  Aims: The primary objective of this study is to search for and identify wave
modes within a sunspot penumbra.
  Methods: Infrared spectropolarimetric time series data are inverted using a
model comprising two atmospheric components in each spatial pixel. Fourier
phase difference analysis is performed on the line-of-sight velocities
retrieved from both components to determine time delays between the velocity
signals. In addition, the vertical separation between the signals in the two
components is calculated from the Stokes velocity response functions.
  Results: The inversion yields two atmospheric components, one permeated by a
nearly horizontal magnetic field, the other with a less-inclined magnetic
field. Time delays between the oscillations in the two components in the
frequency range 2.5-4.5 mHz are combined with speeds of atmospheric wave modes
to determine wave travel distances. These are compared to expected path lengths
obtained from response functions of the observed spectral lines in the
different atmospheric components. Fast-mode (i.e., modified p-mode) waves
exhibit the best agreement with the observations when propagating toward the
sunspot at an angle ~50 degrees to the vertical.
