Sparse Gabor Transform and Its Application in Seismic Data Analysis

Considering the limitation of the Gabor transform (GT) due to the uncertainty principle, where time and frequency resolution cannot both be maximized simultaneously, we propose a postprocessing strategy for the time-frequency spectrum (TFS) to mitigate this limitation and improve time-frequency concentration. In the frequency band of seismic data, the time and frequency window sizes of the GT are fixed, implying that the GT's TFS is formed by the 2-D convolution of a high-resolution TFS with a Gaussian-shaped point spread function (PSF). Therefore, based on compressed sensing theory, we use sparse constraints to the TFS and solve the 2-D deconvolution of the GT's TFS using the alternating direction method of multipliers algorithm to eliminate the influence of the time-frequency window function. The PSF used for deconvolution is determined by the variances of the time and frequency windows, and by altering the size of the PSF, we can obtain frequency-sparse GT (FSGT) and time-sparse GT (TSGT). Simulation signals demonstrate the effectiveness of this postprocessing strategy. For actual data, we prove that the sparse Gabor transform can enhance time-frequency concentration and improve the accuracy of seismic data analysis by integrating thin layer identification and frequency-dependent amplitude variation with offset attributes.