Pre‐stack seismic inversion based on ‐norm regularized logarithmic absolute misfit function

Abstract

Ill‐posedness is one of the most common and intractable issues that arise when solving geophysical inverse problems. Ill‐posedness could be induced by various factors such as noise, band‐limited intrinsic property of seismic data and inappropriate forward operators. Regularization has been proven to be an effective method widely accepted for mitigating the adverse effects of ill‐posedness. Aiming to improve the stability and fidelity of the pre‐stack seismic inversion process, we implement the inversion in a Bayesian framework, with a logarithmic absolute criterion taken as a likelihood function, and an ℓ1−2‐norm metric as a priori constraint. Here, we exploit the linear approximation as the forward operator, and optimize the regularized misfit function by the alternating direction method of multipliers. Applications of the method to synthetic and real data sets yielded improved inversion results in terms of accuracy and resolution, and demonstrated the robustness of the method to noise.

Prestack Seismic Inversion via Nonconvex L1-2 Regularization

“…Zhong et al proposed a L 1/2 norm regularization to reconstruct highly incomplete seismic data and obtained obviously better results [25]. Recently, Huang et al used L 1−2 norm regularized logarithmic absolute misfit function to improve the stability and fidelity of the prestack seismic inversion [26]. In the same year, they combined with the logarithmic absolutecriterion-based misfit function with L 1−2 norm-based penalty for P-P and P-SV waves joint inversion and achieved good performance in both resolution and accuracy [27].…”