We used aftershocks of the 2011 Mineral, Virginia, earthquake to study geometrical spreading at hypocentral distances less than 60 km in the central Virginia seismic zone. Sixty‐nine aftershocks, occurring from 25 August 2011 through 24 December 2011, provided the data. We used the coda‐normalization method to estimate the attenuation coefficient associated with geometrical spreading. We filtered the time‐domain signals in several octave‐wide frequency bands and examined attenuation of peak S‐wave amplitude in the 1.0–30.0 Hz frequency range. Amplitude was assumed to decrease as a function of hypocenter distance R according to R−γ. The coefficient of attenuation γ was examined for the three‐component S‐wave amplitudes, with corrections for SH and SV radiation patterns.
We observed no systematic frequency dependence of γ. The coefficient of attenuation for the radial and transverse components, assuming infinite quality factor Q, derived as a weighted mean over the entire range of frequencies (1–30 Hz), are both 1.51±0.05. The weighted mean value of the attenuation coefficient on the vertical component over the same range of frequencies is 1.45±0.05, slightly less than for the horizontal components. We corrected the data assuming three Q models. The estimated geometrical spreading coefficients are in the 1.30–1.46 range, depending on the assumed Q model and component, which is only slightly less than the estimates of γ determined assuming infinite Q. The estimated attenuation coefficients differ significantly from the value of 1.0 expected for a whole space. The results for the horizontal components are in agreement with previous full‐wavefield modeling. However, the observed vertical‐component attenuation is substantially less than that predicted by the synthetics. The depths of the earthquakes are less than 8 km, so these results may not be representative of geometrical spreading in parts of eastern North America where earthquakes occur at greater depths.
Online Material: Table of earthquake hypocenters and focal mechanisms.