Accurate Predictions of Mean Geomagnetic Dipole Excursion and Reversal Frequencies, Mean Paleomagnetic Field Intensity, and the Radius of Earth's Core Using McLeod's Rule
The geomagnetic spatial power spectrum R(sub n)(r) is the mean square magnetic induction represented by degree n spherical harmonic coefficients of the internal scalar potential averaged over the geocentric sphere of radius r. McLeod's Rule for the magnetic field generated by Earth's core geodynamo says that the expected core surface power spectrum (R(sub nc)(c)) is inversely proportional to (2n + 1) for 1 less than n less than or equal to N(sub E). McLeod's Rule is verified by locating Earth's core with main field models of Magsat data; the estimated core radius of 3485 kn is close to the seismologic value for c of 3480 km. McLeod's Rule and similar forms are then calibrated with the model values of R(sub n) for 3 less than or = n less than or = 12. Extrapolation to the degree 1 dipole predicts the expectation value of Earth's dipole moment to be about 5.89 x 10(exp 22) Am(exp 2)rms (74.5% of the 1980 value) and the expected geomagnetic intensity to be about 35.6 (mu)T rms at Earth's surface. Archeo- and paleomagnetic field intensity data show these and related predictions to be reasonably accurate. The probability distribution chi(exp 2) with 2n+1 degrees of freedom is assigned to (2n + 1)R(sub nc)/(R(sub nc). Extending this to the dipole implies that an exceptionally weak absolute dipole moment (less than or = 20% of the 1980 value) will exist during 2.5% of geologic time. The mean duration for such major geomagnetic dipole power excursions, one quarter of which feature durable axial dipole reversal, is estimated from the modern dipole power time-scale and the statistical model of excursions. The resulting mean excursion duration of 2767 years forces us to predict an average of 9.04 excursions per million years, 2.26 axial dipole reversals per million years, and a mean reversal duration of 5533 years. Paleomagnetic data show these predictions to be quite accurate. McLeod's Rule led to accurate predictions of Earth's core radius, mean paleomagnetic field intensity, and mean geomagnetic dipole power excursion and axial dipole reversal frequencies. We conclude that McLeod's Rule helps unify geo-paleomagnetism, correctly relates theoretically predictable statistical properties of the core geodynamo to magnetic observation, and provides a priori information required for stochastic inversion of paleo-, archeo-, and/or historical geomagnetic measurements.