ALBERT

Description: An approach to detect afterslips in the source process of giant earthquakes is presented in the normal-mode frequency band (0.3–2.0mHz). The method is designed to avoid a potential systematic bias problem in the determination of earthquake moment by a typical normal-mode approach. The source of bias is the uncertainties in Q (modal attenuation parameter) which varies by up to about ±10per cent among published studies. A choice of Q values within this range affects amplitudes in synthetic seismograms significantly if a long time-series of about 5–7 d is used for analysis. We present an alternative time-domain approach that can reduce this problem by focusing on a shorter time span with a length of about 1 d. Application of this technique to four recent giant earthquakes is presented: (1) the Tohoku, Japan, earthquake of 2011 March 11, (2) the 2010 Maule, Chile earthquake, (3) the 2004 Sumatra-Andaman earthquake and (4) the Solomon earthquake of 2007 April 1. The Global Centroid Moment Tensor (GCMT) solution for the Tohoku earthquake explains the normal-mode frequency band quite well. The analysis for the 2010 Chile earthquake indicates that the moment is about 7–10per cent higher than the moment determined by its GCMT solution but further analysis shows that there is little evidence of afterslip; the deviation in moment can be explained by an increase of the dip angle from 18° in the GCMT solution to 19°. This may be a simple trade-off problem between the moment and dip angle but it may also be due to a deeper centroid in the normal-mode frequency band data, as a deeper source could have steeper dip angle due to changes in geometry of the Benioff zone. For the 2004 Sumatra-Andaman earthquake, the five point-source solution by Tsai et al. explains most of the signals but a sixth point-source with long duration improves the fit to the normal-mode frequency band data. The 2007 Solomon earthquake shows that the high-frequency part of our analysis (above 1mHz) is compatible with the GCMT solution but the low-frequency part requires afterslip to explain the increasing amplitude ratios towards lower frequency. The required slip has the moment about 19per cent of the GCMT solution and the rise time of 260s. The total moment of these earthquakes are 5.31 × 1022 Nm (Tohoku), (1.86–1.96) × 1022 Nm (Chile), 1.33 × 1023 Nm (Sumatra) and 1.86 × 1021 Nm (Solomon). The moment magnitudes are 9.08, 8.78–8.79, 9.35 and 8.11, respectively, using Kanamori's original formula between the moment and the moment magnitude. However, the trade-off problem between the moment and dip angle can modify these estimates for moment up to about 40–50per cent and the corresponding magnitude ±0.1.