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Table 1

Spatially averaged travel-time shift introduced by the perturbation to the sunspot model, ⟨ ΔQSτ(RS + pert) ⟩  −  ⟨ ΔQSτ(RS) ⟩.

Sunspot perturbation Travel-time shift (s)
f p1 p2

Wilson depression:
50 km deeper +0.4 −2.2 3.8
50 km shallower −0.3 +1.9 +3.2

Alternative magnetic field −2.4 −2.8 -3.3

Sound-speed perturbations:
A = 0.1, h =  −2 Mm      0.0 −0.4 −0.8
A = 0.1, h =  −3 Mm      0.0 −0.8 −0.6
A = 0.1, h =  −4 Mm      0.0 −0.8 −0.2
A = 0.5, h =  −1.5 Mm ... −1.2 ...

Notes. Negative (positive) indicates that the waves travel faster (slower) through the perturbed model than the reference sunspot model. The systematic error introduced by the measurement procedure is ≈0.1 s. The noise level for seven days of SOHO/MDI observations for the f, p1, and p2 mode is 3.7 s, 3.5 s, and 1.6 s respectively. The travel-time shifts in bold lie above the noise level.

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