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Localization of underwater acoustic (UWA) sources using observed signals is a popular research topic that has many potential applications, both military and civilian (e.g., navigation of underwater vehicles, mine hunting, marine mammal studies). This work adopts an inverse problem framework where the temporal and spatial structure of multipath observed at an array of sensors deployed in an ocean waveguide is exploited to determine the source position. The proposed method aims at deriving useful spatial information as side information from high-frequency signals used for underwater acoustic communication. The approach involves several steps: (i) estimating channel responses and segmenting wavefronts to recover the temporal and spatial structure of multipath arrivals at the receiver array; (ii) computing a coarse source position estimate with no a priori knowledge of its location and only crude environmental information; (iii) refining the source location using model-based tomographic methods that match observed vs. predicted wavefront arrival patterns across the array through ray tracing. The Coarse Source Localization (CSL) scheme uses an algorithm for free-space localization based on time differences of arrival, and several modifications are discussed to adapt it to non-homogeneous underwater waveguides. The ensuing Model-Based Source Localization (MBSL) scheme uses an iterative linearized least-squares algorithm and benefits from the good accuracy of CSL to attain very fast convergence and avoid local extrema of its multimodal cost function. The algorithms are tested in simulation and using experimental data (CALCOM'10) for high-frequency transmissions at ranges from 200 m to 1 km.