An Adaptive Time-Varying Seismic Super-Resolution Inversion Based on L_pRegularization

The time-varying seismic super-resolution inversion technique becomes more and more attractive in seismic exploration. However, most existing inversion methods suffer from amplitude loss and manual adjustment parameters. In this letter, we present an adaptive time-varying seismic super-resolution inversion method based on the L\!_{p} (0< p< 1) regularization to address these issues. First, the L\!_{p} -norm with 0< p< 1 is applied to constrain the reflectivity to obtain a sparser and more robust solution than the L_{1} regularization. To solve the nonconvex inversion problem adaptively, second, we provide a new algorithm called singular value decomposition (SVD)-Hadamard product parametrization (HPP). The idea of the new algorithm is to apply an HPP to express the L\!_{p} (0< p\leq 1) regularization into a sum of the L_{2} regularizations that are easy to be programed and solved. Then, the SVD is adopted to solve each L_{2} regularization. It is convenient to apply the L-curve method or its variants to determine the regularization parameters at each iteration for finishing the inversion adaptively. Finally, synthetic and field data examples are tested to validate the effectiveness of the proposed method.