Moment Tensor Resolvability: Application to Southwest Iberia

We present a method to assess the uncertainty of earthquake focal mechanisms based on the standard theory of linear inverse problems. We start by computing the uncertainty of the moment tensor, M. We then map the uncertainty of M into uncertainties of 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 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 when data (waveform) are available, as well as when no waveforms are available. The latter is particularly useful for network design. One of the most interesting applications that we show are maps of DC resolvability, which are computed without waveforms. Examples are shown for earthquakes in Southwest Europe. We find that the resolvability depends critically on source depth. Shallow DC sources (10~km) are theoretically better resolved than deeper sources (40 and 60~km). The DC resolvability of the 40-km deep event improves considerably when the Portuguese network is supplemented by stations in Spain and Morocco. Adding a few OBS stations would improve the resolvability. However, a similar improvement in resolvability can be achieved with a densification of land stations. A dense land network is able to resolve M well in spite of the large azimuthal gap, which spans ∼200^o.