Estimates of the spatial and temporal variability of ocean sound speed on the New Jersey shelf were obtained using acoustic signals measured by a set of freely drifting buoys. The range- and time-dependent inversion problem is computationally intensive and a linearized perturbative algorithm was applied to obtain results in an efficient manner. The inversion algorithm uses estimates of modal travel time to determine sound speed as a function of range and depth. In order to handle the high volume of data associated with the acoustic sensing network, the modal travel time estimation process was automated using an adaptive time-frequency signal processing method known as time-warping. Time-warping is a model-based transform that converts the frequency-dependent modal arrivals to monotones in the warped domain where they can be easily filtered. The data analyzed in this paper were collected on 16 March 2011 on the New Jersey shelf when the ocean was relatively well-mixed. While the observed sound-speed variations are small, both spatial and temporal trends are observed in the results. Furthermore, the estimated sound-speed profiles show good agreement with temporally and spatially collocated measurements.