Spatial distribution of the dominant frequencies of the vertically propagating waves for a maximum frequency of 10 mHz for (left) linear and (right) nonlinear regimes. Dashed blue lines denote β = 1 contours, white solid horizontal lines indicate the transition region and black solid lines indicate magnetic field lines. The vertical white dashed lines indicate the vertical slices for which the time-height diagrams are shown in Figs. 1 and 2.