We propose a wavelet-based method to characterize acoustic impedance discontinuities from a multiscale analysis of seismic reflected waves. Our approach relies on the analysis of ridge functions which contain most of the information of the wavelet transform in a sparse support. This method falls in the framework of the wavelet response (WR) introduced by Le Gonidec et al. which analyses the impedance multiscale behaviour by propagating dilated wavelets into the medium. We further extend the WR by considering its application to broad-band seismic data. We take into account the bandpass filter effect related to the limited frequency range of the seismic source. We apply the method to a deep-water seismic experiment performed in 2008 during the ERIG3D cruise to demonstrate the potential of ridge functions as multiscale seismic attributes. In conjunction to the analysis of seismic data acquired by the deep-towed SYSIF system (200–2200 Hz), we use ground truth data to characterize the fine scale structure of superficial sediments by using the continuous wavelet transform (CWT). The availability of in situ measurements allows to validate the relationship between CWT and WR and to estimate the attenuation of seismic waves into the sediments. Once validated, the method is applied on a whole seismic profile and WR ridge functions are computed for two particular reflectors. The reflector thicknesses fall below the resolution limit of the seismic experiment making the WR seismic attributes a super-resolution method.