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Small-amplitude surface gravity waves in the ocean were registered by DONET (JAMSTEC) ocean-bottom pressure gauges at epicenter distance of 800 km just after the passage of seismic waves from the disastrous 2011 Tohoku earthquake. These gravity waves were observed more than an hour before the arrival of the leading wave of the 2011 Tohoku tsunami. This fact gives us the grounds to call these waves tsunami forerunners. The amplitude and period of the tsunami forerunners amounted to 3 cm and 150 s, respectively. We assume physical mechanism of generation of the forerunners is related to horizontal movements of ocean-bottom slopes, caused by passage of low-frequency Love and Rayleigh waves. For simulation of the process of generation of tsunami forerunners we used 3D numerical model based on the linear potential theory. Dynamics of bottom movement during the passage of seismic waves was restored with the use of DONET ocean-bottom seismometers data. The results of our numerical experiments are in good agreement with the observed values. It confirmed, that horizontal movements of ocean-bottom slopes play the key role in the tsunami forerunners generation whereas the role of vertical movements is negligible. 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).