How good are routinely determined focal mechanisms? Empirical statistics based on a comparison of Harvard, USGS and ERI moment tensors

How good are typical fault-plane solutions? This question is increasingly relevant given the moment tensor catalogues provided by various agencies, routinely determined from digital global seismic network data, and upon which many studies rely. The quality of the fault-plane solution affects studies where observed seismic-wave amplitudes, or amplitude ratios, are compared to those predicted by the catalogue mechanism. We present an error-estimation methodology based on the empirical statistics of differences between moment tensor solutions derived by three agencies: Harvard, USGS and ERI. The results suggest that catalogue quality is good, with a median correlation coefficient of 2429 earthquakes common to a pair of catalogues of 0.89. The methodology first associates the catalogues to identify common events occurring between January 1980 and June 1995. Post-July 1994, over 99 per cent of the USGS catalogue is contained in the Harvard catalogue and 89 per cent in ERI's. 73 per cent of the ERI catalogue is in Harvard's, indicating Harvard's is the most complete. Next, we compute pairwise radiation-pattern correlation coefficients for shallow, intermediate and deep earthquakes. The median P correlation increases with depth: 0.88 --> 0.93 --> 0.96. Based on a pairwise comparison of seismic moment M-0, we expect average absolute amplitude uncertainties of around +/- 40-60 per cent. Finally, a relation is derived between the radiation-pattern correlation coefficient and the uncertainty in amplitude by computing empirical statistics between azimuthally averaged rms amplitude and amplitude-ratio differences and the radiation-pattern correlation coefficient for different phase slownesses. We find rms amplitude uncertainties for P slownesses of 6 s deg(-1) are about +/- 0.15 and increase at lower slownesses. A tangent transformation of an amplitude ratio, tan theta = R-A/R-B, permits uncertainties to be cast in angular terms. For example, the sP/P uncertainty at 5 s deg(-1) is +/- 10 degrees for deep earthquakes, meaning that for a predicted amplitude ratio of 1.0 the value could range between 1.4 and 0.7 or for an amplitude ratio of zero it could be +/- 0.17. We also derive orientation uncertainties associated with moment tensor principal axes and earthquake slip vectors. For a typical shallow earthquake, the slip vector uncertainty is 14 degrees.