4.2 The resolution of undulations on the 410-km and 660-km discontinuities
Figure 10 shows the depths of the 410-km and the 660-km discontinuities and the thickness of the MTZ resolved for models T2, T5, and T8. The checkerboard pattern of the undulations on the 410-km and 660-km discontinuities are resolved for T5 and T8 but the amplitude of the undulations is underestimated. The resolved thickness of the MTZ varies, on average, 12 km and 6 km less than in the original T8 and T5 models. The resolution of the undulations in T2 is poor despite using a larger set of waveforms for 48 earthquakes. From experiments, we have found that the resolution does not improve if we densify the grid of stations to a 1-degree spacing. Therefore, fluctuations of the depth of the 410-km or 660-km discontinuities with a wavelength of about 200 km are intrinsically unresolvable from long-period Ssds waveforms because the Fresnel zone of Ss410s and Ss660s in the upper mantle at the dominant frequency of about 0.05 Hz is about 500 km, much wider than the undulations of the 410-km and 660-km discontinuities in T2.