Observed frequency variations of solar p-mode travel times as evidence for surface effects in sunspot seismology

Using helioseismic holography, we measure acoustic (p-mode) travel-time perturbations, observed within solar active regions, as functions of frequency and phase speed. We find evidence for a frequency variation, at fixed phase speed, of the travel times that has not previously been reported. This variation is not expected from typical sound-speed models of sunspots, which result from the inversion of travel times and may indicate a significant contribution to the travel times from structures with vertical scales smaller than about 1 Mm near the solar surface.