Context : Solar p-mode oscillations exhibit a systematic offset towards higher frequencies due to shortcomings in the 1D stellar structure models , in particular , the lack of turbulent pressure in the superadiabatic layers just below the optical surface , arising from the convective velocity field .

Aims : 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 \left \langle \mathrm { 3 D } \right \rangle averages for improved results on the oscillation frequencies .

Methods : We appended temporally and spatially averaged \left \langle \mathrm { 3 D } \right \rangle stratifications to 1D models to compute adiabatic oscillation frequencies that we then tested against solar 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 \left \langle \mathrm { 3 D } \right \rangle model , and we reduced the density that is caused by the turbulent pressure .

Results : We obtain the same results with our \left \langle \mathrm { 3 D } \right \rangle models as have been reported previously .
Our depth-dependent corrected 1D models match the observations to almost a similar extent as the \left \langle \mathrm { 3 D } \right \rangle 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 \Gamma _ { 1 } is less pronounced than anticipated .
The turbulent elevation directly from the \left \langle \mathrm { 3 D } \right \rangle model does not match the observations properly .
Considering different reference depth scales for the \left \langle \mathrm { 3 D } \right \rangle 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 \delta v _ { nl } = 26.21 B _ { z } \left [ \mu \mathrm { Hz } / \mathrm { kG } \right ] , which is able to render the solar activity cycles correctly .

Conclusions :