Adaptive step length for robust AVO inversion

Abstract

Some more robust norms such as Hybrid norm and Huber norm which combine the L1 norm and L2 norm have been applied to the robust inversion. Iterative Reweighted Least Squares (IRLS) is usually effectively used to solve robust norms. In order to avoid solving inverse matrix in IRLS, the nonlinear conjugate gradient (NLCG) has been introduced to solve the IRLS problem, and can be directly applied to the robust norm. The step length is an important factor in the iterate algorithm, which can be obtain by exact or inexact line search. Generally, the exact line search is faster than the inexact line search. In this paper, we introduce an adaptive step length based on the residual for the robust methods which can be performed under different objective function. Especially for the robust norms, it doesn’t need complex solution process like exact line search does. Based on the residual vector, the adaptive step length can adaptively adjust the model parameter to accelerate the descent of the objective function. This paper describes the step length apply to Amplitude Variation with Offset(AVO) inversion with NLCG, and compare it to exact line search under the robust norms with data includes Gaussian and non-Gaussian noise.