Induction vectors have been extensively calculated using data from 19 Japanese observatories for a dozen years preceding the huge 2011 Tohoku earthquake (EQ). At 6 observatories anomalous variations of induction vectors were separated in the years of 2008-2010 that can be identified as middle-term precursors. These observatories are located not at the shortest distance from the EQ epicenter, that is in agreement with the widely known phenomenon of spatial selectivity of EQ precursors. The analysis of horizontal tensors reveals a conductivity anomaly under the central part of the Boso peninsula (at 30 km from Tokyo) with a WNW-ESE strike coinciding both with the Sagami trough strike and the strike of well conducting 3 km thick sediments. A joint analysis of geoelectric and tectonic data leads to a preliminary conclusion that the Boso conductivity anomaly connects two large scale conductors: Pacific sea water and a deep magma reservoir beneath a volcanic belt. Between two so different conductors an unstable transition zone can be expected which should be sensitive to changes of stress. Applying our original processing including two steps analysis and elimination of annual and monthly periods, a short-term two-month-long precursor of bay-like form was successfully separated at the observatory of Kanozan, KNZ (over the Boso anomaly) despite its strong noise. All the results were obtained with advanced multi-windows multi-rr (remote reference) robust programs with a coherency control. Dependence of the results of induction vector calculation on geomagnetic activity was carefully studied, and this dependence is relatively strong when the magnetotelluric field and noise have approximately the same magnitude. But even in this case we could identify the precursor field.