Constraint on the focal mechanism of the 2011 Tohoku earthquake from the radial modes

Different from other normal modes of the Earth's free oscillation that depend on all the six components (M_rr, M_tt, M_pp, M_rt, M_rp, and M_tp) of the centroid moment tensor, the amplitudes of the radial modes depend on the M_rr component (e.g., scalar moment (M₀), dip (δ), and slip (λ)) and hypocenter depth of the focal mechanism, and hence can be easily used to constrain these parameters of the focal mechanism. In this study, we use the superconducting gravimeter (SG) records after the 2011 Tohoku earthquake to analyze the radial modes ₀S₀ and ₁S₀. Based on the solutions of the focal mechanism provided by the GCMT and USGS, we can obtain the theoretical amplitudes of these two radial modes. Comparing the theoretical amplitudes with the observation amplitudes, it is found that there are obvious differences between the former and the latter, which means that the GCMT and USGS focal mechanisms cannot well represent the real focal mechanism of the 2011 event. Taking the GCMT solution as a reference and changing the depth and the three parameters of the M_rr moment, the scalar moment (M₀) and the dip (δ) have significant influences, but the effects of the slip (λ) and the depth are minor. After comparisons, we provide a new constraint (M₀ = 5.8 ± 0.09 × 10²² N·m, δ = 10.1 ± 0.08°, λ = 88°, and depth = 20 km) for the focal mechanism of the 2011 event. In addition, we further determine the center frequency (1.631567 ± 2.6e^-6 mHz) and quality factor (2046.4± 50.1) of the ₁S₀ mode.