1. The inclusion of possible SPdKS-SKPdS phases, or any other phases, has been automatically taken into account in the calculation of the sensitivity kernels for the seismic signals used in the paper. The structure sensitivities are calculated for measurement windows --- there is no assumption made whatsoever on what phases are in the measurement windows. By analyzing the structural sensitivity, the anomalous time shift can only be created by having a structure anomaly in the Earth’s outer core (Fig 5, the paper). This time shift can not be created by a change in earthquake position (Fig S4, the paper). This is probably counter intuitive in ray theory, but seismic waves at this period have large Fresnel zones, and seismic waves with their “rays” completely off an anomaly will still see the anomaly the same way (Fig S4d, the paper).