The Instantaneous Velocity of the Magnetic Poles according to Global Models of the Geomagnetic Field

Abstract

A new approach is proposed to calculate the instantaneous velocity of magnetic poles. The method uses the spatial distribution of the vector of the horizontal component H, calculated from analytical models of the main geomagnetic field for the current and the nearest epochs. The horizontal component was calculated using the coefficients of two models: IGRF13 and COV-OBSx2. The equation for the velocity of pole movement is obtained from the condition that the horizontal field component at the pole point is equal to zero at any moment in time, which allowed us to determine the directions of instantaneous velocity. To find the position of the pole and the velocity of its movement between epochs, it is proposed to use a hermitian spline, which describes a smooth curve, whose tangent coincides with the velocity vector in each epoch. It is shown that the velocity vector of the pole movement depends linearly on the derivative of the horizontal component with respect to time and is inversely proportional to the derivative of H with respect to coordinates. It has been established that higher harmonics are primarily responsible for the acceleration of the pole movement. This is due to their significant contribution to the horizontal component in the polar regions. The obtained instantaneous velocities were compared with the average or interval ones, which are determined from the position of the pole for neighboring epochs. When using the IGRF13 model to calculate the coefficients, artifacts were found in the trajectory of the poles: large deviations in both the directions and magnitudes of the instantaneous velocity vectors compared to interval ones. For the COV-OBSx2 model, no such artifacts were found. It has been assumed that the observed systematic differences in the vectors of instantaneous and interval velocities calculated using the IGRF13 model are associated with the methodological features of constructing this model. In particular, the interval between generations of the IGRF13 model is 5 years, while for the COV-OBSx2 model it is 2 years and splines were used to construct the latter model. It is noted that the direction of interval velocities for these two models can differ by 40°. Limitations on the applicability of the method associated with sudden changes in the trajectory of the pole are determined. In this case, the method may be unstable, since when calculating the time derivatives of the field at a given epoch, models of the nearest epochs are used. In the case of sudden changes in the pole trajectory, the values of these derivatives strongly depend on the chosen method of numerical differentiation with respect to time. For the reliability of the proposed method, it is required to know the geomagnetic field in the vicinity of the pole at time intervals shorter than those in the IGRF13 model.