Analysis of the Thelliers' Method of Paleointensity Determination 1

Estimation of Statistical Errors

Abstract

In obtaining paleointensity estimates of the geomagnetic field and their uncertainties, least squares fitting is performed on the data to obtain the slope of the linear NRM-TRM relation. Since both the X and Y coordinates (the TRM and NRM components) contain errors, variances of both coordinates should be used in the calculation of the slope (i.e., paleointensity). We propose a method to calculate variances based on experimental errors. Numerical analysis indicates that errors vary with temperature, and that data near the Curie point contain large statistical errors, even when samples show an ideal behavior. Contrary to the usual belief, heating in nonmagnetic space does not reduce overall errors; the original method of double heating with the field direction reversed gives more well balanced errors and therefore better performance. Further, we suggest the use of WILLIAMSON's (1968) method instead of YORK'S (1966) original argorithm in the calculation of the slope of the NRM-TRM linear relation, because the former method reflects the error level in individual data points while the latter does not. The standard error obtained by the present method is a good measure of the overall reliability of paleointensity data.