The 2011 Tohoku earthquake (M-w = 59.1) highlighted previously unobserved features for megathrust events, such as the large slip in a relatively limited area and the shallow rupture propagation. We use a Finite Element Model (FEM), taking into account the 3D geometrical and structural complexities up to the trench zone, and perform a joint inversion of tsunami and geodetic data to retrieve the earthquake slip distribution. We obtain a close spatial correlation between the main deep slip patch and the local seismic velocity anomalies, and large shallow slip extending also to the North coherently with a seismically observed low-frequency radiation. These observations suggest that the friction controlled the rupture, initially confining the deeper rupture and then driving its propagation up to the trench, where it spreads laterally. These findings are relevant to earthquake and tsunami hazard assessment because they may help to detect regions likely prone to rupture along the megathrust, and to constrain the probability of high slip near the trench. Our estimate of similar to 40 m slip value around the JFAST (Japan Trench Fast Drilling Project) drilling zone contributes to constrain the dynamic shear stress and friction coefficient of the fault obtained by temperature measurements to similar to 0.68 MPa and similar to 0.10, respectively.