  We develop a physically motivated, spherical corona model to investigate the
frequency-dependent time lags in AGN. The model includes the effects of Compton
up-scattering between the disc UV photons and coronal electrons, and the
subsequent X-ray reverberation from the disc. The time lags are associated with
the time required for multiple scatterings to boost UV photons up to soft and
hard X-ray energies, and the light crossing time the photons take to reach the
observer. This model can reproduce not only low-frequency hard and
high-frequency soft lags, but also the clear bumps and wiggles in reverberation
profiles which should explain the wavy-residuals currently observed in some
AGN. Our model supports an anti-correlation between the optical depth and
coronal temperatures. In case of an optically thin corona, time delays due to
propagating fluctuations may be required to reproduce observed time lags. We
fit the model to the lag-frequency data of 1H0707-495, Ark 564, NGC 4051 and
IRAS 13224-3809 estimated using the minimal bias technique so that the observed
lags here are highest-possible quality. We find their corona size is ~7-15 r_g
having the constrained optical depth ~2-10. The coronal temperature is ~150-300
keV. Finally, we note that the reverberation wiggles may be signatures of
repeating scatters inside the corona that control the distribution of X-ray
sources.
