  Solar p-mode oscillations exhibit a systematic offset towards higher
frequencies due to shortcomings in the 1D stellar structure models, especially,
the lack of turbulent pressure in the superadiabatic layers just below the
optical surface, arising from the convective velocity field. We study the
influence of the turbulent expansion, chemical composition, and magnetic fields
on the stratification in the upper layers of the solar models in comparison
with solar observations. Furthermore, we test alternative <3D> averages for
improved results on the oscillation frequencies. We appended temporally and
spatially averaged <3D> stratifications to 1D models to compute adiabatic
oscillation frequencies that we then tested against observations. We also
developed depth-dependent corrections for the solar 1D model, for which we
expanded the geometrical depth to match the pressure stratification of the
solar <3D> model, and we reduced the density that is caused by the turbulent
pressure. We obtain the same results with our <3D> models as have been reported
previously. Our depth-dependent corrected 1D models match the observations to
almost a similar extent as the <3D> model. We find that correcting for the
expansion of the geometrical depth and the reducing of the density are both
equally necessary. Interestingly, the influence of the adiabatic exponent Gam1
is less pronounced than anticipated. The turbulent elevation directly from the
<3D> model does not match the observations properly. Considering different
reference depth scales for the <3D> averaging leads to very similar
frequencies. Solar models with high metal abundances in their initial chemical
composition match the low-frequency part much better. We find a linear relation
between the p-mode frequency shift and the vertical magnetic field strength
with dvnl = 26.21Bz microHz/kG, which is able to render the solar activity
cycles correctly.
