A robust method for instantaneous frequency estimation via inverse spectral decomposition

Abstract

Instantaneous frequency is an important seismic attribute, which can indicate thin beds and lithofacies boundaries. However, instantaneous frequency attribute is susceptible to noise when it is obtained by the traditional Hilbert transform (HT) method. We propose a robust method for instantaneous frequency estimation. The method first obtains the time-frequency distribution of the seismic signal by inverse spectral decomposition (ISD) and then calculates the analytic signal through the window HT transform. Inverse spectral decomposition achieves high-resolution time-frequency distribution by adding sparse constraint to the corresponding inverse problem, and therefore the noise can be suppressed. The algorithm we choose to solve the mix ℓ2 − ℓ1 problem is the fast iterative shrinkage-thresholding algorithm (FISTA). Compared with the traditional iterative least squares (IRLS) algorithm, FISTA can achieve a better computational efficiency. We perform the method on a quadratic frequency modulation (QFM) signal, a synthetic data based on a wedge model and field data sets to demonstrate its performance, compared with the HT method and the time-frequency adaptive filtering method.