On the Application Limits of the \({{D}_{{{{V}_{2}}}}}\) Parameter in the Study of Variations of the Ancient Geomagnetic Field

Abstract—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 thought to directly reflect the directions of the geomagnetic field on the considered interval of geological time. For this purpose, three main parameters are used: the scatter S_b (or S) of the virtual geomagnetic poles, the elongation E of the distribution of paleomagnetic directions, and the elongation direction \({{D}_{{{{V}_{2}}}}}\) of the distribution of paleomagnetic directions. The correct use of these parameters to describe paleosecular variation requires the fulfillment of certain, sometimes rather strict conditions. These conditions for parameters S_b and E were considered in a number of previous publications, while the limits and conditions of application of \({{D}_{{{{V}_{2}}}}}\) have not been studied in detail so far. The results of mathematical modeling presented in this paper allow us to evaluate the stability of the calculated parameter values as a function of sampling latitude, the number of samples used to determine this parameter, the length of the time series from which this parameter is estimated, as well as the inclination shallowing and the degree of averaging if \({{D}_{{{{V}_{2}}}}}\) is estimated from sedimentary rocks. We also consider the extent to which the \({{D}_{{{{V}_{2}}}}}\) parameter can be sensitive to the presence and characteristics of the equatorial dipole component in the total geomagnetic field.