On 11 March 2011, the Tohoku‐oki earthquake in eastern Japan and the devastating tsunami that followed it caused severe damage and numerous deaths. To clarify the rupture process of the earthquake, we inverted teleseismic P‐wave data applying a novel formulation that takes into account the uncertainty of Green's function, which has been a major error source in waveform inversion. The estimated seismic moment is 5.7 × 1022 Nm (Mw = 9.1), associated with a fault rupture 440 km long and 180 km wide along the plate interface. The source process is characterized by asymmetric bilateral rupture propagation, but we also found continuous slips up‐dip from the hypocenter, which led to a large maximum slip (50 m), long slip duration (90 s), and a large stress drop (20 MPa). The long slip duration, large stress drop, extensional (normal faulting) aftershocks in a previously compressional stress regime, and low‐angle normal slips at approximately the depth of the plate interface suggest that the earthquake released roughly all of the accumulated elastic strain on the plate interface owing to exceptional weakening of the fault. The stress accumulated on the plate interface was about 20 MPa near the trench and 0–10 MPa in the down‐dip source region.

S U M M A R YIn principle, we can never know the true Green's function, which is a major error source in seismic waveform inversion. So far, many studies have devoted their efforts to obtain a Green's function as precise as possible. In this study, we propose a new strategy to cope with this problem. That is to say, we introduce uncertainty of Green's function into waveform inversion analyses. Due to the propagation law of errors, the uncertainty of Green's function results in a data covariance matrix with significant off-diagonal components, which naturally reduce the weight of observed data in later phases. Because the data covariance matrix depends on the model parameters that express slip distribution, the inverse problem to be solved becomes nonlinear. Applying the developed inverse method to the teleseismic P-wave data of the 2006 Java, Indonesia, tsunami earthquake, we obtained a reasonable slip-rate distribution and moment-rate function without the non-negative slip constraint. The solution was independent of the initial values of the model parameters. If we neglect the modelling errors due to Green's function as in the conventional formulation, the total slip distribution is much rougher with significant opposite slip components, whereas the moment-rate function is much smoother. If we use a stronger smoothing constraint, more plausible slip distribution can be obtained, but then the moment-rate function becomes even smoother. By comparing the observed waveforms with the synthetic waveforms, we found that high-frequency components were well reproduced only by the new formulation. The modelling errors are essentially important in waveform inversion analyses, although they have been commonly neglected.

We simultaneously estimate 2.5 years of afterslip and viscoelastic relaxation, as well as coseismic slip, for the 2011 Tohoku-oki earthquake. Displacements at inland GPS and seafloor GPS/Acoustic stations are inverted using viscoelastic Green's functions for a model with an upper elastic layer and lower viscoelastic substrate. The result shows that afterslip is isolated from the rupture area and possibly asperities of historical earthquakes and has almost decayed by 10 September 2013, 2.5 years after the main shock. The inversion result also suggests that observed landward postseismic displacements at the seafloor GPS/Acoustic stations are caused by the viscoelastic relaxation, whereas trenchward displacements at inland stations are mainly an elastic response to afterslip.

S U M M A R YWe have developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. A common strategy for obtaining slip distribution in previous studies is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. The inverse problem is non-linear for cases with unknown fault geometries, but the non-linearity of the problems is actually weak, when we can assume the fault surface to be a flat plane. In particular, when a clear trace of coseismic faults is observed on the Earth's surface, only the dip angle is an unknown parameter to determine the fault geometry. Then, we regarded the dip angle as an hyperparameter that prescribed the structure of parametric models, and obtained the best estimate of the dip angle using Akaike's Bayesian Information Criterion (ABIC). With the best estimate of the dip angle, we can obtain the slip distribution on the fault based on the maximum-likelihood principle. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much lower dip angle than the previous analyses.