  Today's picture of the internal solar rotation rate profile results
essentially from helioseismic analyses of frequency splittings of resonant
acoustic waves. Here we present another, complementary estimation of the
internal solar rotation rate using the perturbation of the shape of the
acoustic waves. For this purpose, we extend a global helioseismic approach
developed previously for the investigation of the meridional flow
\cite{schad11, schad12, schad13} to work on the components of the differential
rotation. We discuss the effect of rotation on mode eigenfunctions and thereon
based observables. Based on a numerical study using a simulated rotation rate
profile we tailor an inversion approach and also consider the case of the
presence of an additional meridional flow. This inversion approach is then
applied to data from the MDI (Michelson Doppler Imager aboard the Solar
Heliospheric Observatory (SoHO)) instrument and the HMI (Helioseismic and
Magnetic Imager aboard the Solar Dynamics Observatory (SDO)) instrument. In the
end, rotation rate profiles estimated from eigenfunction perturbation and
frequency splittings are compared.
  The rotation rate profiles from the two different approaches are
qualitatively in good agreement, especially for the MDI data. Significant
differences are obtained at high latitudes $> 50^{\circ}$ and near the
subsurface. The result from HMI data shows larger discrepancies between the
different methods. We find that the two global helioseismic approaches provide
complementary methods for measuring solar rotation. Comparing the results from
different methods may help to reveal systematic influences that affect analyses
based on eigenfunction perturbations, like meridional flow measurements.
