  We apply time-distance helioseismology, local correlation tracking and
Fourier spatial-temporal filtering methods to realistic supergranule scale
simulations of solar convection and compare the results with high-resolution
observations from the SOHO Michelson Doppler Imager (MDI). Our objective is to
investigate the surface and sub-surface convective structures and test
helioseismic measurements. The size and grid of the computational domain are
sufficient to resolve various convective scales from granulation to
supergranulation. The spatial velocity spectrum is approximately a power law
for scales larger than granules, with a continuous decrease in velocity
amplitude with increasing size. Aside from granulation no special scales exist,
although a small enhancement in power at supergranulation scales can be seen.
We calculate the time-distance diagram for f- and p-modes and show that it is
consistent with the SOHO/MDI observations. From the simulation data we
calculate travel time maps for surface gravity waves (f-mode). We also apply
correlation tracking to the simulated vertical velocity in the photosphere to
calculate the corresponding horizontal flows. We compare both of these to the
actual large-scale (filtered) simulation velocities. All three methods reveal
similar large scale convective patterns and provide an initial test of
time-distance methods.
