Using the critical angle information of a reflection event, it is possible to calculate several essential physical parameters that are key to reliable geological characterization of the subsurface. However, estimation of the critical angle usually requires several steps of seismic processing. For this reason, an approach which is capable of estimating the critical angle directly from the data is of interest. Once the critical angle is estimated, it is possible to estimate further the Poisson's ratio and the seismic velocities. In this work, we propose an approach which can perform this estimation, based on spectral recomposition of seismic data. We design an inversion scheme in order to reconstruct the seismic spectrum of wavelets of a reflection event, which subsequently allows us to estimate the critical angle of near-surface reflection events without performing prior velocity analysis. After finding the critical angle, we show next how to estimate the Poisson's ratio and the compressional- and shear-wave velocities of the medium above the reflector. The approach leads to quite accurate values for Poisson's ratio even for noisy data, in case the number of layers is not large.

Using post-critical reflection data, it is possible to obtain useful information that allows more reliable geological characterization of the subsurface. However, the strong distortion caused by the phase shift in post-critical wavelets makes the use of post-critical reflections rather challenging. For this reason, an approach which is capable of estimating the phase shift of each wavelet of a reflection event in a data-driven manner is desirable. In this vein, in case the frequency spectrum of a wavelet can be correctly estimated, it is possible to estimate the instantaneous phase shift. In this work, we propose an approach which can perform such estimation based on spectral recomposition of seismic data. We design an inversion approach in order to reconstruct the seismic spectrum of the wavelets of a reflection event, which subsequently allows us to estimate the instantaneous phase of each wavelet of the near-surface reflection events without performing prior velocity analysis and/or critical-angle estimation. After finding the instantaneous phase for each wavelet of a reflection event, we show next how one can find the respective phase shifts that can then be corrected.