  X-ray reverberation is a powerful technique which maps out the structure of
the inner regions of accretion disks around black holes using the echoes of the
coronal emission reflected by the disk. While the theory of X-ray reverberation
has been developed almost exclusively for standard thin disks, recently
reverberation lags have been observed from likely super-Eddington accretion
sources such as the jetted tidal disruption event Swift J1644+57. In this
paper, we extend X-ray reverberation studies into the super-Eddington accretion
regime, focusing on investigating the lags in the Fe K{\alpha} line region. We
find that the coronal photons are mostly reflected by the fast and optically
thick winds launched from super-Eddington accretion flow, and this funnel-like
reflection geometry produces lag-frequency and lag-energy spectra with unique
characteristics. The lag-frequency spectra exhibits a step-function like
decline near the first zero-crossing point. As a result, the shape of the
lag-energy spectra remains almost independent of the choice of frequency bands
and linearly scales with the black hole mass for a large range of parameter
spaces. Not only can these morphological differences be used to distinguish
super-Eddington accretion systems from sub-Eddington systems, they are also key
for constraining the reflection geometry and extracting parameters from the
observed lags. When explaining the X-ray reverberation lags of Swift J1644+57,
we find that the super-Eddington disk geometry is preferred over the thin disk,
for which we obtain a black hole mass of 5-6 million solar masses and a coronal
height around 10 gravitational radii by fitting the lag spectra to our
modeling.
