Abstract: Audio-Magnetotellurics (AMT) is an electromagnetic geophysical method based on passive measurements of the induced electric currents in the ground by atmospheric sources which mostly originate from global lightning activity. Each lightning strike generates different waves with distinct time-frequency properties. Two major difficulties arise in AMT acquisition and processing. The first one lies in the relatively low signal-to-noise ratio of natural signals compared to anthropogenic signals. The second one is the so-called AMT dead-band, a specific frequency band (generally from 1 kHz to 5 kHz) where the level of natural signals energy remains low. Using the continuous wavelet transform, we identify electromagnetic (EM) waves in the time-frequency plane and we then invert the response function. Two criteria are used for detection: high signal-to-noise ratio and specific shape of local maxima in the time-frequency plane. The determination of AMT response functions are based on a hierarchical bootstrap scheme. We illustrate this methodology on AMT data acquired near Chambon-La-Forêt magnetic observatory. By using the new procedure on this dataset, we are able to, on the one hand, drastically reduce the AMT dead-band width, and on the other hand, greatly reduce the confidence interval of the AMT response functions.