Adaptive individual weight-gain AVO inversion with smooth nonconvex regularization

Amplitude variation with offset (AVO) inversion is a widely used approach to obtain reliable estimates of elastic parameter in the fields of seismic exploration. However, the AVO inversion is an ill-posed problem because of the band-limited characteristic of seismic data. The regularization constraint plays an important role in improving inversion resolution. Total variation (TV) class regularization based on L $$_1$$ norm has been introduced in seismic inversion. But, these methods may underestimate the high-amplitude components and obtain low-resolution results. To tackle these issues, we propose to combine a smooth nonconvex regularization approach with adaptive individual weight-gain. Compared with the L $$_1$$ norm regularizers, the proposed smoothed nonconvex sparsity-inducing regularizers can lead to more accurate estimation for high-amplitude components. Different from previous regularization methods, the proposed approach also assigns different weight regularization parameters for different strata, which we call adaptive individual weight-gain strategy. To ensure sufficient minimization of the constructed objective function, a spectral Polak–Ribiere–Polyak conjugate gradient method with line search step size is used. Further, we prove that the proposed algorithm converges to a stationary point. The synthetic data tests illustrate that our approach has improved performance compared with the conventional TV class regularization methods. Field data example further verifies the higher resolution of the proposed approach.