Spatially structured regularization multichannel sparse pulse deconvolution

Sparse spike deconvolution, sometimes referred to as sparse spike inversion, is a nonlinear high-resolution processing method. Conventional pulse deconvolution assumes that the reflection coefficient series follows a Gaussian distribution, making its deconvolution process linear. In contrast, sparse spike deconvolution assumes that the reflection coefficient series follows a sparse distribution and performs inversion under the sparse function regularization, making the deconvolution process nonlinear. Sparse spike deconvolution can significantly improve the resolution of seismic data compared to conventional methods; however, its high-frequency components exhibit stronger multiple solutions and instability. To address this, this paper proposes a spatial structure regularized multichannel sparse spike deconvolution method. First, based on the spatial continuity and predictability of seismic signals, the method estimates and characterizes the spatial structure of the seismic signal using structure tensors. Then, a prediction error filter is designed along the dip direction, ensuring that the seismic signal has minimal prediction error. Building on this, the prediction error filter is introduced as a spatial structure constraint into the regularization conditions of sparse spike deconvolution, establishing a multichannel sparse spike deconvolution objective function with the sparse and spatial structure constraints. Finally, an iterative reweighting algorithm is employed to numerically solve the objective function and obtain the reflection coefficient series. We compare and analyze the proposed method against conventional methods using both model data and actual data, and we validate the reliability of this method through synthetic seismic records based on well logs. The results based on model data and actual data indicate that the proposed method effectively suppresses the influence of random noise on the deconvolution results and enhances the accuracy of high-frequency seismic signal recovery.