Observed travel-time shifts, Δτ. The left panel shows the travel-time shifts along y = 0 for modes f through p₄, which heal as the distance from the sunspot, x, increases. The right panel shows the travel-time shifts of p₄ modes as functions of y at four different values of x. Notice the spread in the transverse direction as x increases. The hatched and cross-hatched area indicate the locations of the penumbra and umbra, respectively.The data is averaged over patches of size 16 × 16 Mm² to filter out spatial scales that are dominated by noise. Error bars give the standard deviation of the mean.