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Small-amplitude free gravity waves in the ocean were registered by DONET (Dense Oceanfloor Network System for Earthquakes and Tsunamis) ocean-bottom pressure gauges just after the passage of surface seismic waves during the 2011 Tohoku earthquake. The amplitude and period of these free gravity waves amounted to 3 cm and 150 s, respectively. These free gravity waves were observed more than an hour before the leading wave of tsunami, so they can be considered as tsunami forerunners. Based on theoretical estimates we assume that generation mechanism of these free gravity waves is related to horizontal movements of ocean-bottom slopes during the passage of low-frequency Love and Rayleigh waves. To simulate these free gravity waves generation we used 3D numerical model based on the linear potential theory. Dynamics of bottom movement during the passage of seismic waves was reconstructed with the use of DONET ocean-bottom seismometers data. The results of our numerical simulation are in good agreement with the observed values. We made two different simulations for two different types of bottom boundary conditions: (1) only vertical movements and (2) only horizontal movements of ocean bottom. The results of these simulations confirmed that horizontal movements of ocean-bottom slopes play the key role in the free gravity waves generation whereas the role of vertical movements is negligible. We made another simulation to find, whether residual (coseismic) bottom deformation generates free gravity waves with the observed amplitudes or not. The results of this simulation showed that it is necessary to take into account dynamics of bottom movement in the far-field. This work was supported by the Russian Foundation for Basic Research, projects 16-55-50018, 16-35-00232. DONET data were transfered and processed according to Implementing Agreement Between Faculty of Physics of Lomonosov Moscow State University and Japan Agency for Marine-Earth Science and Technology on Early tsunami detection methods on the base of real-time seafloor observatory network (2013). Keywords: free gravity waves, surface seismic waves, linear potential theory, 2011 Tohoku tsunami, bottom slopes