy losses due to dissipative processes in a bubbly liquid increases attenuation. Attenuation may also be higher in ash-gas mixtures and foams if the effects of momentum and mass transfer between the phases were considered in the calculations. ?? 2001 Elsevier Science B. V. All rights reserved.
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Trends in long-period seismicity related to magmatic fluid compositions