Constructing stochastic models for dipole fluctuations from paleomagnetic observations

Records of relative paleointensity are subject to several sources of error. Temporal averaging due to gradual acquisition of magnetization removes high-frequency fluctuations, whereas random errors introduce fluctuations at high frequency. Both sources of error limit our ability to construct stochastic models from paleomagnetic observations. We partially circumvent these difficulties by recognizing that the largest affects occur at high frequency. To illustrate we construct a stochastic model from two recent inversions of paleomagnetic observations for the axial dipole moment. An estimate of the noise term in the stochastic model is recovered from a high-resolution inversion (CALS10k.2), while the drift term is estimated from the low-frequency part of the power spectrum for a long, but lower-resolution inversion (PADM2M). Realizations of the resulting stochastic model yield a composite, broadband power spectrum that agrees well with the spectra from both PADM2M and CALS10k.2. A simple generalization of the stochastic model permits predictions for the mean rate of magnetic reversals. We show that the reversal rate depends on the time-averaged dipole moment, the variance of the dipole moment and a slow timescale that characterizes the adjustment of the dipole toward the time-averaged value. Predictions of the stochastic model give a mean rate of 4.2 Myr−1, which is in good agreement with observations from marine magnetic anomalies.