Observed amplitude perturbations around the sunspot NOAA 9787 with respect to the quiet Sun using SOHO/MDI observation. From left to right the results for f, p₁, p₂, p₃, and p₄ modes are shown. The black circle shows the outer boundary of the penumbra. The upper panels show the linear amplitude, δA, while the lower panels are replots of Fig. 2 of Liang et al. (2013); for better comparison, here we show δA_L13 = A_L13−1 instead of A_L13 as in Fig. 2 of Liang et al. (2013). The central points of the squares in p₁ and p₃ panels are the positions of the cross-covariance functions shown in Fig. 7. The measurement results in the near field are not shown in the plots; the near field is defined as x−x₀< 3λ, where λ is the typical wavelength for each mode, and x₀ = −43.73 Mm is the leftmost point of these plots over which ⟨ φ_n ⟩ in Eq. (18) is averaged (see Table 1 in Liang et al. 2013 for details).