The effects of noise due to random undetected tilts and paleosecular variation on regional paleomagnetic directions

Random tilting of a single paleomagnetic vector produces a distribution of vectors which is not rotationally symmetric about the original vector and therefore not Fisherian. Monte Carlo simulations were performed on two types of vector distributions: (1) distributions of vectors formed by perturbing a single original vector with a Fisher distribution of bedding poles (each defining a tilt correction) and (2) standard Fisher distributions. These simulations demonstrate that inclinations of vectors drawn from both distributions are biased toward shallow inclinations. There is a greater likelihood of statistically “drawing” a vector shallower than the true mean vector than of drawing one that is steeper. The estimated probability increases as a function of angular dispersion and inclination of the true mean vector. Consequently, the interpretation of inclination-only data from either type of distribution is not straightforward, especially when the expected paleolatitude is greater than about 50°. Because of the symmetry of the two distributions, declinations of vectors in each distribution are unbiased. The Fisher mean direction of the distribution of vectors formed by perturbing a single vector with random undetected tilts is biased toward shallow inclinations, but this bias is insignificant for angular dispersions of bedding poles less than 20°. This observation implies that the mean pole calculated from a large set of paleomagnetic directions obtained for coeval rocks over a region will be effectively unbiased by random undetected tilts of those rocks provided the angular dispersion of the undetected tilts is less than about 20°. However, the bias of the mean can be significant for large (>20°) angular dispersion of tilts. The amount of bias of the mean direction maximizes at about 10°–12° in mid-latitude regions but is usually less than 8°. Consequently, large (>12°) inclination discordances are probably not the result of random undetected tilts, even if the angular dispersion of the tilts exceeds 20°.