Iterative reweighted least M-estimate AVO inversion
Yang Liu 1 3 Jiashu Zhang 1 Guangmin Hu 21 Sichuan Key Lab of Signal and Information Processing, Southwest Jiaotong University, Chengdu, Sichuan 610031, China.
2 School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China.
3 Corresponding author. Email: yunglau@163.com
Exploration Geophysics 46(2) 159-167 https://doi.org/10.1071/EG13038
Submitted: 26 April 2013 Accepted: 13 March 2014 Published: 9 April 2014
Abstract
The l1 norm and its variants, such as the hybrid l1/l2 norm and the Huber norm, that are used to solve amplitude variation with offset (AVO) inversion optimisation problems, are mostly known to give a more robust solution than the classical least-squares (l2 norm) method by reducing the influence of outliers significantly, although never ignoring it. To deal with data having many outliers, biweight norm using iteratively reweighted least-squares (IRLS) as robust inversion method can improve robustness by ignoring outliers in computing the misfit measure. However, biweight norm uses a higher-order descending weighting on the measured data, which results in poor performance when dealing with the well measured data. Hampel’s three-part redescending M-estimate function as robust measure could be considered as a three-part combination of the l2 norm and l1 norm with excluding outliers, which could perform better. This paper describes an iterative reweighted least M-estimate (IRLM) algorithm as a robust AVO inversion. The synthetic and field seismic data tests show that the IRLM algorithm gives far more robust model estimates than the conventional Huber norm and biweight norm.
Key words: AVO, Hampel’s three-part redescending M-estimate function, IRLM algorithm, outliers, robust.
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