Reference sunspot model and perturbations to it. The magnetic field lines of the reference model are shown by the black curves (Sect. 2.2). The dashed black curves are the magnetic field lines of the alternative magnetic field model (Sect. 2.4). Two Wilson depressions modified by ± 50 km have been considered (red curves, Sect. 2.3). The ellipses along the axis of the sunspot indicate the locations of the various sound-speed perturbations (Sect. 2.5). The size of the ellipses corresponds to the full width at half maximum of the Gaussian perturbations. The uppermost sound-speed perturbation is shown in light blue to be easily distinguished from the perturbation half a megameter below. The right panel shows mode kinetic energy density, ρ ∥ v ∥ ², for the f mode at kR_⊙ = 450 (black), for p₁ at kR_⊙ = 420 (blue), and for p₂ at kR_⊙ = 390 (red), where ρ is density and v is the velocity eigenfunction for quiet-Sun model CSM_A. Mode kinetic energy density is a useful indicator of the vertical sensitivity of the modes.