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 \sim 7 –15 r _ { g } having the constrained optical depth \sim 2 –10 .
The coronal temperature is \sim 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 .