Weighted $\boldsymbol{l_1}$-norm constrained sparse regularization and alternating directions method of multipliers for seismic time-frequency analysis

Abstract

Seismic time-frequency analysis is of great importance in seismic signal processing.We study a sparse inversion-based algorithm for computing the time-frequency analysis of reflection seismograms.We first formulate the forward problem using the windowed inverse Fourier transform,and then we establish a weighted $l_1$-norm constrained minimization model for solving the unknown model parameter vector (the Fourier frequency coefficients).To realize the minimization problem, an alternating directions method of multipliers (ADMM) is applied. Numerical experiments based on the well-known short time Fourier transform (STFT), the continuous wavelet transform (CWT) and the proposed algorithm are analyzed. It indicates from the comparison results that the proposed model and the related algorithm can produce a spectral decomposition of the seismic data with high resolution thanthat of the STFT and CWT.