  Power spectral analyses of the dipole moment of the earth's magnetic field
inferred from ocean sediment cores and archeomagnetic data from time scales of
100 yr to 4 Myr have been carried out. The power spectrum is proportional to
1/f where f is the frequency. These analyses compliment previous work which has
established a 1/f^2 spectrum for variations at time scales less than 100 yr.
Power spectral analyses of inclination and declination inferred from lake
sediments from time scales of 10 yr to 30 kyr have also been performed. The
spectra are constant above time scales of 3 kyr, proportional to 1/f^2 from
time scales of 500 yr to 3 kyr, and constant again below time scales of 500 yr.
The 3 kyr time scale is associated with the decay time of the quadrupole
moment. We test the hypothesis that reversals are the result of variations in
dipole intensity with a 1/f spectrum which occasionally are large enough to
cross the zero intensity value. Synthetic binormal time series with a 1/f power
spectrum representing variations in the earth's dipole moment are constructed.
Synthetic reversals from these time series exhibit statistics in good agreement
with the reversal record. 1/f noise behavior is reproduced with a model of
magnetic diffusion in the earth's core driven by dynamo action modeled as a
random amplification or destruction of the local magnetic field.
