Distributions of paleomagnetic directions and poles

Abstract

In the studies of paleosecular variation (PSV) of the geomagnetic field, it has usually been assumed that the distribution of either field directions or their corresponding poles can be described by an axisymmetric distribution, typically a Fisher distribution. Because the mapping between the directions and poles is nonlinear, both of them cannot belong to a circular distribution. To study the shape of distributions of directions and poles, we define two new angles for the field direction (azimuth A and plunge P) and four new angles for the pole (translation T, stretch S, near-sidedness N, right-handedness R), which are free from the singularities near the poles of the conventional angles (inclination, declination, latitude, longitude). We obtain expressions for these quantities and examine which of the two (direction or pole) more closely follow a circular distribution. If the assumptions of homogeneity and isotropy of Gauss coefficients is valid as assumed in the homogeneous background model (HBM), it can be shown that the distribution of field directions is highly anisotropic as well as strongly latitude dependent, while that of poles is nearly independent of latitude and well approximated by a circular distribution. However, the distributions of directions and poles observed from paleomagnetic data of the last 5 Ma are not compatible with this simple scheme. To explain this difference, it is necessary to increase the contribution from the quadrupole harmonic component g 2 1 (or h 2 1). The departure of the actual data from the homogeneous model suggests that the dynamo process in the core has inherent asymmetry which creates such a feature persistently over the time scale of millions of years.