SAMPLING BIAS IN VGP LONGITUDES

I derive probability densities for virtual geomagnetic pole (VGP) longitudes for a general statistical model of local magnetic field variations. I show that even for very simple statistically homogeneous models of secular variation, the distribution of VGP longitudes is peaked 90-degrees away from the sampling longitude. Thus, when sites are distributed unevenly, a non-uniform overall distribution of VGP longitudes is to be expected. Analysis of the recent geomagnetic field indicates that this bias can be significant, particularly when random errors in paleomagnetic data are allowed for. It is possible that some of the deviations from uniformity seen in recent compilations of paleomagnetic reversal and secular variation data are a statistical artifact resulting from the distortion of the VGP transformation, and the non-uniformity of paleomagnetic sampling sites.