Assessing data quality in fault slip analysis: Simulations using random faults

Fault-slip analysis assumes that measured slip lineations on faults represent the direction of maximum resolved stress produced by single homogenous state of stress. To devise criteria for recognising natural data that do not comply with this assumption, the performance of fault-slip methods is examined when used to analyse unsuitable data; namely, faults and slip lineations with randomly chosen orientations. Data quality is often judged by examining the average discrepancy between the orientation of actual slip lineation on each fault and the lineation theoretically predicted from the best-fit tensor. In this work, however, it is found that random faults also yield small angular misfits in conditions where eight or less faults are used. This criterion is therefore only useful for large samples of faults. Another test of data quality is to use the existence of tensors that are compatible with a given data set. However, even for random data, tensors can be found that are capable of explaining the lineation orientations. For example, the existence of compatible stress orientations deduced from the right dihedra method is no proof that the data meet the assumptions of the method. The probability of finding such tensors depends on the tolerance used when assessing fit, and the total number of trial tensors used. A more useful check on data quality is the proportion of trial tensors that fit data sets. For random data this proportion is found to decrease rapidly with sample size. For sample sizes greater than five faults, the expected proportion of tensors fitting is very small (<1%). Statistical tests are proposed. This study emphasises the dangers of palaeostress determinations from small numbers of faults. All of the tests of quality increase in power as the number of faults in the sample increases. It is concluded that stress estimates based on eight or less faults should be treated with grave suspicion

Numerical processing of palaeostress results

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

STRESSTAT: A Basic program for numerical evaluation of stress inversion results

STRESSTAT allows the statistical treatment of palaeostress results and stress determinations based on the inversion of earthquake focal mechanism data. Results of this kind are firstly expressed as normalised stress tensors by assigning nominal values to two missing components of the tensor. Our normalisation scheme assigns a mean stress of zero and an octahedral shear stress equal to one. The tensors so obtained can be averaged by calculation of the mean tensor, involving the summation of corresponding tensor components. The dispersion of stress results is expressed by the octahedral shear stress of the mean tensor. In a similar fashion, a measure of the difference between tensors is derived by subtraction of one normalized tensor from another. STRESSTAT is written in two versions for the PC (QuickBasic and Visual Basic)

Paleostresses deduced from striated faults: Are they up to scratch?

A major restriction on the application of fault-slip analysis methods is the availability of a collection of faults whose displacements where induced by the resolved shear stresses associated with a single stress tensor, and where the slip on individual faults are not influenced by the slip on other nearly faults. How does the prospective user of these methods know that the available data meet these requirements? To help answer this, the performance of fault-slip methods were examined when used to analyze unsuitable data; namely, faults and slip lineations with randomly chosen orientations. A favourite criterion for judging data quality is the average discrepancy between the orientation of actual lineation on each fault and the lineation theoretically predicted from the best-fit tensor. However in this work it is found that random faults also yield small angular discrepancies in conditions where 8 or less faults are used. This criterion is only useful for large samples of faults. Another test is to use the existence of tensors that are compatible with a given data set. For random data, there is possibility that tensors can be found that are capable of explaining the lineation orientation. For example, the existence of compatible stress orientations deduced from the right dihedron method is no proof of data meeting the assumptions of the method. The probability of finding such tensors depends on the tolerance used to assess fit, and the total number of trial tensors used. However a more useful check is to use the proportion of trial tensors that are found to fit random datasets. This proportion decreases rapidly with sample size. In sample sizes greater than five faults the expected proportion of tensors fitting is very small (<1%). Statistical tests are proposed. A powerful test on data quality is found to be one based on the consistency of the best-fit tensors obtained from sub-samples of the data set. A bootstrap method is able to detect poor quality data from a lack of consistency in the resulting tensors. This study emphasizes the dangers of palaeostress determinations from small numbers of faults. All of the tests of quality increase in power as the number of faults in the sample increases

Dipslip: A QuickBasic stress inversion program for analysing sets of faults without slip lineations

A simple computer program is described for estimating palaeostress tensors from orientation data from a set of fault planes. The computation is based on a novel technique that allows the tensor to be estimated in situations where directions of slip on the faults cannot be determined, but where the senses of the dip-slip component of slip on the faults are known. The new technique greatly broadens the scope of palaeostress analysis, permitting the analysis of faults lacking slickenlines but exhibiting offsets of horizontal marker beds

Late Pliocene-Pleistocene stress field in the Teruel grabens (eastern Spain): Contribution of a new method of stress inversion

Samples of non-striated fracture surfaces within clastic materials of Late Pliocene–Pleistocene age from the Teruel grabens (eastern Spain) have been analysed using a stress inversion method based on observations of slip sense. The results obtained at 21 sites are compared with Late Miocene–Early Pliocene extensional stress tensors previously inferred from striated faults in the same area. The similarity between both sets of stress states suggests that the extensional Miocene–Pliocene stress field essentially continues (with minor changes) into Pliocene–Pleistocene times. The main changes involve (a) the dominant trend of σ3 trajectories, which evolve from ESE to ENE; (b) the waning of the compressional component caused by Europe–Iberia–Africa convergence; and (c) the progressive trend towards a multidirectional extension regime. Stress deflection caused by large-scale extensional faults as well as switching of σ2 and σ3 axes induced by fracture development are common within this stress field. They produce groups of local stress ellipsoids with σ3 axes orthogonal to each other and either orthogonal or parallel to the faults bounding the grabens. The regional consistency of the new results gives support to the new inversion method and demonstrates its utility in research on young sedimentary rocks, where ‘gaps’ in palaeostress records may exist due to absence of striated faults

Analysis of non-striated faults in a recent extensional setting: the Plio-Pleistocene Concud fault (Jiloca graben, eastern Spain)

The integration of palaeostress results obtained from the analysis of non-striated faults and joints affecting Plio-Pleistocene deposits near the Concud fault (southern Jiloca graben, eastern Spain) yields a multidirectional tension stress field (vertical s1, s2zs3) where the primary s3 trajectories trend ENE. The results also show strong deflections of stress trajectories, with many local s3 axes being either orthogonal or parallel to the trace of the Concud fault. The stress field persisted throughout the period of activity of the fault, i.e. Late Pliocene and Pleistocene. The agreement between the present results and the regional picture gives support to the stress inversion method and shows its usefulness in palaeostress analysis of young, poorly lithified rocks