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Pre‐stack seismic inversion based on ℓ 1 − 2 ‐norm regularized logarithmic absolute misfit function
Author(s) -
Huang Guangtan,
Chen Xiaohong,
Luo Cong,
Chen Yangkang
Publication year - 2020
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.13012
Subject(s) - a priori and a posteriori , inverse problem , logarithm , inversion (geology) , computer science , algorithm , mathematics , mathematical optimization , geology , mathematical analysis , seismology , philosophy , epistemology , tectonics
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 ℓ 1 − 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.