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Abstract Previous studies of rapid geomagnetic changes have highlighted the most extreme changes in direction and field strength found in paleomagnetic field models over the past 100 ky. Here we study distributions of rates of change in both time and space. Field models based on direct observations provide the most accurate values for rates of change, but their short duration precludes a complete description of field behavior. Broader representation is provided by time‐varying paleofield models, here including GGF100k, GGFSS70, LSMOD.2, CALS10k.2, HFM.OL1.A1, pfm9k.2, and SHAWQ‐iron age although variability across models and lack of temporal and spatial resolution of fine scale variations make direct comparisons difficult. For the paleofield we define rapid changes as exceeding the peak overall value of 0.4° yr⁻¹for directional changes and 150 nT yr⁻¹for intensities as established by thegufm1model spanning 1590–1990 CE. We find that rapid directional changes are associated with low field strength and can spread across all latitudes during such episodes. Distributions of directional rates of change exhibit high skewness for models that include excursions. Rates of change in field intensity exceeding 150 nT yr⁻¹arise in brief intervals during the Holocene particularly associated with the strong field Levantine Iron Age Anomaly. Around the Laschamp excursion there are also rare localized occurrences of rapid intensity change. Limitations in current models make it difficult to define absolute rates for past changes, but we see that rapid changes are essential field characteristics not observed in the modern field that should nevertheless be regarded as an essential for Earth‐like dynamo simulations. 

SUMMARY It is well known that the axial dipole part of Earth’s magnetic field reverses polarity, so that the magnetic North Pole becomes the South Pole and vice versa. The timing of reversals is well documented for the past 160 Myr, but the conditions that lead to a reversal are still not well understood. It is not known if there are reliable ‘precursors’ of reversals (events that indicate that a reversal is upcoming) or what they might be. We investigate if machine learning (ML) techniques can reliably identify precursors of reversals based on time-series of the axial magnetic dipole field. The basic idea is to train a classifier using segments of time-series of the axial magnetic dipole. This training step requires modification of standard ML techniques to account for the fact that we are interested in rare events—a reversal is unusual, while a non-reversing field is the norm. Without our tweak, the ML classifiers lead to useless predictions. Perhaps even more importantly, the usable observational record is limited to 0–2 Ma and contains only five reversals, necessitating that we determine if the data are even sufficient to reliably train and validate an ML algorithm. To answer these questions we use several ML classifiers (linear/non-linear support vector machines and long short-term memory networks), invoke a hierarchy of numerical models (from simplified models to 3-D geodynamo simulations), and two palaeomagnetic reconstructions (PADM2M and Sint-2000). The performance of the ML classifiers varies across the models and the observational record and we provide evidence that this is not an artefact of the numerics, but rather reflects how ‘predictable’ a model or observational record is. Studying models of Earth’s magnetic field via ML classifiers thus can help with identifying shortcomings or advantages of the various models. For Earth’s magnetic field, we conclude that the ability of ML to identify precursors of reversals is limited, largely due to the small amount and low frequency resolution of data, which makes training and subsequent validation nearly impossible. Put simply: the ML techniques we tried are not currently capable of reliably identifying an axial dipole moment (ADM) precursor for geomagnetic reversals. This does not necessarily imply that such a precursor does not exist, and improvements in temporal resolution and length of ADM records may well offer better prospects in the future. 

There has been longstanding controversy about whether the influence of lateral variations in core-mantle boundary heat flow can be detected in paleomagnetic records of geomagnetic field behavior. Their signature is commonly sought in globally distributed records of virtual geomagnetic pole (VGP) paths that have been claimed to exhibit specific longitudinal preferences during polarity transitions and excursions. These preferences have often been linked to thermal effects from large low seismic velocity areas (LLVPs) in the lowermost mantle, but the results have been contested because of potential sensitivity to sparse temporal and spatial sampling. Recently developed time varying global paleofield models spanning various time intervals in 1–100 ka, three of which include excursions, allow us to complement assessments of spatial distributions of transitional VGP paths with distributions of minimum field intensity. Robustness of the results is evaluated using similar products from four distinct numerical dynamo simulations with and without variable thermal boundary conditions and including stable geomagnetic polarity, excursions and reversals. We determine that VGP distributions are less useful than minimum field intensity in linking the influences of thermal CMB structure to geographical variations in actual paleofield observables, because VGP correlations depend strongly on good spatial sampling of a sufficient number of relatively rare events. These results provide a basis for evaluating comparable observations from four paleofield models. The distribution of VGP locations provide unreliable results given the restricted time span and available data locations. Rough correlations of global distributions of minimum intensity with areas outside the LLVPs give some indications of mantle control during excursions, although the results for the eastern hemisphere are complex, perhaps highlighting uncertainties about the hemispheric balance between thermal and compositional variations in the lowermost mantle. However, access to other geomagnetic properties (such as intensity and radial field at the CMB) provides a strong argument for using extended and improved global paleofield models to resolve the question of mantle influence on the geodynamo from the observational side. 

SUMMARY Earth’s internal magnetic field is dominated by the contribution of the axial dipole whose temporal variations are wide ranging and reflect characteristic timescales associated with geomagnetic reversals and large scale palaeosecular variation, ranging down to decadal and subannual field changes inferred from direct observations. We present a new empirical power spectrum for the axial dipole moment based on composite magnetic records of temporal variations in the axial dipole field that span the frequency range 0.1 to 5 × 105  Myr–1 (periods from 10 million to 2 yr). The new spectrum is used to build a stochastic representation for these time variations, based on an order 3 autoregressive (AR) process and placed in the context of earlier stochastic modelling studies. The AR parameter estimates depend on the frequency of transitions in the spectral regime and may be influenced by Ohmic diffusion, advection and torsional oscillations in Earth’s core. In several frequency ranges across the interval 200–5000 Myr–1(5000 to 200 yr periods) the empirical power spectrum lies above the AR3 model and may be influenced by Magneto–Coriolis (MC) waves in Earth’s core. The spectral shape and parameter estimates provide a potentially useful guide for developing assessments of whether numerical dynamo simulations meet criteria for being considered Earth like.