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 <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> 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 <inline-formula> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> 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.