Inversion-driven attenuation compensation using synchrosqueezing transform

Attenuation is a fundamental mechanism as seismic wave propagates through the earth. The loss of high-frequency energy and concomitant phase distortion can be compensated by inverse Q filtering to enhance the resolution of seismic data. Since the attenuation process depends on time and frequency, it is routinely performed in the time-frequency domain. The synchrosqueezing transform (SST), which provides highly localized time-frequency representations for the nonstationary signals due to reduced spectral smearing, is applied to implement the inverse Q filtering scheme. However, the amplitude compensation process is unstable because energy amplification is involved. To stabilize it, the amplitude compensation is regarded as an inverse problem with an L1-norm regularization term in the SST domain. The iteratively reweighted least-squares algorithm is used to solve the regularized inverse problem. Synthetic and real data examples illustrate the stability and effectiveness of the proposed method.