  At intermediate and high degree $l$, solar p- and f modes can be considered
as surface waves. Using variational principle, we derive an integral expression
for the group velocities of the surface waves in terms of adiabatic
eigenfunctions of normal modes, and address the benefits of using
group-velocity measurements as a supplementary diagnostic tool in solar
seismology. The principal advantage of using group velocities, when compared
with direct analysis of the oscillation frequencies, comes from their smaller
sensitivity to the uncertainties in the near-photospheric layers. We address
some numerical examples where group velocities are used to reveal
inconsistencies between the solar models and the seismic data. Further, we
implement the group-velocity measurements to the calibration of the specific
entropy, helium abundance Y and heavy-element abundance Z in the
adiabatically-stratified part of the solar convective envelope, using different
recent versions of the equation of state. The results are in close agreement
with our earlier measurements based on more sophisticated analysis of the solar
oscillation frequencies (Vorontsov et al. 2013, MNRAS 430, 1636). These results
bring further support to the downward revision of the solar heavy-element
abundances in recent spectroscopic measurements.
