On the probability of selecting a sample with inclination less than the true mean from a circular distribution: paleomagnetic and tectonic implications

Abstract

The method of Fisher, if used properly, will yield an unbiased estimate of inclination, and hence of paleolatitude. However, paleomagnetic data bases for essentially all continents contain significant numbers of studies that consist of very few sites, and/or have sampled very small areas and/or stratigraphic intervals. Such studies probably do not include the full range of variation of the geomagnetic field and hence may not provide an acceptable estimate of mean inclination and paleolatitude. If so, the value of inclination obtained is more likely to be too shallow than too steep, leading to an estimate of paleolatitude that is too low. Even studies that properly average the non-axial dipole elements of the geomagnetic field to near zero are slightly more likely than not to produce an estimate of mean inclination that is lower than the true inclination. Important tectonic conclusions have been drawn, and continue to be drawn, from paleomagnetic data bases for most of the earth's orogenic belts. All of these contain multiple examples of inadequate sampling. A potential bias of paleolatitudes toward the equator thus exists because of the nature of distributions on the surface of a sphere. It is important to determine by how much estimates of inclination may be biased toward the horizontal. A simple and straightforward method to determine the probability of drawing a sample for which I < I o is described. The method is illustrated using the Fisher distribution, but will work for any circular distribution. It is shown that a bias toward shallow inclinations is consistently present, but that it is trivial except for highly scattered data sets, or rock units originally magnetized at very high paleolatitudes.