Separate diffracted wave with apex-shifted hyperbolic Radon transform based on L1-2 minimization

The apex-shifted hyperbolic Radon transform (ASHRT) can flexibly address the limitation of seismic wave event apexes at zero offset, and offer advantages over the conventional hyperbolic Radon transform in separating diffracted waves. When using Radon transform to solve wavefield separation problems, it is generally required that the Radon transform possesses a sparse solution, and methods for solving sparse solutions using norm constraints have been widely applied. In this study, we introduce the L1-2 norm constraint method into the sparse ASHRT and demonstrate that, compared to the L1 norm constraint, the L1-2 norm constraint achieves better sparsity. By applying this method to synthetic data, simulated data, and real data as processing examples, we validate the sparsity, resolution, and feasibility of the proposed method. Finally, we analyze the parameter sensitivity and robustness of the method to provide a reference for future researches.