Steep reflections from the earth's core reveal small-scale heterogeneity in the upper mantle

We investigate arrivals of seismic phases reflected from the core-mantle boundary (PcP waves) and those reflected from the inner-core boundary (PKiKP waves) at subcritical angles, with the goal of measuring their amplitude ratios. This adds invaluable data points required to study the density jump across the inner-core boundary (ICB). One nuclear explosion and one earthquake, both with favourable focal mechanisms are identified as sources that produce an excellent and abundant record of arrivals of both PcP and PKiKP waves at multiple stations. There is only a limited number of detections of both types of waves on the same seismogram, while more frequently, either one or another of the two phases is detected. Thus, for those cases where at least one phase is above a detectable level, we observe a highly significant negative correlation (anti-correlation) of phase appearances on seismograms, where PcP and PKiKP phase-detections are treated as dichotomous, categorical random variables that can take values detected or undetected. The fact that similar anti-correlation in detection is observed for both explosive and tectonic sources makes less likely the possibility that source effects or a specific near source structure is responsible for this phenomenon. Although laterally varying structure near the core-mantle boundary (CMB) can account for the magnitude of observed fluctuations in the amplitude ratio of PKiKP to PcP, the Fresnel volumes surrounding their ray paths are well separated at the CMB at the frequencies of interest. This separation excludes the possibility that complex structure at or near the CMB is the dominant effect responsible for the observed anti-correlation. We demonstrate that the interaction of the wavefield with near-receiver heterogeneities is an important additional source of amplitude fluctuations across arrays of stations, and the likely cause of the anti-correlation between PKiKP and PcP detections and their spatial coherences at regional arrays. The combined effects of heterogeneities near the surface and the CMB have a profound impact on the estimates of the PKiKP/PcP amplitude ratios and the subsequent estimates of the density jump at the ICB.