The traveltimes of underside shear wave reflections (i.e. SS precursors) are widely used data for mapping the topography of mantle discontinuities in the upper mantle. Here, we examine the accuracy of ray theory in estimating the contribution of shear velocity heterogeneity in the mantle to SS–S400S, SS–S670S and S400S–S670S traveltimes. We analyse stacks of spectral-element method waveforms computed for 34 shallow earthquakes and 16 020 globally distributed virtual seismometers. The waveforms are computed for three versions of shear velocity model S20RTS with variable strengths of the volumetric shear velocity perturbations within the layered structure of the Preliminary Reference Earth Model. We find that ray-theoretical corrections account for only 50 per cent of the traveltime variation due to large-scale velocity heterogeneity. For current tomographic models, as represented by S20RTS, this translates into unpredictable long- and short-wavelength errors in maps of mantle discontinuity depths of about 5 km. This amounts to roughly 10 per cent of published variations in mantle discontinuity depths. However, relative errors will be significantly larger if ray-theoretical traveltime corrections are based on (forthcoming) models of shear velocity with much stronger heterogeneity at the smallest scales.