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Broadband receiver functions developed from teleseismic P waveforms recorded on the midperiod passband of Regional Seismic Test Network station RSCP are inverted for vertical velocity structure beneath the Cumberland Plateau, Tennessee. The detailed broadband receiver functions are obtained by stacking source‐equalized horizontal components of teleseismic P waveforms. The resulting receiver functions are most sensitive to the shear velocity structure near the station. A time domain inversion routine utilizes the radial receiver function to determine this structure assuming a crustal model parameterized by many thin, flat‐lying, homogeneous layers. Lateral changes in structure are identified by examining azimuthal variations in the vertical structure. The results reveal significant rapid lateral changes in the midcrustal structure beneath the station that are interpreted in relation to the origin of the East Continent Gravity High located northeast of RSCP. The results from events arriving from the northeast show a high‐velocity midcrustal layer not present in results from the southeast azimuth. This velocity structure can be shown to support the idea that this feature is part of a Keweenawan rift system. Another interesting feature of the derived velocity models is the indication that the crust‐mantle boundary beneath the Cumberland Plateau is a thick, probably laminated transition zone between the depths of 40 and 55 km, a result consistent with interpretations of early refraction work in the area.