Regional estimates of radiated seismic energy

We revise the spectral technique for estimating radiated energy from recordings of large earthquakes at regional distances (Δ < 200 km) by correcting for geometric spreading and for site amplification as explicit functions of frequency. We analyze 65 recordings of the 1999 Hector Mine earthquake as functions of frequency, distance, and azimuth. For r > 27.5 km from the source, we model the geometrical spreading of the regional wavefield as r^–γ where γ = 0.5 for f ≤ 0.2 Hz and γ = 0.7 for f ≥ 0.25 Hz. We fit the spectral falloff with distance using a frequency-dependent attenuation Q = 400(f /1.5)^0.6, where Q = 400 for f ≤ 1.5 Hz. There is little directivity apparent in the corrected velocity spectra: the velocity spectra observed to the northwest along strike are amplified by a factor of 2.5 from 0.3 to 1.0 Hz and those to the southeast are amplified by a factor of 1.6 from 0.3 to 0.7 Hz. We group the stations in NEHRP site classes, using average 1-D velocity structures to estimate site amplification as a function of frequency and assuming 0.40 ≤ κ ≤ 0.55 sec for the near-surface attenuation. We increase the amplification of the soft-soil sites from 0.1 to 1.0 Hz by a factor that reaches 1.7 at 0.3 Hz because they are more strongly amplified than the NEHRP-D velocity structure predicts. We combine the 65 single-station estimates of radiated energy using an equal-azimuth weighting scheme that compensates for station distribution and incorporates the observed directivity, yielding a regional estimate of E_s = 3.4 ± 0.7 × 10²² dyne cm. This regional estimate of radiated energy corresponds closely to the teleseismic estimate of E_s = 3.2 × 10²² dyne cm.