Authors: Hamilton, J. (Georgia State University); Sadykov, V.M. (Georgia State University); Kitiashvili, I.N. (NASA Ames Research Center); Wray, A.A. (NASA Ames Research Center)

The ability to diagnose the physical characteristics of the solar atmosphere and dynamic processes therein, including waves, requires interpretation of the observations in broadband emission and spectral lines/Stokes profiles. One possibility to interpret such observations is to combine the synthesis of the emission and spectrum with the 3D simulations of the solar atmosphere. In this work, we consider the realistic 3D Radiative hydrodynamic simulations of a 6.4 Mm x 6.4 Mm region of the quiet Sun by StellarBox code. Using RH1.5D radiative transfer code, we synthesize five spectral lines formed in the lower solar atmosphere, Fe I 6713 Å, 6301 Å, and 6302 Å (formed at 0-300 km) and Na I Doublet, 5890 Å and 5896 Å (500-1000 km), with high-resolution for about 30 minutes of the solar time. We compute Doppler shifts of the spectral lines and explore their cross-spectrum and oscillation phase differences as a function of wave frequency and spatial resolution. Initial analysis shows the presence of upward-propagating acoustic waves in the frequency range of 5 mHz to 9 mHz. The signatures of waves in the oscillation phase-frequency plot are most prominent at the spatial scales of ~1 Mm that roughly correspond to the solar granulation characteristic scales. The signatures weaken for the resolutions that are both higher and lower than ~1 Mm, indicating a potential of diagnosing the characteristic spatial scales of the waves from the cross-spectrum and phase-frequency relations.