Numerical processing of palaeostress results

Abstract

Statistical evaluation of the results of palaeostress analysis is hindered by the fact that the common fault-slip methods provide incomplete information about the stress tensor. Our favoured approach to solving this problem involves assigning nominal values to the missing components of the tensor to subsequently create a normalised palaeostress tensor. The proposed normalised stress is deviatoric and has an octahedral shear stress of unity. The difference between two normalised tensors can then be expressed by a single parameter, the palaeostress difference, D. This procedure facilitates the comparison of different palaeostress results, such as those calculated from different sites or those obtained from different inversion methods applied to the same data. A numerical entity termed the palaeostress tensor average is proposed to summarise collections of normalised palaeostress tensor results. Following the description of the palaeostress tensor average, end-member relationships between stress tensors have been used to identify the likely range of values for a proposed measure of dispersion within a sample of palaeostress tensors. Observations from a Monte-Carlo experiment are used as the basis for determining significant values of the dispersion measure. The proposed numerical measures may provide another tool to aid the scientific assessment of the interpretations of current palaeostress inversion solutions.