Temporal variations of coda Q: An attenuation-coefficient view

Spatial and temporal variations of coda wave attenuation were identified in many studies, and particularly in relation to major earthquakes and volcanic eruptions. Both the coda quality factor, Qc, and its frequency dependence often change following such events, which is often attributed to variations in the properties of large volumes of the subsurface. However, Qc is also strongly sensitive to the assumed theoretical models, which are usually insufficiently accurate for constraining the actual relationships between the geometrical spreading, anelastic dissipation, and scattering. This inaccuracy often leads to significant exaggeration of attenuation effects and complicates the interpretation of temporal variations. To resolve this problem, this study uses a phenomenological approach based on the temporal attenuation coefficient χ instead of Qc. The attenuation coefficient often linearly depends on frequency f, with intercept γ = χ ( 0 ) related to the geometrical spreading and slope giving the “effective quality” factor Qe as d χ / df = π Q e - 1 . Two published examples of temporal variations of local-earthquake coda are revisited: a non-volcanic (Stone Canyon in central California) and volcanic area (Mount St. Helens, Washington). In both cases, linear χ ( f ) patterns are found, with the effects of γ on coda decay rates being significantly stronger than those of Q e - 1 . At Stone Canyon, γ ranged from 0.035 to 0.06 s−1 and Qe varied from 3000 to 10,000, with γ increasing and Qe decreasing during the winter season. At Mount St. Helens, γ remained constant at ∼0.18 s−1, and Qe changed from 400 before the eruption to 750 after it. The observed temporal variations are explained by the near-surface changes caused by seasonal variations in the non-volcanic case and gas-, magma-, and geothermal-system related in the volcanic case. Scattering attenuation does not appear to be a significant factor in these areas, or otherwise it may be indistinguishable due to its fundamental trade-off with the background structure and anelastic attenuation in the data.