Estimating the rupture directivity and source parameters of moderate to small earthquakes using the second seismic moment

The second seismic moments can be used to estimate finite source attributes such as rupture length, width, duration, velocity, and propagation direction from the apparent characteristic durations of the apparent source time functions (ASTFs) without a predefined rupture model. The ASTFs can be obtained by deconvolution of the empirical Green's function (EGF). The use of second seismic moments to resolve finite-source models has been shown to be effective in small to moderate earthquakes in California (McGuire et al., 2001; McGuire, 2004; Meng et al., 2020) and appears to be a promising tool for improving seismic hazard assessment, including for future use in real time. Since information on source parameters and rupture propagation is crucial for seismic hazard assessment, it is important to evaluate the sensitivity and thus the reliability of the result in the presence of uncertainties in the input variables, which can be large, especially in real time and when the coverage of the network varies. To this end, we performed a test with a synthetic seismic source and computed the ASTFs. We then applied 1000 random perturbations to the hypocentral depth, focal mechanism, number of recording stations, and observed characteristic source duration separately, and then performed the inversion to evaluate how much each data-induced uncertainty can affect the accuracy of the resulting characteristic rupture size, propagation, and rupture velocity in terms of both mean and dispersion.