Radiative transfer effects on Doppler measurements as sources of surface effects in sunspot seismology

We show that the use of Doppler shifts of Zeeman-sensitive spectral lines to observe waves in sunspots is subject to measurement-specific phase shifts arising from (1) the altered height range of spectral line formation and the propagating character of p-mode waves in penumbrae and (2) Zeeman broadening and splitting. We also show that these phase shifts depend on wave frequencies, strengths and line-of-sight inclinations of magnetic fields, and the polarization state used for Doppler measurements. We discuss how these phase shifts could contribute to local helioseismic measurements of surface effects in sunspot seismology.