Geodetic observations of surface displacements during and following earthquakes such as the March 11, 2011 great Tohoku earthquake can be used to constrain the spatial extent of coseismic slip and postseismic afterslip, and characterize the spectrum of earthquake cycle behaviors. Slip models are often regularized by assuming that slip on the fault varies smoothly in space, which may result in the artificial smearing of fault slip beyond physical boundaries. Alternatively, it may be desirable to estimate a slip distribution that is spatially compact and varies sharply. Here we show that sparsity promoting state vector regularization methods can be used to recover slip distributions with sharp boundaries, representing an alternative end-member result to very smooth slip distributions. Using onshore GPS observations at 298 stations during and in the ∼2 weeks following the Tohoku earthquake, we estimate a band of coseismic slip between 30 and 50 km depth extending 500 km along strike with a maximum slip of 64 m, corresponding to a minimum magnitude estimate of MW = 8.8. Our estimate of afterslip is located almost exclusively down-dip of the coseismic rupture, with a transition between 40 and 50 km depth and an equivalent moment magnitude MW = 8.2. This depth may be interpreted as coincident with the transition from velocity strengthening to velocity weakening frictional behavior, consistent with the upper limit of cold subduction estimates of the thermal structure of the Japan trench.