  We investigate the linear correlation coefficient between the intensities at
different wavelengths in photospheric and chromospheric spectral lines. Waves
that propagate vertically through the stratified solar atmosphere affect
different wavelengths at different times. This leads to a characteristic
pattern of (non-)coherence of the intensity at various wavelengths. We derived
the correlation matrices for several photospheric and chromospheric spectral
lines from observations. For comparison with the observations, we calculate
correlation matrices for spectra from LTE modeling approaches, 1-D NLTE
simulations, and a 3-D MHD simulation run. We apply the correlation method also
to temperature maps at different optical depth layers. We find that all
photospheric spectral lines show a similar pattern: a pronounced asymmetry of
the correlation between line core and red or blue wing. The pattern cannot be
reproduced with a simulation of the granulation pattern, but with waves that
travel upwards. All chromospheric spectral lines show a more complex pattern.
In the case of Ca II H, the 1-D NLTE simulations of monochromatic waves produce
a correlation matrix that qualitatively matches to the observations. The
photospheric signature is well reproduced in the matrix derived from the 3-D
MHD simulation. The correlation matrices of observed photospheric and
chromospheric spectral lines are highly structured with characteristic and
different patterns in every spectral line. The comparison with matrices derived
from simulations and simple modeling suggests that the main driver of the
detected patterns are upwards propagating waves. Application of the correlation
method to 3-D temperature cubes seems to be a promising tool for a detailed
comparison of simulation results and observations in future studies.
