Abstract
We present a method to assess the uncertainty of earthquake focal mechanisms based on the standard theory of linear inverse problems. We compute the uncertainty of the moment tensor, M, then map it into uncertainties of the strike, dip, and rake.
The inputs are: source and station locations, crustal model, frequency band of interest, and an estimate of data error. The output is a six-dimensional (6D) error ellipsoid, which shows the uncertainty of the individual parameters of M.
We focus on the double-couple (DC) part of M. The method is applicable both with and without waveforms.
The latter is particularly useful for network design. As an example we present maps of DC resolvability for earthquakes in southwest Europe, computed without waveforms.
We find that the resolvability depends critically on frequency range and source depth. Shallow DC sources (10 km) are theoretically better resolved than deeper sources (40 km and 60 km).
The DC resolvability of a 40-km-deep event improves considerably when the Portuguese network is supplemented by stations in Spain and Morocco. The DC resolvability can be further improved by using a few ocean bottom seismometer (OBS) stations or a dense land network.
A dense land network is able to resolve M well in spite of the large azimuthal gap, which spans similar to 200 degrees. The theoretical resolution analysis also explains the success of single-station inversions when using a broad frequency range, as exemplified by an application using waveforms of a M-w 6 earthquake offshore Iberia.