Extraction of instantaneous frequency from seismic data via the generalized Morse wavelets

• We propose a robust estimation of instantaneous frequency in wavelet domain.
• The generalized Morse wavelets are applied during the procedure.
• The distribution of the effective signal is determined by the L1-norm minimization.
• IST algorithm and FISTA algorithm are applied to tackle this optimization problem.
• Exponential thresholding scheme with a dynamic stopping criterion is implemented.

The instantaneous frequency extracted by the Hilbert transform is susceptible to noise. We propose a robust method to extract instantaneous frequency from seismic data in wavelet domain. A new class of analytic wavelets with some desirable properties, called the generalized Morse wavelets (GMWs), is applied in the proposed method. Based on the proposed discretization scheme, the GMW family can constitute a tight frame and then we can determine the distribution of the effective signal by solving the optimization problem. We use the iterative shrinkage–thresholding (IST) algorithm and fast iterative shrinkage–thresholding algorithm (FISTA) to tackle this l1l1-norm minimization problem. To improve the convergence rate of the iterative solution, we implement the exponential thresholding scheme with a dynamic stopping criterion. Compared with the conventional instantaneous frequency extraction method based on Hilbert transform, the proposed method is proved to yield higher precision and better anti-noise performance. Experimental results on synthetic signals and real seismic data demonstrate the validity of the method.