Post-critical SsPmp and its applications to virtual deep seismic sounding (VDSS)—3: back-projection imaging of the crust–mantle boundary in a heterogeneous lithosphere, theory and application

Virtual deep seismic sounding (VDSS) uses the arrival time of post-critical SsPmp relative to the direct S wave to infer Moho depth at the Pmp reflection point. Due to the large offset between the virtual source and the receiver, SsPmp is more sensitive to lateral variations of structures than near-vertical phases such as Ps, which is used to construct conventional P receiver functions. However, the way post-critical SsPmp is affected by lateral variations in lithospheric structure is not well understood, and previous studies largely assumed a 1-D structure when analysing SsPmp waveforms. Here we present synthetic tests with various 2-D models to show that lateral variations in lithospheric structures, from the lithosphere-asthenosphere boundary (LAB) to sedimentary basins, profoundly affect traveltime, phase and amplitude of post-critical SsPmp, and that a 1-D approximation is usually inappropriate when analysing 2-D data. Despite these strong effects we show, with synthetic examples and the ChinArray data from the Ordos Block in northern China, that a simple ray-theory-based back-projection method can retrieve the geometry of the crust-mantle boundary (CMB) given array observations in cases with moderate lateral variations in the CMB and/or the LAB. The success of our back-projection method indicates that ray-theory approximations are sufficient in modelling SsPmp traveltimes in the presence of moderate lateral heterogeneity. In contrast, we show that the ray theory is generally insufficient in modelling SsPmp phase shifts in a strongly heterogeneous lithosphere due to non-planar downgoing P waves incident at the CMB. Nonetheless, our results demonstrate the feasibility of direct imaging of the CMB with post-critical SsPmp even in the presence of 2-D variations of lithospheric structure.