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.
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