To study the resolving power of teleseismic P waveforms for receiver structure, we model synthetic waveforms using a time domain waveform inversion scheme beginning with a range of initial models to estimate the range of acceptable velocity structures. To speed up to waveform inversions, we implement Randall's (1989) efficient algorithms for calculating differential seismograms and include a smoothness constraint on all the resulting velocity models utilizing the ''jumping'' inversion technique of Shaw and Orcutt (1985). We present the results of more than 235 waveform inversions for one-dimensional velocity structures that indicate that the primary sensitivity of a receiver function is to high wavenumber velocity changes, and a depth-velocity product, not simply velocity. The range of slowness in a typical receiver function study does not appear to be broad enough to remove the depth-velocity ambiguity; the inclusion of a priori information is necessary. We also present inversion results for station RESCP, located in the Cumberland Plateau, Tennessee. Our results are similar to those from a previous study by Owens et al. (1984) and demonstrate the uncertainties in the resulting velocity estimate more clearly. ¿ American Geophysical Union 1990