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Description: Virtual Deep Seismic Sounding (VDSS) has recently emerged as a novel method to image the Moho and potentially other lithospheric boundaries. The behavior of SsPmp, the post-critical reflection phase at the Moho that is utilized in VDSS, is rich with complexities not yet widely utilized. Here, motivated by observations from the Ordos Plateau in North China, we use synthetic seismograms computed with a broad range of 1D models to evaluate how different parts of the lithosphere along the ray path of SsPmp affect its phase, amplitude, and arrival time. Our findings include: (1) When the crust-mantle boundary is a sharp discontinuity, the SsPmp phase shift relative to the direct S wave is controlled by lower-crustal Vp, upper-mantle Vp and ray parameter. This property indicates the possibility of using SsPmp to constrain Vp in the lower crust and uppermost mantle. (2) When the crust-mantle boundary is a velocity-gradient zone, SsPmp arrival times vary as different functions of ray parameter from cases with a sharp crust-mantle boundary, because different rays turn at different depths. This feature allows measurement of the vertical velocity gradient in the crust-mantle transition zone with SsPmp. (3) When the virtual source (location of S-to-P conversion at the free surface) is in a sedimentary basin, SsPmp amplitude can be significantly reduced due to low S-to-P reflected energy at the virtual source. This may cause the absence of SsPmp despite appropriate source-receiver geometry. In addition to 1D models, we further conduct 2D waveform modeling and find that the SsPmp arrival time relative to direct S is not only controlled by crustal thickness at the reflection point, but also by lateral variation of Vs beneath the virtual source and receiver. Therefore, in areas with significant lateral heterogeneity in the lithosphere the accuracy of crustal-thickness measurements from SsPmp arrival times depends on our knowledge of the variability of lithospheric structure across a broad region.