in $\delta\tau$ with $\phi$ at inclinations $\theta$ sufficient for the ramp effect to take hold. In each case, negative travel time perturbations are substantial at small $\sin\phi$ but much reduced at ‘intermediate’ $\phi$, typically around $90^\circ$. Comparison with the flux figures suggests a strong link between both acoustic and magnetic wave energy losses and travel time lags.

For magnetic field inclinations $\theta$ sufficient that $\omega>\omega_c\cos\theta$, the atmosphere is opened up to wave penetration and therefore to both types of mode conversion. With $\phi=0^\circ$, the fast magnetically-dominated waves emerging from $a=c$ return to the surface after reflection near $\omega/k_h=a$ with a different (advanced) phase compared to that of the simply reflecting acoustic waves in quiet Sun. However, if $\phi\ne0^\circ$ (or $180^\circ$), the fast wave loses more energy near its apex to the Alfvén wave, and seeming suffers a further phase retardation that we might interpret as partially cancelling the underlying negative travel time perturbation.

Using acoustic holography to probe sunspot penumbral oscillations, @SchBraCal05aa also detected directionally dependent phase perturbations, finding that phase shift varies with the angle between the line-of-sight and the magnetic field, with equivalent phase travel time variations with viewing angle of order 30 s. These results seem similar 