On the Application Limits of the Parameter in Studying Variations of the Ancient Geomagnetic Field

To describe secular geomagnetic variation on geological timescales, statistical models have been widely used in recent decades. Currently, the most popular among these is the TK03 model (Tauxe and Kent, 2004). As other statistical models, TK03 numerically characterizes the amplitude of secular geomagnetic variation and the shape of the distribution of paleomagnetic directions which are considered as directly reflecting the directions of the geomagnetic field on the considered interval of geological time. For this purpose, three main parameters are used: the scatter Sb (or S) of the virtual geomagnetic poles, the elongation E of the distribution of paleomagnetic directions, and the direction of elongation of the distribution of paleomagnetic directions. The correct application of these parameters to describe ancient secular variation requires the satisfaction of certain, sometimes rather strict conditions. These conditions for the Sb and E parameters were considered in a number of previous publications, while the limits and conditions of application of parameter have not been studied in detail so far. This paper presents the results of mathematical modeling that allow us to evaluate the stability of the calculated values of this parameter as a function of the latitude of sampling, the number of samples used for its determination, the length of the time series on which this parameter is determined, as well as inclination shallowing and the degree of averaging when is estimated in sedimentary rocks. We also consider the extent to which the parameter can be sensitive to the presence and characteristics of the equatorial dipole component in the total geomagnetic field.