科研之友
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摘要
The l(1) norm and its variants, such as the hybrid l(1)/l(2) 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 (l(2) 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 l(2) norm and l(1) 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.
