LAUSR

We develop an approach to calculate earthquake source directivity and rupture velocity for small earthquakes, using the whole source time function rather than just an estimate of the duration. We apply themethod to an aftershock sequence within the subducting plate beneath North Island, New Zealand, and investigate its resolution. We use closely located, highly correlated empirical Green’s function (EGF) events to obtain source time functions (STFs) for this well-recorded sequence. We stack the STFs from multiple EGFs at each station, to improve the stability of the STFs. Eleven earthquakes (M 3.3–4.5) have sufficient azimuthal coverage, and both P and S STFs, to investigate directivity. The time axis of each STF in turn is stretched to find the maximum correlation between all pairs of stations. We then invert for the orientation and rupture velocity of both unilateral and bilateral line sources that best match the observations. We determine whether they are distinguishable and investigate the effects of limited frequency bandwidth. Rupture orientations are resolvable for eight earthquakes, seven of which are predominantly unilateral, and all are consistent with rupture on planes similar to the main shock fault plane. Purely unilateral rupture is rarely distinguishable from asymmetric bilateral rupture, despite a good station distribution. Synthetic testing shows that rupture velocity is the least well-resolved parameter; estimates decrease with loss of high-frequency energy, and measurements are best considered minimum values. We see no correlation between rupture velocity and stress drop, and spatial stress drop variation cannot be explained as an artifact of varying rupture velocity.