altitudes, these figures would display greater (anti-) symmetry [ (see Section \[sec:BVP\])]{}. The parallel acoustic flux is very similar to the vertical fluxes displayed in the top right panel of Figure \[fig:Fz\], with an additional $\cos\theta$ factor.

Travel Time Perturbations {#TD}
-------------------------

‘Travel time’ perturbations $\delta\tau$ (relative to quiet Sun) are displayed in Figure \[fig:tau\], on a $10^\circ\times10^\circ$ resolution grid. They show clear manifestations of the acoustic cutoff at $\theta=30^\circ$– $40^\circ$ for 5 mHz, and $\theta=50^\circ$– $60^\circ$ at 3 mH where greater inclination is needed to overcome it. Below these inclinations, $\delta\tau$ is small, and typically negative, suggesting a weak speed-up due to the magnetic field. At higher inclinations, substantial travel time perturbations are seen at all orientations $\phi$, most cleanly at 5 mHz.

With only about $3{\leavevmode\kern.1em\raise.5ex\hbox{\the\scriptfont0 1}\kern-.1em/\kern-.15em\lower.25ex\hbox{\the\scriptfont0 2}}$ skips fitting into the computational box for $k_h=0.5$ $\rm Mm^{-1}$ (see Table \[tab:skip\]), the corresponding $\delta\tau$ measurements become very noisy at 3 mHz (not shown). Even the $k_h=0.75$ results appear unreliable at this lower frequency. The large positive $\delta\tau$ at around $\theta=50^\circ$ in the $B_0=500$ G, $\nu=3$ mHz, $k_h=0.75$ $\rm Mm^{-1}$ case should therefore be regarded with some suspicion; it requires confirmation in wider boxes.

There are also clear variations 