Q-Factor Estimation by Compensation of Amplitude Spectra in Synchrosqueezed Wavelet Domain

We propose a stable <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>-estimation approach based on the compensation of amplitude spectra in the time–frequency domain after a synchrosqueezed wavelet transform (SSWT). SSWT employing a post-processing frequency reallocation method to the original representation of a continuous wavelet transform (CWT) for improving its readability provides the sharper time–frequency representation of a signal when compared with the other traditional time–frequency methods such as CWT or S-transform. For <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>-estimation, we transform a seismic trace into the time–frequency domain using SSWT at first. Then, we derive the amplitude compensation in the SSWT domain. By searching the predetermined <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> range, the comparison between the compensated amplitude spectrum and the reference one in the SSWT domain is carried out. The output optimized <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula>-factor estimation is evaluated by the minimum of the mean square error. For the robust and fast stabilization form of the amplitude compensation in the SSWT domain with noise amplification damping, the seismic pulse is truncated with a limited length and the obtained time–frequency maps using an SSWT are smoothed. The synthetic vertical seismic profiling data and the real stacked seismic data applications illustrate the effectiveness and the ability of the proposed method.