2.3 Common reflection point imaging
By 1-D common reflection point (CRP) mapping, we convert the Ssds-S difference times to the locations of the Ssds reflecting points in the upper 800 km of the mantle beneath the USArray. We use the TauP software (Crotwell et al. 1999) and the PREM velocity structure to calculate Ssds reflection points and traveltimes. At a depth d, 1,716 reflection points are uniformly distributed on a 1° × 1° horizontal grid between 25°N and 50°N and between -130°E and -65°E. The horizontal grids are separated by 5 km from 10 to 1,000 km, for a total of 199 depths. For a grid point X, we select waveforms for which the Ssds reflection points are within the 1° × 1° bin around X and for which the theoretical Ssds arrival time differs more than 15 s from the theoretical arrival times of sS, ScS, and sScS, and more than 50 s from the arrival time of SS to avoid wave interference. If fewer than five waveforms are available, we deem the mean displacement of Ssds to be inaccurately determined.
Since we use shallow focus earthquakes, the source-side and the receiver-side reflections have identical traveltimes. From synthetic seismograms for PREM, we have verified that they are equally strong so we attribute half of the mean Ssds amplitude to a source-side reflection. To construct the CRP images, we estimate source-side reflections of the 337 earthquakes and receiver-side reflections for the 1,716 grid points sequentially following two steps. First, we determine the mean of the Ssds displacement for each earthquake at the theoretical arrival time of Ssds. We assume that the mean displacement source-side reflection has been amplified and that receiver-side structures do not contribute coherent signals. Second, we subtract this mean value from the Ssds displacement of each waveform, assuming that the residual displacement to be due to coherent reflections beneath the USArray. We exclude events with fewer than 20 seismograms. After mapping the Ssds signals onto the grid ray theoretically, we average the receiver-side reflection amplitudes with 1°x1° bins, which are narrower than the Fresnel zones of 10-s period Ssds reflections in the mantle transition zone, as shown by SB19. We have also implemented the approach by SB19, who estimates the source-side and receiver-side contributions to Ssds in one step using a sparse-matrix inversion solver. This approach yields smaller amplitudes of the Ssds reflections but the overall character of the CRP image, including the depths of the 410-km and 660-km discontinuities, are similar (Supplementary Figure S1).