Comparison of ray-approximation travel-time shifts derived from different arc-size configurations. Top panel: schematic plot of the arc-to-arc geometry whereby the end points of multiple ray paths, Γi(λ, Δ), are arranged. The arc-to-arc geometry consists of two opposing arcs aligned in the north-south direction, separated by an angular distance Δ, and centered at the latitude λ. The central angle subtended by an arc is denoted by θc. The number of points on the arc, N, depends on the arc length. Middle panel: single-ray and arc-averaged travel-time shifts cut at a latitude of 30° north for different configurations in which the arc subtends central angles of 0° (i.e., the single-ray case), 30°, 60°, and 90°, as a function of distance. The flow model used is MC1. Bottom panel: differences between the single-ray travel-time shift and the other three arc-averaged travel-time shifts.
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