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We developed a 3-D, viscoelastic finite element model of the M9 2011 Tohoku-oki, Japan earthquake capable of predicting postseismic displacements due to viscoelastic relaxation and afterslip. We consider seismically inferred slab geometries associated with the Pacific and Philippine Sea Plate and a wide range of candidate viscoelastic rheologies. For each case, we invert for afterslip based on residual surface displacements (observed GPS minus that predicted due to viscoelastic relaxation) to develop combined viscoelastic relaxation and afterslip models. We are able to find a mechanical model that fully explains all observed geodetic on-land and seafloor horizontal and vertical postseismic displacements. We find that postseismic displacements are in about equal parts due to viscoelastic relaxation and afterslip, but their patterns are spatially distinct. Accurately predicting both horizontal and vertical on-land postseismic displacements requires a mantle wedge viscosity structure that is depth dependent, reflecting the manner in which temperature, pressure, and water content influence viscosity. No lateral heterogeneities within the mantle wedge viscosity structure beneath northern Honshu are required. Westward-directed postseismic seafloor displacements may be due flow via low-temperature, plastic creep within the lower half of a Pacific lithosphere weakened by plate bending. The distribution of afterslip is controlled by the location of coseismic slip from the Tohoku-oki and other regional historic earthquakes. The paradigm by which afterslip is thought of as the dominant postseismic mechanism immediately following earthquakes, with viscoelastic relaxation to follow in later years, is shown to no longer be valid. (C) 2016 Elsevier B.V. All rights reserved.