Propagating and incorporating the error in anisotropy-based inclination corrections

Sedimentary rock palaeomagnetic inclinations that are too shallow with respect to the ambient field inclination may be restored using anisotropy-based inclination corrections or techniques that rely on models of the past geomagnetic field. One advantage of the anisotropy technique is that it relies on measured parameters (declinations, inclinations, bulk rock magnetic fabrics and particle magnetic anisotropy) that have measurement errors associated with them, rather than relying on a geomagnetic field model and statistical treatment of the data. So far, however, the error associated with the measurements has not been propagated through the corrections and the reported uncertainties are simply the alpha(95) 95 per cent confidence circles of the corrected directions. In this paper we outline different methodologies of propagating the error using bootstrap statistics and analytic approximations using the case example of the Shepody Formation inclination correction. Both techniques are in good agreement and indicate a moderate, similar to 15 per cent, uncertainty in the determination of the flattening factor (f) used in the correction. Such uncertainty corresponds to an similar to 0.31 degrees increase of the confidence cone and a bias that steepens the mean inclination by 0.32 degrees. For other haematite-bearing formations realistic uncertainties for f ranging from 0 and 30 per cent were used (together with an intermediate value of 15 per cent) yielding a maximum expected increase in the confidence cones and steepening of the inclinations of similar to 1 degrees. Such results indicate that for moderate errors of f the inclination correction itself does not substantially alter the uncertainty of a typical palaeomagnetic study. We also compare the uncertainties resulting from anisotropy-based corrections to those resulting from the elongation/inclination (E/I) technique. Uncertainties are comparable for studies with a large sample number (>100), otherwise the anisotropy-based technique gives smaller uncertainties. When anisotropy data are not available, it is possible to estimate a correction using flattening factors (f) obtained from the literature. A range of flattening factors has been observed for both magnetite and haematite-bearing rocks (0.4 <= f <= 1 for haematite and 0.54 <= f <= 1 for magnetite), but the exact value is specific to the anisotropy of the formation. To evaluate the maximum effects of inclination shallowing, the smallest f (for magnetite or haematite) should be used.