Application of an adaptive acquisition regularization parameter based on an improved GCV criterion in pre-stack AVO inversion

Abstract

In exploration geophysics, AVO inversion is undoubtedly the most common inverse problem which is ill-posed and must be regularized. Once regularization is used, the selection of the regularization parameter will become an important problem to solve. In practice, the proper regularization parameter value is usually data dependent and determined empirically. For one work area, inversion engineers often give a fixed parameter. In such a case, the results of AVO inversion will be accompanied by strong artificial subjective factors. Besides, it is difficult to guarantee that the fixed parameter could be applied to each trace of the seismic data. In this paper, we first emphasize the importance of the regularization parameter selection for the inverse problems. Then, based on a traditional GCV function, we propose an adaptive acquisition regularization parameter method which can be used in regularization for arbitrary norm conditions, and derive the theoretical formula of the adaptive computation of the regularization parameter. Applying this method to the AVO inversion of synthetic data and field data, we have found that the improved GCV method has better accuracy and robustness than the traditional method.