A robust data-driven AVO inversion with logarithm absolute error loss function

Abstract

Amplitude variation with offset (AVO) inversion is a widely used approach to obtain reliable estimates of elastic parameter. Tikhonov and total variation regularization are commonly used methods to address ill-posed problem of AVO inversion. However, these model-driven methods are only for special geological structure such as smoothness or blockiness. In this letter, a robust data-driven-based regularization method with logarithm absolute error loss function (DDI-Log) for AVO inversion is proposed. In DDI-Log, the information of well-log data and the complex geology are considered in a sparse representation framework. In pre-stack seismic data, outlier noise can negatively influence inversion results. Thus, different from the previous data-driven inversion based on $$L _2$$ norm loss function, we extend the logarithm absolute error function as the loss function. In the iteration, a new spectral PRP conjugate gradient method is used to solve the large-scale optimization problem. The synthetic data and field data tests illustrate that the proposed approach is robust against outlier noise and that the resolution and accuracy of the solutions are improved.