High-resolution time-frequency hilbert transform using sparsity-aware weighting function

Instantaneous complex attributes that rely on conventional Hilbert transformation are normally susceptible to random noise and abrupt frequency variations in seismic signals. Moreover, conventional filtering methods diminish the spectral bandwidth needed to suppress noise when estimating seismic attributes. This has a significant impact on the resolution in thin-bed layers, which demand wide-band data to image properly. Therefore, in this paper, we address the noise and resolution problems in seismic attributes by applying a sparsity-aware weighting function that makes use of Geman-McClure and Laplace functions to a sparsity-based adaptive S-transform. The proposed filter not only suppresses the random noise but also increases the resolution of the Hilbert transform in the calculation of seismic attributes. Finally, to corroborate the superiority of the proposed method over some state-of-the-art approaches in synthetic and real data sets, the results are compared with the sparsity-based adaptive S-transform and the robust windowed Hilbert transform.