Multichannel sparse deconvolution of seismic data with shearlet–Cauchy constrained inversion
Chengming Liu, Deli Wang, Tong Wang, Fei Feng, Yonggang Wang · Journal of Geophysics and Engineering · 2017
Multiscale and multidirectional transforms were introduced to represent non-spiky reflectivity instead of assuming spiky reflectivity in the deconvolution problem. The study found that an alternative sparse shearlet coefficient can be used to accurately represent the non-spiky reflectivity and solve the problem in a multichannel way. Such non-spiky reflectivity can help in avoiding the loss of weak reflection events, which is likely to occur in conventional methods due to over sparse constraints on spiky reflectivity. Moreover, compared to single-trace deconvolution methods, the multichannel method can enhance the continuity of reflection events and suppress high-frequency noise in the deconvolved data. Seismic inversion is usually considered an ill-conditioned problem because even very low-level noise can cause large errors in results, and normally requires the regularization of deconvolution operators. In this study, we propose the multichannel sparse deconvolution of seismic data with shearlet–Cauchy constrained inversion. Firstly, a stable method enabling accurate reflectivity estimation was developed based on maximum a posteriori estimation in Bayesian statistics. Then sparse shearlet coefficients are used to represent non-spiky reflectivity. According to the different distributions of noise and signal in the shearlet domain, thresholding methods can be used to suppress noise and increase the noise resistance of the proposed method. A comparison of synthetic data with field seismic data demonstrated the validity of the proposed method.