Source models of great earthquakes from ultra low-frequency normal mode data

We present a new earthquake source inversion technique based on normal mode data for the simultaneous determination of the rupture duration, length and moment tensor of large earthquakes with unilateral rupture. We use ultra low-frequency (f <1 mHz) mode singlets and multiplets which are modelled using Higher Order Perturbation Theory (HOPT), taking into account the Earth's rotation, ellipticity and lateral heterogeneities. A Monte Carlo exploration of the model space is carried out, enabling the assessment of source parameter tradeoffs and uncertainties. We carry out synthetic tests to investigate errors in the source inversions due to: (i) unmodelled 3-D Earth structure; (ii) noise in the data; (iii) uncertainties in spatio-temporal earthquake location; and, (iv) neglecting the source finiteness in point source inversions. We find that unmodelled 3-D structure is the most serious source of errors for rupture duration and length determinations especially for the lowest magnitude events. The errors in moment magnitude and fault mechanism are generally small, with the rake angle showing systematically larger errors (up to 20°). We then investigate five real thrust earthquakes (Mw⩾8.5): (i) Sumatra-Andaman (26th December 2004); (ii) Nias, Sumatra (28th March 2005); (iii) Bengkulu (12th September 2007); (iv) Tohoku, Japan (11th March 2011); (v) Maule, Chile (27th February 2010); and, (vi) the 24 May 2013 Mw8.3 Okhotsk Sea, Russia, deep (607 km) event. While finite source inversions for rupture length, duration, magnitude and fault mechanism are possible for the Sumatra-Andaman and Tohoku events, for all the other events their lower magnitudes only allow stable point source inversions of mode multiplets. We obtain the first normal mode finite source model for the 2011 Tohoku earthquake, which yields a fault length of 461 km, a rupture duration of 151 s, and hence an average rupture velocity of 3.05 km/s, giving an independent confirmation of the compact nature of this event. For all the other earthquakes studied, our new source models agree well with previous studies. We do not find any unexplained systematic differences between our results and those in the literature, suggesting that for the wave frequencies considered, the moment magnitude and the fault mechanism of the earthquakes studied do not show a strong frequency dependence.