SUMMARY In this study, we examine the role of palaeosecular variation (PSV) in the use of statistics for palaeomagnetic studies, and we provide new reliability criteria for palaeomagnetic poles or directions. We first conclude that Fisher statistics should not be applied to average palaeomagnetic directions but to virtual geomagnetic pole (VGP) distributions instead. Secondly, we strongly advocate that typical properties of geomagnetic field behaviour are taken into account in the assessment of palaeomagnetic data sets. The latitude‐dependent properties (E, S, k) provide useful guidelines for the reliability of a palaeomagnetic data set. A reliable assessment of these properties depends on the (sufficient) number of palaeomagnetic samples being taken. Therefore, as an additional instrument of assessing data sets, we provide a N‐dependent A95 envelope, bounded by an upper limit A95max, and a lower limit A95min that helps to ascertain whether or not a distribution has sufficiently well‐sampled PSV and therefore geomagnetic field behaviour. Applying these criteria is indispensable for studies of geomagnetic behaviour, or for studies aiming at using TK03.GAD for inclination error correction through the elongation/inclination (E/I) method. For palaeomagnetic studies aimed at geological reconstructions, they form helpful guidelines and increase the confidence in the rocks having faithfully recorded the field. An analysis of published Eastern Mediterranean data shows that the vast majority of studies do not conform to the Van der Voo criteria, in particular with respect to N and A95. We have provided criteria that are on the one hand more lenient (lower N may still provide relevant information), and on the other hand more strict (for high N the criterion of A95 < 16° should be adapted to a requirement of lower A95, e.g. A95 < 5° for N > 80).

15It is now widely thought that geomagnetic polarity reversals occur spontaneously as a 16 result of normal dynamo action rather than being externally triggered. If this is the case, 17 then it may well be that periods of time in which the geomagnetic reversal frequency was 18 Families. J. Geophys. Res. 96,[3923][3924][3925][3926][3927][3928][3929][3930][3931][3932][3933]. We demonstrate that this is probably a result 6 of the previous study being affected by an artefact of their correction for within-site 7 scatter. The usefulness of our Jurassic record is severely limited by the restricted 8 palaeolatitudinal span of the available data. However, our record for the CNS is sufficient 9 to allow us to conclude that it was likely that secular variation then was different from 10 that in the 0-5 Ma period. This supports the hypothesis of a link between PSV and 11 reversal frequency and therefore endorses PSV analysis as a first-order tool for 12 determining geomagnetic stability in the past. 13 14

The selection of paleointensity data is a challenging, but essential step for establishing data reliability. There is, however, no consensus as to how best to quantify paleointensity data and which data selection processes are most effective. To address these issues, we begin to lay the foundations for a more unified and theoretically justified approach to the selection of paleointensity data. We present a new compilation of standard definitions for paleointensity statistics to help remove ambiguities in their calculation. We also compile the largest-to-date data set of raw paleointensity data from historical locations and laboratory control experiments with which to test the effectiveness of commonly used sets of selection criteria. Although most currently used criteria are capable of increasing the proportion of accurate results accepted, criteria that are better at excluding inaccurate results tend to perform poorly at including accurate results and vice versa. In the extreme case, one widely used set of criteria, which is used by default in the ThellierTool software (v4.22), excludes so many accurate results that it is often statistically indistinguishable from randomly selecting data. We demonstrate that, when modified according to recent single domain paleointensity predictions, criteria sets that are no better than a random selector can produce statistically significant increases in the acceptance of accurate results and represent effective selection criteria. The use of such theoretically derived modifications places the selection of paleointensity data on a more justifiable theoretical foundation and we encourage the use of the modified criteria over their original forms.

The dominant dipolar component of the Earth’s magnetic field has been steadily weakening for at least the last 170 years. Prior to these direct measurements, archaeomagnetic records show short periods of significantly elevated geomagnetic intensity. These striking phenomena are not captured by current field models and their relationship to the recent dipole decay is highly unclear. Here we apply a novel multi-method archaeomagnetic approach to produce a new high-quality record of geomagnetic intensity variations for Hawaii, a crucial locality in the central Pacific. It reveals a short period of high intensity occurring ~1,000 years ago, qualitatively similar to behaviour observed 200 years earlier in Europe and 500 years later in Mesoamerica. We combine these records with one from Japan to produce a coherent picture that includes the dipole decaying steadily over the last millennium. Strong, regional, short-term intensity perturbations are superimposed on this global trend; their asynchronicity necessitates a highly non-dipolar nature.

The Earth's inner core grows by the freezing of liquid iron at its surface. The point in history at which this process initiated marks a step-change in the thermal evolution of the planet. Recent computational and experimental studies have presented radically differing estimates of the thermal conductivity of the Earth's core, resulting in estimates of the timing of inner-core nucleation ranging from less than half a billion to nearly two billion years ago. Recent inner-core nucleation (high thermal conductivity) requires high outer-core temperatures in the early Earth that complicate models of thermal evolution. The nucleation of the core leads to a different convective regime and potentially different magnetic field structures that produce an observable signal in the palaeomagnetic record and allow the date of inner-core nucleation to be estimated directly. Previous studies searching for this signature have been hampered by the paucity of palaeomagnetic intensity measurements, by the lack of an effective means of assessing their reliability, and by shorter-timescale geomagnetic variations. Here we examine results from an expanded Precambrian database of palaeomagnetic intensity measurements selected using a new set of reliability criteria. Our analysis provides intensity-based support for the dominant dipolarity of the time-averaged Precambrian field, a crucial requirement for palaeomagnetic reconstructions of continents. We also present firm evidence for the existence of very long-term variations in geomagnetic strength. The most prominent and robust transition in the record is an increase in both average field strength and variability that is observed to occur between a billion and 1.5 billion years ago. This observation is most readily explained by the nucleation of the inner core occurring during this interval; the timing would tend to favour a modest value of core thermal conductivity and supports a simple thermal evolution model for the Earth.