Multichannel seismic data attenuation compensation via curvelet‐based sparsity promotion

Abstract

AbstractDue to subsurface viscosity and heterogeneity, the vertical resolution of observed seismic data is decreased after wave propagation, generating nonstationary seismic data with amplitude attenuation and phase distortion. Inverse Q filtering techniques are always used to enhance the vertical resolution of seismic data. However, the majority of inverse Q filtering methods treat attenuation compensation trace by trace, which may produce non‐robust compensation results with poor transverse continuity and amplify noise energy in noisy cases. Thus, we develop a novel sparsity‐promoting inversion‐based multichannel seismic data attenuation compensation approach by introducing a sparse constraint for curvelet coefficients of multichannel compensated data, which takes the transverse continuity of compensated data into account. Besides, the proposed method with a sparse constraint for curvelet coefficients has a better noise‐resistance property, which can attenuate the noise energy in noisy cases during attenuation compensation, improving compensation accuracy and robustness. To improve its computational efficiency, a fast iterative shrinkage–thresholding algorithm is adopted to solve the established lasso problem. Synthetic data examples with different noise levels and two post‐stack field data examples validate the effectiveness of the proposed multichannel method. Its compensation results have superior vertical resolution, transverse continuity and noise robustness in comparison to the conventional single‐channel compensation method using a damped least squares algorithm.