1887
Volume 43, Issue 2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

[

In spite of some minor drawbacks such as nonuniqueness and higher computational cost, finding the least-absolute ( norm) error solution to solve an optimisation problem is mostly known to give a better answer than the classical least-squares ( norm) method. This is because the robust property of the median value is affected little by outlier values and the solution of the least norm error corresponds to the solution of minimum median error. Several variants of the norm such as the Huber norm and the Hybrid norm have the same robust properties as the norm. The optimisation methods based on norm obtain their robustness by reducing the influence of outliers significantly, although never ignoring it. Therefore, if the proportion of outliers increases, most of the methods based on norm may begin to be affected by the outliers. In such a case, other types of robust measures such as Tukey’s Biweight (Bisquare weight) norm, which excludes outliers in computing the misfit measure, could perform better. This paper describes the application of the Biweight norm using the IRLS (iteratively reweighted least-squares) method as a robust inversion and shows its possible improvement in robustness when dealing with data having many outliers.

,

This paper describes the application of Tukey’s Biweight norm using the IRLS (iteratively reweighted least squares) algorithm as a robust inversion in seismic application and shows its possible improvement in robustness over the norm inversion when dealing with data having many outliers.

]
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2012-06-01
2026-01-13

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/content/journals/10.1071/EG12014
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Robust inversion using biweight norm and its application to seismic inversion
Exploration Geophysics 43, 70 (2012); https://doi.org/10.1071/EG12014
/content/journals/10.1071/EG12014
/content/journals/10.1071/EG12014
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  • Article Type: Research Article
Keyword(s): biweight norm; IRLS; l1 norm; robust inversion; robust norm; weighted least-squares

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