Figure 10 . Depth maps of the 410-km, 660-km discontinuities, and MTZ thickness using the CRP imaging method for 8° 8° (a, b, c) , 5° 5° (d, e, f), and 2° 2° (g, h, l) input topography models.
Figure 11 explores how undulations on the 410-km discontinuity would be resolved if they are embedded in 3-D velocity heterogeneity. We analyze waveform simulations for model T5-410-S40, described above. Figure 11 shows the resolved depth variation of the 410-km and the 660-km discontinuities and the MTZ thickness before (in a, c, and e) and after (in b, d, and f) ray-theoretical traveltime corrections have been applied to remove the effects of shear-velocity heterogeneity on the traveltimes. Figure 11a and 11b show that without traveltime corrections for 3-D heterogeneity, the resolved harmonic undulations of the 410 are overprinted by an east-to-west deepening. The ray-theoretical traveltime corrections remove the regional trend but the traveltime corrections do not accurately remove the effects of shear-velocity heterogeneity because the depth variations of the 410-km discontinuity are not perfectly resolved (compare Figures 11b and 10d). The 660-km discontinuity. a horizontal boundary in T5-410-S40, is resolved with the same east-to-west deepening without traveltime correction. After traveltime corrections, the 660-km discontinuity does not have a distinct harmonic or tectonic structure but the topography indicates that the corrections are imperfect or that the effects of the 410-km discontinuity on the traveltimes may be projected as spurious 660-km discontinuity structures. As shown also in Figure 9, the ray-theoretical corrections are too strong, but smaller than a factor of two (Figure 9). The map of MTZ thickness, with a distorted checkerboard pattern, remains largely unchanged before and after the traveltime correction, though the checkerboard depth ranges become larger. The synthetic test of the joint effect of 3D mantle structure and undulations on the 410-km discontinuity suggests that the MTZ thickness can be determined more robustly than the absolute depths of 410-km and 660-km discontinuities using the CRP imaging approach.