Uncertainties in Earthquake Source Spectrum Estimation Using Empirical Green Functions

We analyze the problem of reliably estimating uncertainties of the earthquake source spectrum and related source parameters using Empirical Green Functions (EGF). We take advantage of the large dataset available from 10 seismic stations at hypocentral distances (10 km < d < 50 km) to average spectral ratios of the 2001 M5.1 Anza earthquake and 160 nearby aftershocks. We estimate the uncertainty of the average source spectrum of the M5.1 target earthquake by performing propagation of errors, which, due to the large number of EGFs used, is significantly smaller than that obtained using a single EGF. Our approach provides estimates of both the earthquake source spectrum and its uncertainties, plus confidence intervals on related source parameters such as radiated seismic energy or apparent stress, allowing the assessment of statistical significance. This is of paramount importance when comparing different sized earthquakes and analyzing source scaling of the earthquake rupture process. Our best estimate of radiated energy for the target earthquake is 1.24 × 10¹¹ Joules with 95% confidence intervals (0.73 × 10¹¹, 2.28 × 10¹¹). The estimated apparent stress of 0.33 (0.19, 0.59) MPa is relatively low compared to previous estimates from smaller earthquakes (1MPa) in the same region.