Spherical Harmonic Analogues: robust measures of palaeomagnetic field behaviour obtained using an ensemble of geodynamo simulations

Abstract. The palaeomagnetic field provides unique information about the deep Earth and allows past plate motions and true polar wander to be determined. While data are available across much of Earth’s history, the conversion of these into robust descriptions of palaeomagnetic field behaviour prior to 1 Ma has been hampered by their highly inhomogeneous distributions in space and time. To address this, a set of parameters termed spherical harmonic analogues are proposed that use robust statistics to capture global, time-averaged aspects of field behaviour. Global palaeomagnetic direction and intensity data may be combined with outputs from ensembles of numerical geodynamo simulations, using a bespoke Monte-Carlo proxy-based approach, to estimate values of these spherical harmonic analogues using data from long before 1 Ma. The new approach is applied to the intervals 0.1–1 Ma, 1–4 Ma, and 4–15 Ma which were chosen for the moderately uniform distributions of the ages of data within them.  The resulting estimates account for measurement errors and spatial inhomogeneity in the data and perform well in independent validation tests. They therefore provide benchmarks against which statistical field models and geodynamo simulations may be compared. Obtained values suggest that the average axial and nonaxial dipole fields in the interval 0.1–1 Ma were ~50 % higher than long-term averages estimated for the preceding 14 million years. By contrast, the time-variance of the total field may have remained relatively constant over the entire interval providing a potential explanation for why the Bruhnes polarity chron is already one of the longest since 15 Ma.