In order to improve the signal-to-noise ratio of receiver function data, it is typical to stack receiver functions calculated from events at similar distances and back azimuths. We have adapted the velocity spectrum stacking (VSS) technique, used extensively in reflection seismology, to the receiver function method in order to stack data with different ray parameters, thereby improving further the signal-to-noise ratio. Perhaps more importantly, by producing the velocity spectrum stacks we take advantage of the differences in the shapes of the moveout curves of converted phases and reverberations to identify and separate the various phases and to infer velocity structure. By comparison of velocity spectrum stacks produced from the observed data at the IRIS/IDA broad-band station at Obninsk, Russia (OBN) with those produced from PREM synthetics we have identified Ps phases from the 400 and 670 km discontinuities. The P-to-S (Ps) converted phase from the 400 km discontinuity observed at OBN is much larger, compared with that of the 670 km discontinuity, than is predicted by PREM. This suggests a higher velocity contrast at 400 km than in PREM. By adapting a bootstrap method to assess the depth and velocity estimates determined by VSS, we find that the Ps phase from the 670 km discontinuity is best imaged with higher than PREM upper mantle P and S velocities and at a depth of 663 ± 3 km. We find no evidence of a 220 km discontinuity beneath OBN in these data.