Multichannel spatially correlated reflectivity inversion using block sparse Bayesian learning

Abstract

The reflectivity inversion approach based on a variety of regularization terms was extensively developed and applied to image subsurface structure in recent years. In addition, multichannel reflectivity inversion or deconvolution considering the lateral continuity of reflection interfaces or reflectivity in adjacent channels has been developed. However, these processing operations seldom adaptively judge the stratal continuity or automatically alter the parameters of the corresponding algorithm. To use the special correlation of the reflection information contained in the seismic data, a multichannel spatially correlated reflectivity inversion using block sparse Bayesian learning (bSBL) is introduced. The method adopts a covariance matrix that describes the spatial relationship of reflectivity and simultaneously controls the temporal sparsity. With an expectation-maximization algorithm, we can obtain the parameters of the multichannel reflectivity model, including the mean (i.e., the estimated multichannel reflectivity) and the covariance matrix (i.e., the correlation of nonzero reflection impulses). The noise variance in the observed seismic data is also estimated during the inversion processing. Due to the contribution of reflectivity correlation in different traces, the performance of the multichannel spatially correlated reflectivity inversion using bSBL is significantly superior to the trace-by-trace processing method in the presence of a medium level of noise. The synthetic and real data examples illustrate that the lateral continuity is well-preserved in seismic profiles after inversion.