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Compressional wave travel times from a seismic tomography experiment at 9°30′N on the East Pacific Rise are analyzed by a new tomographic method to determine the three‐dimensional seismic velocity structure of the upper 2.5 km of oceanic crust within a 20×18 km² area centered on the rise axis. The data comprise the travel times and associated uncertainties of 1459 compressional waves that have propagated above the axial magma chamber. A careful analysis of source and receiver parameters, in conjunction with an automated method of picking P wave onsets and assigning uncertainties, constrains the prior uncertainty in the data to 5 to 20 ms. The new tomographic method employs graph theory to estimate ray paths and travel times through strongly heterogeneous and densely parameterized seismic velocity models. The nonlinear inverse method uses a jumping strategy to minimize a functional that …