Shaping Regularization-Based Inversion for Robust Seismic Data Interpolation

Seismic image interpolation is a currently popular research subject in modern reflection seismology. The interpolation problem is generally treated as a process of inversion. Under the compressed sensing framework, various sparse transformations and low-rank constraints-based methods have great performances in recovering irregularly missing traces. However, in the case of regularly missing traces, their applications are limited because of the strong spatial aliasing energies. In addition, the erratic noise always poses a serious impact on the interpolation results obtained by the sparse transformations and low-rank constraints-based methods, because the erratic noise far from satisfies the statistical assumption behind them. In this study, I propose a mathematical morphology-based interpolation technique, which constrains the morphological scale of the model in the process of inversion. The inversion problem is solved by the shaping regularization approach. The mathematical morphological constraint-based interpolation technique has a satisfactory robustness to the spatial aliasing and erratic energies. Numerical and filed examples demonstrates the successful performance of the proposed technique.