## Introduction

We derive the rupture process of the 2011 off the Pacific coast of Tohoku Earthquake (*M*9.0) at 14:46 on March 11 (JST) using the strong-motion data.

## Data

Strong motion data recorded at 36 stations (10 K-NET stations and 26 KiK-net stations) shown in Figure 1 are used in the inversion analysis. The velocity waveforms are derived by integration of the original accelerations, band-pass filtering between 0.01 and 0.125 Hz, and resampling down to 1 Hz. The data for inversion are windowed from 10 s before S-wave arrival for a duration between 225 s and 280 s, which varies depending on stations.

## Fault model and discretization of the rupture process

We assume the 510 km × 210 km rectangular fault model that has a strike of 195 degrees and a dip of 13 degrees.
The rupture starting point is set at 38.10N, 142.85E, and a depth of 24 km, referring to the hypocenter information by Hi-net and JMA.

The rupture process is spatially and temporally discretized following the multiple-time-window linear waveform inversion scheme (Olson and Apsel, 1982; Hartzell and Heaton, 1983).
For the spatial discretization, the fault plane is divided into 17 subfaults along the strike and 7 subfaults along dip directions, with a size of 30 km × 30 km each.
For the temporal discretization, the moment rate function of each subfault is represented by 25 smoothed-ramp functions (time windows) progressively delayed by 3.0 s and having a duration of 6.0 s each.
The first-time-window starting time is defined as the time prescribed by a circular rupture propagation with the constant speed of Vftw.
Thus, the rupture process and the strong-motion waveforms are linearly related via Green's functions.

The Green's functions between each subfault and each station are calculated using the discrete wavenumber method (Bouchon, 1981) and the reflection/transmission matrix method (Kennett and Kerry, 1979) assuming a 1-D layered velocity structure model.
The underground structure model is obtained for each station from the 3-D structure model (Fujiwara et al., 2009).
Logging data are also referred to for the KiK-net stations.
The rupture propagation effect inside each subfault is included in the Green's function by the convolution of the moving dislocation effect, following Sekiguchi et al. (2002).

## Waveform inversion

Moment of each time window at each subfault is derived by minimizing the difference between the observed and the synthetic waveforms using the least-squares method. To stabilize the inversion, the slip angle is allowed to vary within ±45 degrees centered at 90 degrees using the non-negative least-squares scheme (Lawson and Hanson, 1974). In addition, we impose the spatiotemporal smoothing constraint on slips (Sekiguchi et al., 2000).

## Results

Figure 2 shows the total slip distribution on the fault.
Figure 3 shows the comparison between the observed and the synthetic waveforms.
Figure 4 shows the rupture progression.
Vftw, the maximum slip, and the seismic moment are 3.2 km/s, 48 m, and 4.42×10^{22} Nm (*M*_{W} 9.0), respectively.