Robust data-driven AVO inversion algorithm based on generalized nonconvex dictionary learning

Abstract

In recent years, a dictionary learning and sparse representation based data-driven amplitude variation with offset (AVO) inversion algorithm has achieved desirable performance. However, in this data-driven inversion (DDI) method, sparse coefficients sequence generated by K-SVD may not always be convergent. Furthermore, the convergence of the data-driven AVO inversion results cannot be guaranteed. On the other hand, using L2 norm as a loss function in the DDI algorithm will lead to a robustness problem when seismic data contains outlier noise. In this paper, we propose a robust AVO inversion algorithm based on generalized nonconvex dictionary learning. The generalized nonconvex dictionary learning algorithm utilizes a family of nonconvex functions as the sparsity-inducing function for accurate estimation and a convergent sparse coefficient sequence. To deal with outlier noise, a smoothed L1 norm is utilized as the loss function. Meanwhile, a new spectral Polak–Ribière–Polyak (PRP) conjugate gradient algorithm is used to optimize the entire robust AVO inversion problem. Furthermore, the convergence analysis of the proposed algorithm is provided. In comparison with the conventional DDI algorithm, the proposed algorithm is robust, convergent, and computationally efficient. Results of synthetic data and field data experiments verify the superior performance of the proposed algorithm.