Sketch for a possible scenario where the δτsn for large distances have non-zero values at the equator in the absence of a deep cross-equator flow. While the target location (cross symbol) is at the equator, the points (filled circles) that are connected by the acoustic ray paths (red curves) are located around the activity belts for large travel distances. The ellipses with arrow heads depict local flows around active regions. If these local flows are not the same in both hemispheres, they will contribute to the δτsn at these large travel distances. However, no contribution is expected at short travel distances (say < 20°) for which the end points do not reach the activity belts.
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