The temporal evolution of the geomagnetic field is analyzed using classical electromagnetics via an eigenvalue approach . The analysis points out the error of thinking of the Earth's field decay as a simple exponential decay, the decay constant being the equivalent inductance / resistance ratio of the Earth's core. In reality the field is characterized by a continuum of characteristic decay times (or eigenvalues). Each eigenvalue is associated with a unique shape. The total field is the sum of each eigenshape (or eigenvector) each decaying at a different rate. Since the weighting factors on each of these shapes is dictated by the initial field penetration of the core, it is likely that higher order eigenvectors will have larger weighting factors than the fundamental, more slowly decaying eigenshapes. Field reversals are an expected consequence of correctly analyzing the field transient.
The conclusions of this work are as follows. First, the age of the Earth's field, accounting for the whole continuum of characteristic eigenvalues, cannot be much more than 10,000 years old. Second, one or more field reversals can be expected in the first 1000 years of the field's existence. These reversals are caused by two sources. The first originates in the weighting of the individual eigenvectors as dictated by the initial core field. The second source is through eddy current induction in the ionosphere and/or vapor canopy.
The third conclusion is that motion effects in the core will not give added longevity to the field; the primary motion of the Earth is in the wrong direction to alter the eigenvalues. Secondary motion, i.e. precession, will only perturb the eigenvalues, and these perturbations have the wrong angular dependence around the globe to collectively couple to the main field.