Modal power spectrum extracted of the vertical velocity component extracted at a height of z = 200 km above the photosphere, from a 12 h long simulation with the boundaries lined by sponges(plotted on a linear scale). The weak reflections from the lower boundary cause the dispersion relation to change in curvature at all points for which ν / (k_h   R_⊙) exceeds a certain threshold. The symbols are the same as those in Fig. 3; note that there are differences between the C-PML and sponge layered simulations at high frequencies. This is because these high-frequency waves are sensitive to the upper boundary.