A robust approach to the calculation of paleostress fields from fault plane data: reply

Abstract

Algebraic methods combined with robust regression techniques are used to calculate paleostress tensors from field observations on faults. Previously, such calculations have involved least-squares regression; however such regression estimates are likely to break down and produce meaningless results if data are included that are inconsistent with the main body of the data. Such inconsistent data are called outliers, i.e. measurements that are discrepant with respect to the majority of the observations. In two dimensions, the trend of the main body of the data, and their outliers, can be found by plotting the data and examining them visually. Least-squares regression can then be safely applied to the data-set once the outliers have been manually removed. However, the paleostress problem possesses a four-dimensional parameter space, and, as a consequence, this approach cannot be used. To overcome this difficulty, a robust regression estimator, involving the least median of squares (LMS), is applied to the estimation of paleostress tensors from fault plane data; not only can the parameters of the tensor be estimated but also the quality of the data-set assessed. For a data-set that is composed of data from several stress fields the dominant reduced stress tensor will be found by the LMS estimator. A computer program, PSALMS, that calculates paleostress directions using this robust estimator is presented.