4. Resolution tests using spectral-element-method waveforms
We analyze synthetic waveforms to test the robustness of our CRP imaging approach, the resolution of 410-km and 660-km discontinuities undulations from long-period Ssds waveform data, and the accuracy of ray-theoretical corrections. The waveforms are computed using the SPECFEM3D-Globe software (e.g., Komatitsch & Tromp, 2002; Komatitsch et al. 2016) modified by us to allow for undulations of the 410-km and 660-km discontinuities. The eight test structures are PREM, S40RTS (Figure 7a), SEMUCB-WM1, TX2015, and structures T2, T5, T8 (Figure 7b), and T5-410-S40. The simulations account for Earth’s ellipticity and anelasticity using the Q structure of PREM. In each structure, the density and velocities in the uppermost mantle extend to the surface. We remove the crust from seismic models to suppress reverberations in the crust that complicate the waveforms following the S wave (Supplementary Figure S5).
The one-dimensional PREM structure with discontinuities at 220 km, 400 km, 670 km depth serves as a baseline model for determining artifacts in the CRP images unrelated to 3-D structure in the upper mantle. In our calculations, S40RTS, SEMUCB-WM1, and TX2015 represent models of the 3-D shear velocity structure in the mantle. We do not include the crustal structure, adopt PREM as the reference mantle structure for each of the three models, and assume the Voigt average shear-velocity variations in the anisotropic SEMUCB-WM1 model. The 220-km, 410-km and 660-km discontinuities are horizontal boundaries at the same depths as in the PREM model. Models T2, T5, and T8 have the same layered velocity structure as PREM but the 410-km and the 660-km discontinuities are sinusoidal boundaries with amplitudes of 15 km and wavelengths of 2°, 5°, and 8°, respectively. The undulations of the 410-km and 660-km discontinuities are oppositely directed so the thickness of the MTZ varies up to 30 km with respect to the average of 270 km. The model T5-410-S40 has the 3-D shear velocity structure of S40RTS and sinusoidal undulations of the 410-km discontinuity with a wavelength of 5°. The 660-km discontinuity is a horizontal boundary in T5-410-S40.