Bias in converging great circle methods

In palaeomagnetic studies remagnetization circles are often observed to converge. The circles represent the simultaneous decay of two magnetic components, and the convergence zones represent estimates of their directions. It is shown that these estimates are biassed, the degree of biassing depending upon the distribution parameters. In particular the ratio of the precision of the underlying distributions ( κ₂ κ₁) is very important. Only when κ₂ κ₁ is very different from unity can converging great circle methods give accurate results. Of the examples available in the literature most appear to satisfy this criterion, but the indiscriminate use of these methods can lead to significantly biasssed results.