  Differences between observed and theoretical eigenfrequencies of the Sun have
characteristics which identify them as arising predominantly from properties of
the oscillations in the vicinity of the solar surface: in the super-adiabatic,
convective boundary layer and above. These frequency differences may therefore
provide useful information about the structure of these regions, precisely
where the theory of solar structure is most uncertain.
  In the present work we use numerical simulations of the outer part of the Sun
to quantify the influence of turbulent convection on solar oscillation
frequencies. Separating the influence into effects on the mean model and
effects on the physics of the modes, we find that the main model effects are
due to the turbulent pressure that provides additional support against gravity,
and thermal differences between average 3-D models and 1-D models. Surfaces of
constant pressure in the visible photosphere are elevated by about 150 km,
relative to a standard envelope model.
  As a result, the turning points of high-frequency modes are raised, while
those of the low-frequency modes remain essentially unaffected. The
corresponding gradual lowering of the mode frequencies accounts for most of the
frequency difference between observations and standard solar models. Additional
effects are expected to come primarily from changes in the physics of the
modes, in particular from the modulation of the turbulent pressure by the
oscillations.
